ILASCD Winter 2025 Journal

Impact • Service • Advocacy

Quarterly Journal - Winter 2025-2026

'I AM NOT A MATH PERSON"

Quick Links

A Letter from the President

9

Whole Child

Book Review: 20

Mathematics of Tabletop Games

24 Resource Corner 28 Rethinking Fact

Amy Warke ILASCD President

Fluency

35 Beyond Right Answers

39 Progression-Based How often do we still hear someone say, “I’m not a math person!” or “I just don’t do math!”? Those words echo in classrooms and conversations alike, and they remind us how deeply our early experiences with math can shape our lifelong relationship with it.

As I reflect on my own journey, I’m reminded of the years I spent practicing math facts through drills and timed tests throughout my elementary years. Despite all that repetition, those facts didn’t truly become

Assessment

49 Strengthening Early Math Thinking

54 From Gaps to Growth

60 Why Math Matters 67 Math Identity 73 Skills-Based Classroom

automatic for me until my first year of teaching,

79 What's the Story?

when I was teaching my own students to learn them.

84 Everyone's a Math

It was then that I began to see math differently: not as something to memorize, but as something to make sense of, to question, and to explore.

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Person

87 Upcoming Events

Welcome (cont.)

ILASCD Leaders

As you read through this Winter Journal

Amy Warke, President awarke2008@gmail.com

edition, you’ll encounter ideas that

Scott England, Past President esengland@umes.edu

feel familiar yet offer refreshing new perspectives on math teaching and

Amy MacCrindle, President-elect amaccrindle@district158.org

learning. Math instruction has its base

Sarah Cacciatore, Treasurer scacciatore@d75.org

in the Eight Mathematical Principles,

Andrew Lobdell, Secretary lobdella@le-win.net

about fostering critical and creative

Debbie Poffinbarger, Media Director debkpoff@gmail.com

from mistakes, building conceptual

yet continues to evolve. Today, it’s

thinking, encouraging students to learn

Ryan Nevius, Executive Director rcneviu@me.com

understanding, and connecting

Bill Dodds, Associate Director dwdodds1@me.com

problem-solving.

Task Force Leaders:

We’re also reimagining what it

Membership & Partnerships Denise Makowski, Amie Corso Reed

means to build strong mathematical

mathematics to meaningful, real-world

foundations. Play, storytelling, inquiry,

Communications & Publications Belinda Veillon, Jacquie Duginske

and consistent integration into daily routines all play vital roles in making

Advocacy & Influence Richard Lange, Brenda Mendoza

math engaging and accessible for

Program Development Jamie Bajer, Heather Bowman, Scott England, Amy MacCrindle, Terry Mootz, Amie Reed, Dee Ann Schnautz, Belinda Veillon, Amy Warke, Doug Wood

every student. Still, we recognize that challenges—such as instructional time and structural constraints—can make implementation complex.

Our Illinois Numeracy Plan provides a strong vision for moving forward, and it 4

invites us to reflect together on how we

math learning can be. I hope these voices

can deepen our collective understanding.

inspire you—to reflect, to reimagine, and

How can we best support teacher

to continue your own journey of growth

leaders, school teams, and district

as a math educator and leader.

leaders as they bring this vision to life?

What additional resources, professional

Amy Warke, Ed.D.

learning, or collaborative opportunities

President, IL ASCD - PD 365

might further strengthen that work?

Within the pages of this edition, you’ll find thought-provoking articles that challenge us to think deeply about what

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A Letter from the Director

Ryan Nevius ILASCD Executive Director rcneviu@me.com

As we welcome a new year, I hope the holiday season offered you moments of rest, reflection, and connection. January always brings a renewed sense of purpose in our work as educators—and with it, excitement for one of the most energizing professional learning experiences in the Midwest: Pump Up Primary Conference, The 45th Annual Pre-K, Kindergarten, 1st, and 2nd Grade Conference, proudly hosted by Illinois ASCD/PD365.

Each spring, thousands of educators gather to celebrate and elevate the art of teaching our youngest learners. As we enter our 45th year, this event remains a practitioner-driven celebration of all things Pre-K through 2nd grade.

Why Attend?

With uncertain budgets, ongoing teacher shortages, and the increasing challenge of finding substitute coverage, prioritizing professional development can feel more difficult than ever. Yet these challenges make time for renewal even more essential. Pump Up Primary provides a purposeful opportunity to step back, recharge, and reinvest in your professional craft.

Attendees leave with: • Practical, classroom-ready strategies • Reenergized purpose and a strong sense of community connection • Access to national experts bringing cutting-edge research and inspiration • Tools, resources, and solutions tailored for the unique needs of early childhood and primary educators 6

Event Highlights for 2026 The 2026 conference—held March 5–6 at the Renaissance Schaumburg Convention Center—promises another unforgettable two-day experience. This year’s features include: • Dynamic national keynote speakers who bring unmatched energy and expertise to early childhood and primary education • Over 120 National and Local Speakers • More than 225 breakout sessions designed specifically for Pre-K, Kindergarten, 1st, and 2nd grade teachers • A high-energy Expo Hall filled with classroom resources, manipulatives, literacy and math tools, tech solutions, and hands-on demonstrations • Dedicated transition times that ensure meaningful engagement between attendees and exhibitors • A fantastic hotel experience with incredible food included in your registration costs.

What makes Pump Up Primary truly exceptional is its loyal, ever-growing community.

Many districts send entire early learning teams to the conference, using it as a shared professional learning experience that strengthens collective practice. During the general session, we often ask participants how many years they have attended. It is not uncommon to see hands raised for 20, 25, and even 30 years—a testament to the conference’s impact and longevity. It’s no surprise that new educators often describe attending Pump Up Primary as the moment they “found their people.”

As we prepare for another record-setting year, we invite you to join us—and to encourage colleagues across Illinois to take part. Together, we can continue shaping joyful and developmentally rich classrooms for our youngest learners.

Registration is now open. We can’t wait to celebrate with you this March!

Registration Details • Hotel Block Information • Vendor Applications Ryan Nevius Illinois ASCD/PD365 Executive Director

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8

Whole Child Rebuilding Mathematical Identity: How Connection-Based Mathematics Classrooms Bring the Illinois Numeracy Plan to Life

Anne Paonessa If you ask a wide range of students how they feel about math, you are likely to hear some of these answers: “I’m just not a math person.”

“I get so nervous, I can’t even think.”

“I used to like math…until the problems started getting harder. I’m just not that good at it.”

For years, math has been framed as a race to the rightor-wrong answer. The students who were good at memorizing the procedures and could then successfully apply them to quickly arrive at the correct answer were praised as “good at math,” while others were quietly deciding that math just wasn’t for them. As the Illinois Comprehensive Numeracy Plan notes, math anxiety and negative perceptions of mathematics now “compound the challenge for learners to succeed,” especially when math is seen as “an exclusive subject reserved for a few, rather than a right for all” (Illinois State Board of Education [ISBE], 2025).

We also know something about the brain: it doesn’t invest deeply in tasks that are of low interest and have a perceived low probability of success (Fitz & 9

Whole Child (cont.)

Price, 2025). When students come to math already convinced they will fail, they naturally protect themselves by disengaging. Recent research continues to confirm that math anxiety undermines achievement, often by interfering with

Learning, and Community, offers one way forward (Paonessa & Zwiers, 2025).

When we align these domains with the ASCD Whole Child tenets and the Illinois Numeracy Plan, we get a roadmap for rebuilding mathematical identity for

True “numeracy” extends beyond procedural fluency to encompass reasoning, problemsolving, and the ability to communicate and apply mathematical ideas... working memory and problem-solving (Ma & Sun, 2025; Finell et al., 2022).

every student, as we shift away from the concept that math is only for an elite few who are “naturally” good at it (ASCD, 2013; ISBE, 2025).

The new Illinois Comprehensive Numeracy Plan gives us a powerful opportunity to change that story. It redefines numeracy as far more than getting to the right answers quickly. True “numeracy” extends beyond procedural fluency to encompass reasoning, problem-solving, and the ability to communicate and apply mathematical ideas and it is grounded in equity and the belief that all students can develop the skills and confidence to thrive mathematically (ISBE, 2025, p. 4).

From “Right Answers” to Mathematical Identity The Numeracy Plan acknowledges that achievement gaps in Illinois remain “significant and longstanding,” especially for students from historically marginalized groups, due in part to inequitable access to high-quality, culturally relevant math instruction (ISBE, 2025). It calls for math to become a pathway of opportunity, not a barrier, by creating conditions where students see mathematics as useful, achievable, and deeply connected to their lives (ISBE, 2025).

The question becomes: How do we bring that vision to life in everyday classrooms?

My work with the four domains of connection: Connections to Self, Others,

That vision aligns closely with emerging research on mathematical identity 10

and belonging. A 2024 student using international assessment data found that students’ sense of school belonging significantly predicted their math achievement, even after controlling for prior performance (Allen et al., 2018). A 2025 dissertation examining high school students’ math sense of belonging showed that students who felt they “fit” in math class reported higher confidence and more persistence with challenging tasks (Stevenson, 2025). Work on “mathematical life stories” underscores how experiences of exclusion or affirmation shape students’ long-term relationships with math (Gweshe & Brodie, 2024).

To me, that is the heart of rebuilding mathematical identity, helping each student think, “Math is a part of my world, and I belong here.” The four domains of connection offer a practical way to do exactly that (Paonessa & Zwiers, 2025).

The Four Domains of Connection in a Numeracy Classroom 1. Connections to Self Whole Child Tenet Lens: Healthy, Supported, Challenged Connections to Self are centered on how students see themselves as mathematicians. Do they see themselves as capable problem solvers, or as people who just try to “get through” math? The Numeracy Plan calls for instruction where “students see themselves as capable, persistent, and confident problem solvers,” not just accurate test takers, and highlights the importance of habits of mind such as perseverance, reasoning, and reflection (ISBE, 2025, p. 2).

Jo Boaler’s mathematical mindset work reinforces this: students who encounter math as a creative, sense-making subject, and who see mistakes as a valuable learning opportunity, develop stronger confidence and have higher math achievement than those who treat math as a subject that they are “naturally” good or bad at (Boaler, 2022). The Illinois plan clearly leans in this direction. It emphasizes that mathematics is not culture-neutral and that communities can help students feel that mathematics belongs to them, that it is meaningful, and that these instructional shifts “align with the vision of numeracy for all” (ISBE, 2025, p. 11).

When we design math experiences that explicitly build on Connections to Self, we: • Normalize and value mistakes as data for learning. Boaler’s work shows that when students see mistakes as evidence of brain growth rather than failure, they engage more deeply and persist longer (Boaler, 2022; 11

Whole Child (cont.)

Sengupta-Irving, 2016).

2. Connections to Others Whole Child Tenet Lens: Safe, Engaged

• Give students chances to choose strategies and explain why a method makes sense to them, not just which method the teacher prefers.

The Numeracy Summit and draft Numeracy Plan frame fluency as efficiency, flexibility, and accuracy, including selecting and adapting strategies, not just recalling procedures (ISBE, 2025).

Connections to Others focuses on the social side of mathematics. The Numeracy Plan calls for discourse-rich classrooms where students justify reasoning, compare strategies, and engage in the Standards of Mathematical Practice (SMPs), especially constructing arguments and critiquing the reasoning of others (ISBE, 2025). Research continues to affirm that belonging and relationships are powerful predictors of math outcomes; a 2025 brief on positive conditions for math learning concluded that students achieve more when they experience strong relationships with teachers, feel a sense of belonging in the math community, and engage in highquality instruction that invites their ideas (Fitz & Price, 2025).

• Help students name their own math strengths through reflective pauses.

For example, “I’m good at visualizing fractions” or “I’m good at explaining my thinking to others,” connecting this to growth over time (Paonessa & Zwiers, 2025).

From a student’s perspective, Connections to Self sounds like: “I used to be afraid to speak up in math. Now we actually talk about mistakes in class.

I can say, 'Here’s what I tried and what I learned from it,' and that feels different.

I get stuck sometimes, but that doesn’t mean I’m bad at math. It just means that I’m learning.”

Connections to Others show up when: • Design structures make thinking visible and shared. Peter Liljedahl’s Building Thinking Classrooms (2020) demonstrates that when students work in visibly random groups at vertical, non-permanent surfaces (whiteboards, windows, chart paper), more students think, talk, and revise their ideas, and they also take more intellectual risks.

This directly supports the Whole Child tenets of Healthy (reducing anxiety), Supported (explicit scaffolds), and Challenged (expecting all students to engage in rich thinking) (ASCD, 2013).

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This domain aligns strongly with the Whole Child tenets of Safe (psychological safety to share ideas) and Engaged (active, social problem-solving) (ASCD, 2013).

• Normalize mathematical discourse as part of learning, not performance.

Students regularly explain their reasoning, ask questions of peers,

...students learn best when classrooms are designed for interaction, where thinking is visible, talk is purposeful, and understanding is coconstructed rather than delivered...

3. Connections to Learning Whole Child Tenet Lens: Engaged, Challenged

and build on one another’s ideas, reinforcing the Numeracy Plan’s emphasis on communication and justification (ISBE, 2025).

Connections to Learning is about meaningmaking, helping students understand why procedures work, when they are useful, and whether an answer is reasonable. The Numeracy Summit presentation and the Numeracy Plan offer a clear conception of fluency as the combination of efficiency, flexibility, and accuracy, including selecting appropriate strategies, adapting them, and evaluating reasonableness (ISBE, 2025).

The plan calls for instruction that “blends understanding concepts (why), practicing skills (how), and applying knowledge to solve real-world problems (when and where)” (ISBE, 2025, p. 7).

• In Essential Connection Skills, we emphasize that students learn best when classrooms are designed for interaction, where thinking is visible, talk is purposeful, and understanding is co-constructed rather than delivered (Paonessa & Zwiers, 2025).

From a student’s perspective, Connection to Others might sound like: “We don’t just sit alone doing problem sets anymore. Most days, we’re standing at the whiteboards in groups, trying to figure out a puzzle. I get to see how other people think, and sometimes my idea helps someone else. It feels like being a part of a team, and I end up understanding the math better.”

Connections to Learning show up when we: • Routinely ask students, “Does this answer make sense?” and build quick 13

Whole Child (cont.) estimation and over/under routines that make “reasonableness” a habit (National Council of Teachers of Mathematics, 2023).

4. Connections to Community Whole Child Tenet Lens: Engaged, Supported Finally, Connections to Community recognizes that math is not just a subject in school, it is a tool for understanding and shaping the world. The Numeracy Plan explicitly states that mathematics is “an important component of cultures throughout the world” and notes that ways of doing mathematics are culturally situated; communities that honor these connections help students feel that mathematics “belongs to them and is a meaningful part of their world” (ISBE, 2025, p.6).

• Use low-floor, high-ceiling tasks that invite multiple solution paths instead of one narrow algorithm (Boaler, 2022).

• Give students opportunities to reflect on their own learning: “What strategy did you use today? How did your thinking change?” (Paonessa & Zwiers, 2025). Current research on motivation and interest in math suggests that when students see purpose and coherence in what they are learning, they are more likely to sustain effort and develop deeper understanding (Eccles & Wigfield, 2020; National Council of Teachers of Mathematics, 2023).

Connections to Community show up when we: • Use local data, such as attendance, neighborhood resources, school lunch waste, or community issues, as the context for math investigations (Turner et al., 2023; Yeh & Otis, 2019).

From a student’s perspective, Connections to Learning might sound like: “We don’t just learn a trick and then move on. My teacher always asks us to show another way or to explain why a method works.

Sometimes that’s harder, but I actually remember it now, and it’s satisfying when math actually makes sense.”

• Invite families and community members to share how they use math in their work and lives, affirming diverse mathematical practices (Turner et al., 2023).

This domain clearly supports the Whole Child tenets of Engaged and Challenged, as students grapple with meaningful, coherent mathematics (ASCD, 2013).

• Connect projects to service-learning or real audiences, so that students experience math as civic and relational, not isolated, individual 14

performance (Paonessa & Zwiers, 2025).

student is Healthy, Safe, Supported, and Challenged, not as a slogan, but in daily practice (ASCD, 2013). For this to take place, we need to collaboratively plan and deliver connection- driven instruction which will positively shape our students’ learning experiences.

Studies on identity and belonging in mathematics emphasize that when students see their cultures, languages, and communities reflected in math tasks, their sense of belonging and confidence grows (Burke, 2017; Gweshe & Brodie, 2024).

The Illinois Comprehensive Numeracy Plan gives us a similar invitation in mathematics. It calls on us to:

From a student’s perspective: “This year, we used data from our own school to make graphs and suggest changes to our bus routes. It felt like math actually mattered, not just for a test but for something real.”

• Address math anxiety and negative perceptions that keep students from engaging (ISBE, 2025; Ma & Sun, 2025).

This domain supports the Whole Child tenets of Engaged (real-world relevance) and Supported (acknowledging students’ full lives and identities) (ASCD, 2013).

• Build conditions where math becomes a pathway of opportunity, particularly for students from historically marginalized groups (ISBE, 2025).

Bringing It Together: The Whole Child, the Four Domains of Connection, and Illinois’ Numeracy Vision Prior IL ASCD Whole Child articles have emphasized the importance of keeping schools human-centered, particularly as instructional demands, accountability pressures, and technology continue to evolve. This body of work reinforces the need to look beyond data points alone and to intentionally design learning environments that attend to the whole child. The ASCD Framework calls on schools to ensure that each

• Ensure teaching blends conceptual understanding, skill practice, and realworld application (ISBE, 2025).

• Center equity, identity, and belonging in professional learning for educators (Allen et al., 2018; Fitz & Price, 2025; ISBE, 2025).

When we see these commitments through the four domains of connection, the “how” becomes clearer: • Connections to Self help students rebuild a sense of themselves as 15

Whole Child (cont.) capable mathematicians (Boaler, 2022; Paonessa & Zwiers, 2025)

sense that they belong in mathematics and that mathematics can help them to better navigate their world (Boaler, 2022; ISBE, 2025; Paonessa & Zwiers, 2025).

• Connections to Others create classrooms where thinking is visible, social, and safe, aligned with Liljedahl’s thinking classrooms and the SMPs (Liljedahl, 2020; National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010).

References Allen, K.A., Kern, M.L., Vella-Brodrick, D., Hattie, J., & Waters, L. (2018). What schools need to know about fostering school belonging: A meta-analysis.

Educational Psychology Review, 30(1), 1-34. https://doi.org/10.1007/ s10648-016-9389-8

• Connections to Learning ensure instruction is coherent, sense-making, and grounded in flexible fluency (ISBE, 2025; National Council of Teachers of Mathematics, 2023).

ASCD. (2013). Whole child tenets. https:// www.ascd.org/whole-child Boaler, J. (2022). Mathematical mindsets: Unleashing students’ potential through creative mathematics, inspiring messages and innovative teaching.

(2nd ed.). Jossey-Bass. https://eric. ed.gov/?id=ED620466

• Connections to Community anchor math in students’ cultures, futures, and civic lives (Turner et al., 2023; Yeh & Otis, 2019).

Together, these domains serve the Whole Child: Healthy, Safe, Engaged, Supported, and Challenged, not as shown in posters on a wall, but in the lived experience of a numeracy-based math class (ASCD, 2013; ISBE, 2025).

Burke, R. (2017). Language and culture in the mathematics classroom: Scaffolding learner engagement. In: Sellars, M. (Ed.), Numeracy in Authentic Contexts (pp. 91-109). Springer. https://doi.org/10.1007/978-98110-5736-6_6

Rebuilding mathematical identity is not an “extra” on top of the Numeracy Plan; it is the work (Allen et al., 2018; Stevenson, 2025). As we design classrooms grounded in connection, we’re not just improving test scores; we’re prioritizing something students needed all along: a

Eccles, J. S., & Wigfield, A. (2020).

From expectancy-value theory to situated expectancy-value theory: A developmental, social cognitive, 16

and sociocultural perspective on motivation. Contemporary Educational Psychology, 61, 101859. https://doi.org/10.1016/j. cedpsych.2020.101859

(Draft 1). Authors. https://www.isbe. net/numeracyplan Liljedahl, P. (2020). Building thinking classrooms in mathematics, grades K-12: 14 teaching practices for enhancing learning. Corwin. https:// www.corwin.com/books/buildingthinking-classrooms-268862

Finell, J., Sammallahti, E., Korhonen, J., Eklöf, H., & Jonsson, B. (2022).

Working memory and its mediating role on the relationship of math anxiety and math performance: A meta-analysis. Frontiers in Psychology, 12, 798090. https:// www.frontiersin.org/journals/ psychology/articles/10.3389/ fpsyg.2021.798090/full

Ma, H., & Sun, C. (2025). The relationship between mathematics anxiety and mathematics achievement of middle school students: The moderating effect of working memory. Behavioral Sciences, 15(11), 1566. https://doi. org/10.3390/bs15111566

Fitz, J., & Price, H. (2025, June). Positive conditions for math learning: An overview of the research [Brief].

Learning Policy Institute. https:// learningpolicyinstitute.org/ product/positive-conditions-mathlearning-brief

National Council of Teachers of Mathematics. (2023, January).

Procedural fluency in mathematics [Position statement]. https://www. nctm.org/Standards-and-Positions/ Position-Statements/ProceduralFluency-in-Mathematics/

Gweshe, L. C., & Brodie, K. (2024).

Learners’ mathematical identities: Exploring relationships between high school learners and significant others.

Mathematics Education Research Journal. Advance online publication. https://doi.org/10.1007/s13394023-00479-5

National Governors Association Center for Best Practices, & Council of Chief State School Officers. (2010).

Common Core State Standards for Mathematics. https://www.isbe. net/Documents/core_standards_ release.pdf Paonessa, A., & Zwiers, J. (2025). Essential connection skills: Strategies for integrating social connections into

Illinois State Board of Education. (2025).

Illinois Comprehensive Numeracy Plan 17

Whole Child (cont.)

Series, 2019 (41). DOI: https://doi. org/10.58295/2375-3668.1276

core content. Corwin. https://www. corwin.com/books/connectionskills-289436 Sengupta-Irving, T. (2016). Doing things: Organizing for agency in mathematical learning. Journal of Mathematical Behavior, 41, 210218. https://www.sciencedirect. com/journal/the-journal-ofmathematical-behavior/vol/41/ suppl/C

Anne Paonessa, Ph.D., is a the coauthor of Essential Connection Skills: Strategies for Integrating Social Connections into Core Content (Corwin, 2025) with Dr. Jeff Zwiers, and she is the founder of ConnectED Classrooms, an organization focused on helping schools embed connection-driven practices into core instruction.

Stevenson, M. L. (2025). High school students’ sense of belonging in math (Doctoral dissertation, California State University, San Bernadino). https://scholarworks.lib.csusb.edu/ etd/2211/

She serves as an adjunct professor at National Louis University, is a mentor for new principals, and is currently working as a School Improvement Specialist supporting CPS schools. With more than 20 years of experience as a teacher, principal, and district administrator, Anne partners with schools and districts to strengthen student engagement, belonging, and learning through inclusive, Whole Child-aligned instructional practices.

Turner, E., Ester Mariñoso, P., Civil, M., Quintos, B., Salazar, F., & Varley Gutiérrez, M. (2023). Parents and teachers doing math together.

In Lamberg, T. & Moss, D., (Eds.), Proceedings of the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 499–507). University of Nevada, Reno. https://files.eric. ed.gov/fulltext/ED658451.pdf Yeh, C., & Otis, B. M. (2019). Mathematics for whom: Reframing and humanizing mathematics. Occasional Paper

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19

Book Review Mathematics of Tabletop Games

by Aaron Montgomery

Click the cover to view on Amazon.

Review by Alex Valencic

For most of the history of education, educators have used games in the classroom. Whether for physical education, as ways to break the monotony of routine instruction, or to allow students to take a break, games have long been integral to any classroom. For the last several decades, these games have included what may casually be called “board games” but are more accurately described as “tabletop games.” Tabletop games, which include games that use cards, dies, boards, pawns, spinners, tiles, miniatures, and any assortment of accessories that do not

easily fit into any category, are generally used in one of three ways: • Engagement • Exploration • Experiences Educators may use tabletop games for engagement when they want to provide students a break from traditional instruction, as a reward at the end of the week or, as I look out the window and see the 12 inches of snow from a recent early winter storm that is showing no signs of melting due to extreme cold, as a way to keep students occupied when 20

the weather prevents them from going outdoors for recess. It is not unusual to find a classroom, regardless of the gradelevel or content area, that has a ready supply of traditional board games such as Monopoly, Scrabble, Sorry, Clue, or chess/checkers, along with card games like Uno, Go Fish, or just a deck of playing cards that can be used for a wide variety of games.

A third way teachers may use games in the classroom is through experiential learning, such as full-blown classroom transformations, long-term simulations or role-playing games, or by converting the classroom itself into a game, known as a transformation or “gamification,” where students are in teams that are completing tasks, earning “experience points,” participating in “real-world” situations (such as designing a business or running a restaurant), and competing for a top position on a leaderboard.

Some educators, wanting to use games for more instructional purposes, may choose to incorporate them into the curriculum as a way of exploring concepts and skills. This may include “educational games” that teach academic vocabulary or math facts through flashcards or simple board games that require students to roll dice, move pawns, and then answer questions related to specific content areas. Teachers may also use traditional games to support academic concepts, such as using Monopoly to teach the basics of finances, Scrabble to practice letter-word recognition and spelling, and counting as students add up scores, or short-term simulations that have students imagine they are in a historical or non-school situation and, through prompts, challenges, and other tasks, have to reach a goal. (Consider here the classic computer game Oregon Trail, the source of deep consternation for school children throughout the 1980s and 1990s.)

All of these are common enough methods of incorporating tabletop games into the classroom that we hardly need to seek out citations to support this claim. Simply visit any classroom anywhere in the state, country, or even the world, and you are almost guaranteed to find evidence of games being used in at least one of these three ways.

However, there is another way that tabletop games can be used in the classroom, which is the focus of Aaron Montgomery’s Mathematics of Tabletop Games (2025), part of the AK Peters/ CRC Recreational Mathematics Series, published by CRC Press, an imprint of the Taylor & Francis Group. Dr. Montgomery presents tabletop games not just as a way to supplement the learning experience for students but also as a source for teaching students about a variety of mathematical 21

Book Review (cont.) the second collection”) can be used to determine the number of possible combinations for an opening hand in the game. The answer, incidentally, is worked out as follows: P(11,2)/2! x P212, 8)/8! = 4,869,460,249,861,350 possible opening hands (p. 8-12). And since the average game time for Ark Nova is 90150 minutes, it would take four players approximately 15,430,388 years to go through every possible opening hand combination–thus all but ensuring the impossibility of ever experiencing the same game twice!

concepts, including combinatorics, geometry, group theory, graph theory, probability, game theory, auctions, logic, and number theory.

The purpose of this book is to link mathematics and tabletop gaming in such a way that the reader can explore ways to answer mathematical questions through games. For example, many games use a combination of cards for players. Thus the game becomes a demonstration, rather than simply discussing a concept such as the

...use games as a way of exploring and understanding mathematical vocabulary...

Another way to teach mathematics through tabletop games, rather than using games as an extension of instruction, is to use games as a way of exploring and understanding mathematical vocabulary, which often has specific uses different from colloquial usage. For example, in the chapter on Group Theory, Dr. Montgomery demonstrates how games that involve placing tiles that are constrained by adjacency rules, such as Carcassone, Galaxy Truckers, and Railroad Ink, to define the following mathematical terms: group, which is defined by three properties: identity, inversion, and closure; and equivalence, which is

Combination Rule, which states that “if k selections are made from a collection of size n without replacement, and the order of selection does not matter, then there are C(n, k) ways to make those selections, where C(n, k) = P(n, k)/k! or n!/k!(n-k)!”

Dr. Montgomery shows how an instructor could use the game Ark Nova to demonstrate how this rule, combined with the Product Rule (”if there are m objects in one collection and n objects in a second collection, then there are m x n pairs of objects where the first object comes from the first collection and the second object comes from 22

Alex T. Valencic is an educator, former small business owner, bibliophile, and geek of all things. As the Professional Learning Coordinator for Freeport SD 145, he supports the development and implementation of innovative educational practices in the classroom and leads the district mentoring leadership team.

He served as FSD’s Elementary Summer Learning Administrator from 2021 to 2024, where they offered academic and enrichment classes that included robotics, 3-D art, and tabletop gaming.

defined by the properties of reflexivity, symmetry, and transitivity (p. 49-50).

Likewise, in chapter 9, which focuses on Number Theory, the game Codenames is used to explore the Fundamental Theory of Arithmetic, and the game Hanabi is used to demonstrate the principles of modular arithmetic.

Whether you are a fellow tabletop gaming enthusiast or just a math educator looking to teach mathematics through a non-traditional format, or are simply looking for a way to change up your traditional curriculum, Mathematics of Tabletop Games provides questions and prompts that can be used to teach mathematical concepts through gaming.

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Resource Corner

ANYONE CAN BE A “MATH PERSON” “Why,” Su asks then, “don’t we approach mathematics the way that we approach art?” READ MORE...

TURNING MATH ANXIETY INTO CURIOSITY: A TEACHER’S TAKE ON GAME-BASED LEARNING Game-based learning isn’t about replacing rigor. It’s about sparking curiosity, reducing fear and fostering a genuine love of learning. READ MORE...

JIGSAW PUZZLES HELP MAKE MATHEMATICS LEARNING MORE ACTIVE AND FUN Using puzzles, both at home and in classrooms, can restore the often-forgotten truth that learning happens in conversation. READ MORE...

NEW MATH STRATEGY EQUALS CONFIDENCE, COMPETENCE Vertical learning encourages students to get out of their seats and work collaboratively with their classmates to solve equations and story problems.

READ MORE...

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EMPOWERING EDUCATORS, FAMILIES, AND STUDENTS THROUGH MATHEMATICS Twana Young is a visionary leader deeply committed to empowering educators, families, and students through mathematics. READ THE INTERVIEW...

MATHEMATICS IS THE SENSE YOU NEVER KNEW YOU HAD | EDDIE WOO | TEDXSYDNEY High school mathematics teacher and YouTube star Eddie Woo shares his passion for mathematics, declaring that "mathematics is a sense, just like sight and touch" and one we can all embrace. WATCH THE VIDEO...

Browse His Youtube Channel 25

Resource Corner (cont.)

TALK NERDY TO ME: TEACHERS WHO USE MATH VOCABULARY HELP STUDENTS DO BETTER IN MATH Using words like ‘factors,’ ‘denominators’ and ‘multiples’ may be part of a constellation of good math teaching practices. READ MORE...

A LITTLE PARENT MATH TALK WITH KIDS MIGHT REALLY ADD UP Mentioning numbers during everyday activities could be more beneficial than workbooks and exercises. READ MORE...

CREATING A CLASS COOKBOOK TO INSPIRE CRITICAL THINKING IN MATH Students get to share their favorite family recipes and practice their problemsolving strategies in this engaging math project. READ MORE...

5 MATH SKILLS YOU CAN TEACH IN THE KITCHEN The kitchen is one of the easiest and most enjoyable places to see math in action. READ MORE...

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USING LEGO TO BREAK THROUGH THE ANXIETY BARRIER IN JR. HIGH MATH I’d love to say it was intentional but it’s really more of a happy accident that this has come to play a big role in decreasing the math anxiety in my students.

READ MORE...

Did You Know? Read More...

5 WAYS TO SHARE MATH WITH KIDS n this playful, inspiring talk, the founder of Math for Love offers teachers and parents alike a five-step guide to sharing the beauty and playfulness of mathematical thinking with children.

WATCH NOW...

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Article Short on Time, Long on Understanding: Rethinking Fact Fluency

James Burnett

For more than a century, helping students learn basic number facts such as 9 + 6 = 15 has been a goal of elementary mathematics. Yet despite generations of effort, many students beyond Grades 3 and 4 still lack automatic recall.

We simply cannot continue relying on the same outdated pattern — a brief flurry of activities to “introduce” strategies, followed by months of repetitive practice in the hope that facts will somehow be committed to memory.

Nowhere is this issue more evident than in the United States, where structural realities make this traditional model almost certain to fail. Why do I make this claim?

Because U.S. schools operate on an unusually short academic calendar, about 180 school days a year. That’s 20 days (one month) fewer than in Australia, and 40 days fewer than in Singapore. Add to that a long summer break — the perfect opportunity for students to forget what they learned — and it’s no surprise that fact fluency erodes rather than deepens over time.

And let’s not mention the number of minutes dedicated to teaching math each day and the instructional time lost to maintaining two measurement systems!

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So while extending the school year may be beyond the control of most districts (and certainly teachers), there is something that can be done right now: adopt a different approach to fact fluency — one that works even when we’re short on time, because it builds long-term understanding.

teachers must ensure that students possess the prerequisite knowledge and skills needed for success. For the Make10 strategy, students should:

In this article, I’ll share a five-stage model for teaching fact fluency. To illustrate the model, I’ll use the Make-10 addition strategy, as it is one of the most widely recognized and explicitly cited strategies in contemporary state and national mathematics standards both in the U.S. and abroad.

• Be able to subitize quantities and recognize visual number patterns

The Five-Stage Model for Building Fact Fluency The visual model below illustrates the five sequential stages of fluency development: Prepare, Introduce, Reinforce, Practice, and Extend.

• Have a deep conceptual understanding of addition • Be able to read, write, and count numbers to at least 20

• Have had experience using fiveframes and ten-frames While the first three are non-negotiable, the fourth is strongly recommended.

A well-structured core program gives kindergarten students opportunities to fill five-frames, helping them see that five is the sub-base of ten. Over time, they use ten-frames to represent numbers greater than five.

2. Introduce Once readiness has been established, we move to introducing the strategy.

Each stage has a purpose and aligns At this stage, students use hands-on with how children move from concrete counters to physically make a ten. A The Five-Stage to Model for Building Fact Fluency experiences abstract reasoning. meaningful context helps anchor the idea The visual model below illustrates the five sequential stages of fluencyfamiliar development: 1. Prepare to something — connecting new Prepare, Reinforce, Practice, and Extend. learning to prior experience.

BeforeIntroduce, introducing any new strategy,

29 Each stage has a purpose and aligns with how children move from concrete experiences to

Rethinking Fact Fluency (cont.)

For example, suppose we want to find the total cost of these two items.

teachers wish to capture students’ reasoning, the vertical alignment of the ten-frames naturally aligns with the horizontal equation that includes the equivalence symbol.

At this point, the link between action, language, and symbol begins to take shape.

ouble ten-frames and counters to represent the value of each item, as shown

Students use double ten-frames and ouble ten-frames andto counters to represent the value each item, as shown counters represent the value ofofeach item, as shown below.

[CAPTION: 9 + 4 = 13]

9 +demonstration 4 = 13] To see this process in action, you[CAPTION: can view a short on my YouTube c

the Number from Down Under, which models how to teach the Make-10 strategy us

To see this process in action, you can

double ten-frames and counters (watch here). ation intentionally leverages the prior understanding that nine is fiveview and a short demonstration on my

YouTube channel, the Number from 3. Reinforce mostintentionally importantly,leverages that nine the is one lessunderstanding than ten. Through careful questioning, tion prior that nine is five and This representation intentionally Down Under, which models how to teach rompted to move counters most importantly, thatthe nineto isfind one the lesstotal thanvalue. ten. Through careful questioning, leverages prior understanding This stage allows students to assimilate and internalize the strategy. It serves as a the Make-10 strategy using double tenompted to move counters to find totalmore, value. connecting the concrete and pictorial models of the introductory phase with the a that nine is five andthe four verbalize their thinking, y. As students move the counters, we want them toand frames and counters.

importantly, nine is one less theirduring practice. fourmost is themove same value as tenthat andwant three.” y.and As students the counters, we them to symbols verbalizeused thinking,

ten.value Through careful 3. Reinforce nd four than is the same as ten and three.”questioning, Because classroom is precious, this stage often moves to pictorial models. Th rk is required, but if teachers wish to capture students’ reasoning, the time vertical This stage allows students to assimilate

students are prompted to move counters

teachers that fromincludes constantly he naturally aligns withtothe horizontal equation thedistributing manipulatives while keeping the learning vis k isten-frames required, but if teachers vertical internalize the strategy. It serves to find the totalwish value.capture students’ reasoning, theand interactive. mbol. e ten-frames naturally aligns with the horizontal equation that includes the

as a bridge — connecting the concrete mbol. Language is key. As students move the shape. card and models introductory A simple canpictorial help remind studentsof ofthe the thinking they developed ear he link between action, language, and symbol begins to takefolding counters, we want them to verbalize phase theis abstract symbols used(for example, n see both parts counters and frames.

Whenwith the card opened, they e link between action, language, and symbol begins to take shape. their thinking, such as: “Nine and four is folded,during four).

When they seepractice. the ten and the remaining three — visually reinforcin the same value as ten and three.” relationship they discovered.

Because classroom time is precious, this stage often moves to pictorial models.

No written work is required, but if 30

3

the matching equation that will help them find the sum. They then record the answer for both related facts. For example, rolling a 9 and a 5 reinforces that 10 + 4 has the same value as 9 + 5.

These free teachers from constantly distributing manipulatives while keeping the learning visual and interactive.

A simple folding card can help remind students of the thinking they developed earlier with counters and frames. When the card is opened, they see both parts (for example, nine and four).

When folded, they see the ten and the remaining three — visually reinforcing the relationship they discovered.

Activities like this are not conceptual, so they cannot be part of the “Introducing” stage — but they are not yet practice either. They deliberately bridge the visual model and the symbolic representation.

We don’t provide enough of these transitional experiences, yet it’s here that students truly begin to own the strategy — moving from manipulation to mental imagery, and from guided reasoning to independent recall.

4. Practice Only after students have grasped the underlying idea do we focus on automating recall. Practice develops accuracy and speed, but it must remain meaningful. I encourage teachers to select or design games that focus specifically on the target facts while gradually incorporating previously learned facts from the Count On and Use Doubles number fact clusters for addition.

[CAPTION: “Nine add four is the same as ten add three.”]

[CAPTION: “Nine add four is the same as ten add three.”]

But it isn’t enough to use this folding card on its own. To truly reinforce the strategy,

students need an activity that bridges the concrete and the abstract, like the one shown below.

But it isn’t enough to use this folding card on its own. To truly reinforce the strategy, students need an activity that bridges the concrete and the abstract, like the one shown on the following page.

Remember that time is critical, so practice sessions should be frequent (daily) and short (up to 5 minutes). It is better to do five 5-minute sessions a week than one 20-30 minute session on one day.

In this task, students write the numerals shown on the right on the six faces of two blank cubes. They roll the cubes and search their activity sheet for 31 5

Rethinking Fact Fluency (cont.)

In this task, students write the numerals shown below on the six faces of two blank cubes.

5. Extend For instance, they can see that 15 can be They roll the cubes and search their activity sheet for the matching equation that will help The final stage—and perhaps the most broken into 14 and 1, and that moving them find the sum. They then record the answer for both related facts. overlooked—is extension: applying the one unit to the other addend creates 30 For example, rolling a 9 and a 5 reinforces that 10 + has the value as 9 + 5. same strategies to greater numbers, +414, an same easier calculation.

Similarly, with fractions, Activities and decimals.

398 + 56, students who think of the “Introducing” stage — strategically like this are not conceptual, so they cannot be part recognize that model this is equivalent to 400 but they are not yet practice either. They deliberately bridge the visual and the If students can successfully use a + 54. This is a mental adjustment that symbolic representation. strategy to calculate 9 + 4 = 13, why simplifies what would otherwise require We don’tthem provideto enough of these transitional experiences, yet it’s here that students truly not encourage use that same a written algorithm. begin to own the strategy — moving from manipulation to mental imagery, and from guided thinking later to solve 29 + 15 = 44? When reasoning to independent recall. students view numbers as quantities, not The same reasoning applies as students symbols, they know they can decompose progress into fractions and decimals.

In 6 and recompose values just as they did 1 5/7 + 4/7, the strategy becomes one of with counters on a double ten-frame. making a whole rather than making ten.

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Likewise, 1.95 m + 2.45 m can be seen as 2.00 m + 2.40 m, again simplifying the calculation through compensation.

forget their facts; it’s that we too often stop teaching for understanding too soon.

When fluency is taught this way, it doesn’t fade over the summer. It endures—because it’s built on understanding.

In both cases, students generalize a strategy first learned in the early grades.

The skill is no longer about “making ten” — it’s about making sense. When students internalize strategies this way, they build a lifelong understanding of how numbers work.

James Burnett is the co-founder of ORIGO Education, an award-winning mathematics education company serving schools across Australia, North America, and beyond.

With more than 30 years’ experience as an educator, author, and curriculum designer, Conclusion he has written and co-authored over 300 The image below shows how the basic mathematics resources, including Stepping addition strategies can be extended across Stones, a comprehensive K–6 program. A the grades. Strong core programs will have frequent keynote presenter throughout these progressions naturally embedded the United States, James is recognised in their developmental sequence, for helping educators make mathematics and effective curriculum leaders will meaningful, enjoyable, and accessible for understand why they are there. every learner. also shares practical The image below shows how the basic addition strategies can beHeextended across the Fact fluency is not a topic to be covered classroom insights through his YouTube grades. Strong core programs will have these progressions naturally embedded in their and tested — it’s a foundation to be channel, the Number from Down Under, developmental sequence, and effective curriculum leaders will understand why they are for expanded, even in classrooms short on which showcases contemporary ideas teaching mathematics. time. The problem isn’t that students there.

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Fact fluency is not a topic to be covered and tested — it’s a foundation to be expanded, even

Article Beyond Right Answers: What Critical Thinking in Math Really Looks Like

Travis Mackey When we think about mathematics instruction, it’s easy to picture problem sets, formulas, and step-by-step procedures. Yet, math classrooms that cultivate critical thinking look and sound different. In these spaces,

In these spaces, students don’t just do math; they think mathematically. students don’t just do math; they think mathematically. It isn’t about the knowledge, but the understanding, which makes it critical thinking.

Critical thinking in math isn’t about harder problems; it’s about deeper reasoning. It’s when students move beyond the “how” to explore the “why” and the “what if.” The goal is not merely procedural fluency, but the development of flexible thinkers who can analyze, justify, and apply mathematical ideas across contexts.

Asking “Why?” and “What If?” Students engaged in critical thinking don’t take formulas at face value. They explore where mathematical rules come from and test their limits.

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Beyond Right Answers (cont.)

“Why does this formula for area always work?”

math is a language for reasoning, not just computation.

“What happens if we double one dimension but not the other?”

Evaluating Multiple Approaches Critical thinking thrives when students compare and evaluate strategies.

This kind of inquiry transforms math from memorization to meaning-making. When students are encouraged to question, they start to see patterns, make conjectures, and build their own understanding of mathematical relationships.

“Would factoring or the quadratic formula be more efficient here?”

“Can we solve this geometrically instead of algebraically?”

Explaining Reasoning, Not Just Answers Critical thinkers can explain their process clearly — in words, numbers, and

When students see there is more than one valid path to a solution, they begin to appreciate the creativity inherent in

When students are encouraged to question, they start to see patterns, make conjectures, and build their own understanding of mathematical relationships. mathematics. This comparison builds adaptability and deepens conceptual understanding.

visuals. They justify how they reached an answer and can defend it to others. Ask students, “Why do you know your answer is correct?” Hopefully, you start to get responses like, “I know my answer works because when I substitute it back, both sides of the equation balance.”

Making Connections Across Concepts Students who think critically connect math ideas across topics and to realworld contexts.

By requiring students to articulate their reasoning, teachers help them internalize mathematical structure and logic. It also allows peers to learn from multiple approaches — reinforcing that

“This slope formula reminds me of the unit rate in proportions.”

“This geometry problem uses the same reasoning as a scale model in science.”

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Connections make math stick. They help students recognize that mathematical thinking is a coherent system, not a collection of isolated rules.

inherently social. When students discuss, defend, and critique reasoning respectfully, they sharpen their own thinking.

Learning from Mistakes Critical thinking also means treating errors as opportunities. Students reflect on missteps, identify misconceptions, and adjust their reasoning.

“I understand your process, but does that always work?”

“Can we prove your conclusion is true for all numbers?”

Collaborative dialogue turns classrooms into communities of reasoning — places where thinking is visible and valued.

“Where did my thinking break down?”

“What assumption did I make that wasn’t true?”

Classroom Example: Turning SurfaceLevel Work into Deep Thinking In an Algebra I classroom, students were working on solving systems of equations.

Initially, most students followed a substitution procedure without much discussion. I paused the class and asked, “Can anyone explain why substitution works?” Silence filled the room until one student replied, “Because we’re replacing one variable with what it equals.”

When classrooms normalize this kind of reflection, they build resilience and foster a growth mindset that extends far beyond math.

Applying Math in New Situations True mathematical understanding shows when students transfer knowledge to unfamiliar contexts.

“This problem is new, but it reminds me of how we used systems of equations in the budgeting project.”

Pressing further, “What if we replaced it with something *not* equal what would happen?” This sparked a discussion about equivalence, balance, and maintaining equality.

Whether through modeling, projectbased learning, or real-world applications, these experiences ask students to synthesize what they know — the essence of critical thinking.

By shifting from procedure to reasoning, we moved the class from doing math to thinking mathematically. Students began to see the connection between

Collaborating and Debating Ideas Finally, critical thinking in math is 37

Beyond Right Answers (cont.)

Travis Mackey, a former math teacher and administrator, has 36 years of experience in education. He is passionate about integrating real-world problem-solving into math instruction. He has led district-level innovation around instructional leadership and student engagement across Illinois.

equations, graphs, and real-world systems — the heart of critical thinking.

Final Thought Critical thinking in math is not a new initiative or an add-on to instruction. It’s the heartbeat of meaningful learning.

When we create classrooms where students question, justify, and connect ideas, we prepare them for more than exams. We prepare them for life’s complex problems that don’t come with answer keys.

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Article Improving Students' Efficacy in Mathematics through Progression-Based Assessment Anderson Trimm

Evan Glazer

Introduction Mathematical literacy is an essential life skill to guide our understanding of economics, finance, science, and engineering. Mathematics influences the development of new algorithms that support the advancement of innovative fields such as artificial intelligence, robotics, and quantum science and engineering. As educators, we should strive to motivate students to continue their mathematics journey so they may be well informed, advance in these fields, and ultimately use their skills to improve the welfare of others.

As students learn mathematics throughout their education, however, they develop varying levels of confidence in whether they are a "math person" or not (Dresel et al., 2024). This happens, in part, due to the manner in which they are assessed. When they make numerous errors, students begin to believe they are not capable of understanding or performing well, and unfortunately, they perceive that they've reached a threshold for how math may be applied in their future.

We believe all students are mathematical thinkers, and we need to find pathways to build efficacy.

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Progression-Based Assessment (cont.)

(Hemmings et al., 2011). In early grades, high performance often provides opportunities to be placed in accelerated or gifted programs. Low performance sets the stage for students to feel frustrated and doubt their potential to

One approach to building efficacy is to acknowledge that students learn and show readiness at different rates. In this article, we promote a progression approach to assessment that gives students choice in the problems they

The net result has been greater self-awareness, willingness to learn from mistakes and tackle new challenges, and improved efficacy, helping them believe they are capable of continuing their mathematics journey. develop as mathematical thinkers. Ability groups intend to provide environments where students can engage in learning at their readiness level. However, even in advanced math classes, students' sense of efficacy is influenced by how well they are performing on their course assessments (Sakellariou, 2022). In essence, students’ sense of whether they are good at math is, in part, attributed to their perceived success.

believe they can solve. This is an evolution of a standards-based report card where students demonstrate performance against designated standards. As an added element, we are using assessment tools with varied difficulty-levels where students respond to questions at their readiness level, and then grow at different rates to achieve different levels of progress. The net result has been greater self-awareness, willingness to learn from mistakes and tackle new challenges, and improved efficacy, helping them believe they are capable of continuing their mathematics journey.

The manner in which students are assessed influences students’ understanding of their success, and that can be problematic with traditional approaches to grading (Brookhart, 2017; Guskey, 2013; Willam, 2011). For example, by calculating the grade by averaging, early mistakes permanently lower a student’s course grade regardless

The Woes of Assessment Practices Past performance in mathematics paired with positive attitudes towards mathematics is a strong indicator of continued success in the subject 40

independently, then they should be gradually challenged further in the classroom as well as on their assessments.

of whether they later mastered the same material. This often results in a lack of motivation, especially when it becomes impossible to earn an A or B, no matter how much the student improves. This can lead to test anxiety, since once points are lost, they cannot be recovered. For the same reason, there is not much motivation to learn from mistakes on a test. The points become the primary concern, as evidenced by the majority of student questions in office hours taking the form “will I get counted off if I write XYZ on a test?” or “can I get a point back on this problem?”, rather than serious questions about the content. Assessment shouldn’t be a motivation killer, but rather a feedback loop for students to want and feel like they could do better.

Making the Switch to ProgressionBased Assessment We endorse a progression assessment approach based on the learners’ readiness. The benefit of this approach is that it provides students the opportunity to build on their previous success rather than experiencing an unproductive struggle with content they do not fully understand. Knowing their level of success provides a fruitful opportunity for both students and educators to identify the next challenge level. The shift in thinking creates an environment where students realize they are on a learning journey of growth rather than learning trials of acceptance. Rather than feeling anxious about whether they can and cannot do math, students are rewarded by working at it until they understand. The goal is to build students' mindset of more self-confidence and to become more resilient when working through their mistakes. The following section describes Dr. Trimm’s transformation in assessment practices and the impact on student learning.

We believe, then, that systems of assessment should be designed so that students are showing signs of success through questions they are ready to solve rather than being measured with the same set of questions for all students. Varying the assessments is not a new phenomenon in education.

Elementary educators, for example, provide different reading levels to students so they can all be engaged with their text at the appropriate challenge level (Fountas & Pinnell, 2017). We argue the same should be true for mathematics. If students can be given problems where they are successful

Starting in the Fall of 2022, I switched to a progression assessment approach, desiring an attitudinal shift towards greater self-awareness, motivation, and a 41

Progression-Based Assessment (cont.) more positive view of mathematics. I also wanted to make sure that students were better-prepared for their future courses.

In traditional grading, deficiencies in core areas can be made up for by doing well in others, so the grade averages out to a successful outcome. For instance, a student might have a failing assessment average, but earn enough points in categories for homework and participation so that they ultimately pass the course, despite serious deficiencies in their understanding. This approach does not set them up for success in future courses.

expectations by acknowledging that students can achieve different levels of success (e.g., sometimes described as “meets” or “exceeds”). There is no partial credit if the standard is not yet met – 70% is no longer “good enough.”

Additionally, students have multiple opportunities to challenge themselves to their potential.

Comparing the Old with the New Approach I have now used this progressionbased assessment system in a variety of mathematics courses ranging from Geometry to AP Calculus to post-calculus electives such as Linear Algebra and

As advocated by Clark (2022) and Talbert (2022), grading should be based on

All that matters is that a student eventually meets clearly-defined learning targets by the end of the course, and provides flexibility for how and when they get there. abundance, rather than scarcity, where students have many opportunities to demonstrate learning and improve over time, without penalty for earlier mistakes. This acknowledges that students do not all start from the same place and do not all learn at the same rate. All that matters is that a student eventually meets clearly-defined learning targets by the end of the course, and provides flexibility for how and when they get there. Further, it also sets high

Differential Equations. My original approach was heavily influenced by that of Talbert (2022). In each of these courses, 15-20 clear learning standards are assessed multiple times throughout the semester. Each standard assessed is scored on a 4-point scale: (1) Beginning, (2) Proficient, (3) Advancing, (4) Distinguished, based on a holistic review of the student’s solution, rather than on points and partial credit.

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As advocated by French et al. (2024), I have also reframed the purpose of my final exam. Rather than think of it as solely a summative assessment of what students recall over the course, it is also one final attempt to level up on any standards on which they may have still needed more time and practice to master.

Most assessments provide students with a choice of problems at different levels, differentiated by depth of knowledge (see Trimm, 2025, for an example). It is assumed that students will not finish the full set of questions, but rather choose the set of problems that they feel confident in solving. Students must be able to solve the more challenging questions for their solution to receive a 3 or 4. After each assessment, students are given feedback, have the opportunity to make corrections, complete targeted additional practice, and are offered an opportunity to be reassessed with a different set of questions to demonstrate understanding at a new level of proficiency. The new performance is the final score, which is different from my past practice of averaging scores, because students have demonstrated a new level of progress.

In sum, letter grades were determined at the end of the semester according to the level of success they achieved, rather than by a weighted average. All requirements for a given letter grade must be met to earn that grade; it is not possible to make up deficiencies in one area by doing well in another, which aims to avoid gaps in understanding. The threshold for passing the course was set so that the instructor could be confident that a student who passed the course would be prepared for success in the following course. Earning an A in the course required students to meet high expectations. The requirements for different letter grades were communicated to the students in the syllabus at the beginning of the semester, to make this as transparent as possible. Students know their progress on each learning standard throughout the semester, which tells them what they need to improve upon to earn the desired letter grade.

In each of these courses, I also assigned a weekly project or problem set on which students worked in pairs, mostly outside of class. These assignments synthesized different learning standards, applied them in a novel context, and/or guided an exploration deeper into the underlying theory. These assignments went into their own grading category as a separate requirement of the course, and could not be used to directly bring up progress levels as determined by solutions on timed, in-class assessments.

Implications and Reflections on Impact While the switch to progression-based assessment has reaped a lot of rewards, 43

Progression-Based Assessment (cont.)

I have had to endure some lessons along the way. I initially thought that grading would be more work through a progression-based approach to assessment. As with trying anything new, there was additional work involved, but by now the grading workload has turned out to be about the same for me, and I find it much more meaningful. Second, my first iteration of this grading system utilized

in the allotted time. To mitigate this problem, I now split my final exam into a required part and an optional part, taken on different days, with the required part covering a subset of core learning standards, and the remaining ones covered on the optional part.

I have learned this system encourages students to take academic risks. If they

In progression-based assessment, students often ask for more assessments because they don’t think of the assessment as a test, but rather a desire to demonstrate they are getting better. Test-anxiety seems to have almost completely disappeared... make mistakes along the way, they know they will be supported and have the opportunity to improve without penalty.

In traditional grading, students are incentivized to figure out what’s on the test so they may earn their desired level of points. What’s more important is what they are learning and what they are able to demonstrate. In progression-based assessment, students often ask for more assessments because they don’t think of the assessment as a test, but rather a desire to demonstrate they are getting better. Test-anxiety seems to have almost completely disappeared, which is consistent with Emeka et al.’s findings

binary scoring, according to whether or not the standard had been met. While this worked well enough initially, over time, I realized that the 4-level system better communicated growth to students. Third, I have learned that some students who have historically relied on partial credit or homework participation are initially challenged to meet course standards.

However, that was ok, because they ultimately became more self-aware of the progressions they need to make in order to be successful. Finally, I initially found it difficult to meet my goal of using the final exam to reassess all standards at the same level as previous assessments 44

(2023) findings on the effects of secondchance assessments on anxiety levels.

remember and apply almost all of the topics from the semester before.”

I also feel like I have a better relationship with students now compared to when I used traditional grading. With traditional grading, as noted in (Clark, 2022), the teacher can at times have an adversarial relationship with students as the keeper of the points. With progression-based assessment, the relationship feels more supportive as a coach. There are transparent expectations that students can work toward throughout the semester, and I am just here to help them reach their goals. My interactions with students after handing back tests and in office hours have been completely transformed, as the discussions are now focused on the content and how to improve.

Students have also frequently commented on equity. For instance, one student noted, “I learn calculus more slowly than others, and progression-based grading allowed my grade to reflect what I understood by the end of the semester.”

Another noted, “As a student from an underserved school, I find that, as I continue through math, the concepts IMSA expects me to know I have never been taught…

Although I have grown a lot, there is no doubt that I am at a disadvantage compared to my peers. For me, progression-based grading allows me time to catch up on concepts I have never learned.”

I have received overwhelmingly positive feedback from students. In my course surveys, students frequently comment on having reduced stress and anxiety, increased motivation, and better retention of what they have learned. For example, one student from first-semester BC Calculus noted,

Finally, students also describe an increased enjoyment of mathematics. As one student reflected, “I was able to understand and apply almost every topic. I was MUCH less stressed with math and really enjoyed the class. The class that I liked the most was math… I felt more capable of understanding the work that I received instead of just finishing it to get it out of the way… I put in an insane amount of

“I put in more work than I had in almost any other math class. I did this because I knew it was going to pay off. BC1 was my second-highest math grade at IMSA because of this. It was critical for my understanding in BC2, as I was able to 45

Progression-Based Assessment (cont.) period. Every problem should not be completed. Don’t spend time on the problems you automatically know how to do, but rather the ones you think you know how to get started and feel you can get through with some thought.

work, and it paid off. I put in that work because the class was fun and I was able to understand.”

Perhaps most strikingly, I have been told on more than one occasion that the tests were actually “fun”!

Transforming Your Assessment Practices by Starting Small Changing to a progression-based assessment approach to assessment requires extra work, but the impact on students’ disposition and success has been worth it. We recognize that changing practices is not easy; however, as educators, we should constantly find ways to improve learning systems for the welfare of our students’ success and enjoyment of learning mathematics. They are more mindful of how they understand mathematics than ever before. Keeping this in mind, we encourage you to sample with progression-based assessment in ways that support your workload, and then build your practice as you see success.

2. Customize quiz questions When a student hasn’t developed proficiency in an important skill area necessary for the next course, provide them with additional opportunities on future assessments. If a student desires to excel in that skill, then provide them the chance to level up with a more challenging problem.

The goal is to provide students with continued opportunities to demonstrate that they understand.

Here are a few ways to get started:

3. Offer chances for revision after minimal feedback When students take an assessment, circle the location where they make an error. Hand back the paper and ask them to make a revision. Often, they can reconcile the mistake, and that will propel them to offer a better solution.

1. Allow student choice on homework on an extended problem set Provide a set of problems with varied difficulty, and ask students to tackle the most challenging problems they are able to do within a given time

Naturally, a teacher has to identify how much they want to vary their assessment based on their capacity, resources, and the impact they see on learning. Our intention is to challenge students at their level of understanding and help them 46

Emeka, C., Zilles, C., West, M., Herman, G., & Bretl, T. (2023). Second-chance testing as a means of reducing students’ test anxiety and improving outcomes. In Proceedings of the ASEE (American Society for Engineering Education) Conference. https://peer. asee.org/second-chance-testingas-a-means-of-reducing-studentstest-anxiety-and-improvingoutcomes.pdf

grow through the assessment process.

We feel it is necessary to keep students engaged in learning mathematics, especially when they face setbacks, so they realize assessment is a necessary tool to support their continued learning.

We desire a sense that all students belong in mathematics, and through these assessment approaches, have built a sense of efficacy for students to embrace new challenges rather than worry about what’s on the test or whether or not they are good at math.

Fountas, I. C., & Pinnell, G. S. (2017). The Importance of Guided Reading Within a Multi‑Text Approach. Fountas & Pinnell Literacy™.

References French, S., Dickerson, A. & Mulder, R.A. A review of the benefits and drawbacks of high-stakes final examinations in higher education. High Educ 88, 893– 918 (2024). https://doi.org/10.1007/ s10734-023-01148-z

Brookhart, S. M. (2017). How to use grading to improve learning. ASCD. Clark, D. (2022). Abundance and scarcity: Spicy takes from Benjamin Bloom.

Grading for Growth. https:// gradingforgrowth.com/p/ abundance-and-scarcity

Guskey, T. R. (2013). The case against percentage grades. Educational Leadership, 71(1), 68–72.

Dresel, M., Daumiller, M., Spear, J., Janke, S., Dickhäuser, O., & Steuer, G. (2024).

Learning from errors in mathematics classrooms: Development over 2 years in dependence of perceived error climate. British Journal of Educational Psychology, 95(1), 180–196. https://doi.org/10.1111/ bjep.12697

Hemmings, B., Grootenboer, P., & Kay, R. (2011). Predicting mathematics achievement: The influence of prior achievement and attitudes.

International Journal of Science and Mathematics Education, 9(3), 691–705. https://doi.org/10.1007/s10763010-9224-5 47

Progression-Based Assessment (cont.)

Dr. Anderson Trimm, a mathematics faculty member at the Illinois Mathematics and Science Academy (atrimm@imsa. edu), has a variety of experience teaching mathematics and physics and is particularly interested in assessment practices that support student growth, confidence, and long-term engagement in mathematics.

Sakellariou, C. (2022). The reciprocal relationship between mathematics self-efficacy and mathematics performance in U.S. high school students: Instrumental variables estimates and gender differences.

Frontiers in Psychology, 13, Article 941253. https://doi.org/10.3389/ fpsyg.2022.941253

Dr. Evan Glazer, President, Illinois Mathematics and Science Academy (eglazer@imsa.edu), is a lifelong mathematics educator who has written books about mathematics, including RealLife Math: Everyday Use of Mathematical Concepts and Using Internet Primary Sources to Teach Critical Thinking in Mathematics. He is deeply interested in the role assessment plays to support students’ learning and their continued interest in mathematics.

Talbert, R. (2023). Grading for Growth: A Guide to Alternative Grading Practices that Promote Authentic Learning and Student Engagement in Higher Education (with D. Clark). Routledge.

Talbert, R. (2022). How specifications grading changed. Grading for Growth. https://gradingforgrowth.com/p/ how-specifications-grading-changed Talbert, R. (2020). Building calculus learning objectives. RTalbert.org. https://www.rtalbert.org/blogarchive/index.php/2020/07/09/ building-calculus-learning-objectives Trimm, A. (2025). Sample progressive assessment: Squeeze Theorem [Unpublished Instructional Document] Illinois Mathematics and Science Academy https://drive.google.com/ file/d/1rQ1BvlysX96NkorSdR2WO VijyLDhm1pD/view?usp=sharing Wiliam, D. (2011). Embedded formative assessment. Solution Tree Press.

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Article Strengthening Early Math Thinking Through Daily Routines, Language & Play

Thamir Aljobori

Early math instruction in preK through grade 3 shapes how students approach problem solving, number relationships, and reasoning for years to come. Strong instruction in the early grades builds confidence, supports cognitive development, and lays the foundation for later success in higher-level mathematics. The Illinois Comprehensive Numeracy Plan emphasizes the importance of early learning environments that promote meaningful math experiences. These experiences help students form ideas through exploration, discussion, and reflection. Daily routines, intentional language, and play can strengthen early math thinking. Here are several practical examples that educators can use in any program model, including classrooms with multilingual learners and students with diverse needs.

bori is an educator and instructional leader with experience in early childhood, multilingual and curriculum design. He works across classroom, policy, and leadership settings, serving Childhood Educator Policy Fellow with Teach Plus Illinois and a Director-at-Large with Mindfully. His work focuses on integrating language development, equity, and whole-child nd he contributes to professional communities through national conference presentations for Edutopia. He holds an MBA, an MEd in Elementary Education, and ESL/Bilingual nts, with ongoing work supporting multilingual learners and district-level program nt.

1. Math in Daily Routines Young children learn best when math is embedded in tasks they already understand. Daily routines give students repeated opportunities to use math in context.

These routines help children develop operational fluency, comparison skills, and logical reasoning.

• Attendance and Counting Teachers often begin the day with attendance. This 49

Strengthening Early Math Thinking (cont.) simple activity offers several math opportunities. Students count how many children are present, how many are absent, and how the totals change throughout the week. Students compare numbers, identify more or less, and describe what they notice.

Students can explain ideas in their home language during small-group conversations while still using English vocabulary during whole-group sharing.

• Using Everyday Language First Teachers begin with familiar terms such as bigger or smaller before introducing greater than or less than.

• Transitions Transitions between activities also support math growth. Teachers can measure walking time, compare the number of steps between classroom areas, or use timers to show the duration of each task.

3. Play as a Context for Math Exploration Play supports repetition, creativity, and collaboration.

• Classroom Jobs Classroom jobs introduce grouping, estimation, and problem-solving.

Students determine how many items are needed, check their count, and adjust if the number changes.

• Block Building Students compare lengths, create symmetrical designs, and explore balance.

• Sorting and Classifying Sorting builds the foundation for data analysis.

2. Building Math Language Through Discussion Math understanding grows when students explain their thinking.

Discussion supports conceptual development, clarity, and reasoning.

• Dramatic Play In pretend stores, students count items, compare prices, and distribute money.

• Outdoor Play Students compare distances, collect natural items, and group them.

• Structured Math Talk Teachers use short prompts that guide discussion: How do you know? What changed? What stays the same?

4. Linking Math Across Languages and Experiences

• Supporting Multilingual Learners 50

and play help students build reasoning, strategy use, and confidence.

Teachers build on what students know from home. Connecting math to family practices increases relevance and engagement.

Thamir Aljobori is an educator and instructional leader with experience in early childhood, multilingual education, and curriculum design. He works across classroom, policy, and leadership settings, serving as an Early Childhood Educator and Numeracy Policy Fellow with Teach Plus Illinois and a Director-at-Large with Educating Mindfully. His work focuses on integrating language development, equity, and whole-child practices, and he contributes to professional communities through national conference presentations and writing for Edutopia. He holds an MBA, an MEd in Elementary Education, and ESL/ Bilingual endorsements, with ongoing work supporting multilingual learners and district-level program improvement.

5. Observation and Assessment in Early Math Assessment focuses on understanding rather than speed.

• Anecdotal Notes Short observations track growth.

• Student Work Samples Drawings, number stories, and photographs show reasoning.

• Performance Tasks Teachers create challenges with blocks, sorting, or estimation.

6. Practical Steps for Educators – Integrate math into daily routines – Use discussion prompts – Encourage bilingual expression – Provide play opportunities – Use observation to plan – Connect math to family practices – Offer materials that support exploration Conclusion Early math learning depends on experiences that help students make sense of ideas. Daily routines, discussion, 51

Pre-Service Teachers in Illinois Receive FREE ILASCD/PD365 Membership!

What’s in it for YOU? Are you a pre-service teacher? Don’t wait until graduation to start building your professional network!

By joining ILASCD/PD365, you’ll:

Connect with experienced teachers, mentors, and school leaders Access practical resources, journals, and classroom-ready strategies Attend exciting conferences and workshops as a volunteer!

Boost your résumé with professional memberships that set you apart Join a statewide community committed to helping you thrive Get published in Journals and publications A pre-service teacher gains connections, career readiness, and credibility by joining ILASCD/P D365. It’s a way to start your professional journey early, surrounded by people and resources that will support you through your first years in the classroom and beyond.

REGISTER HERE!

www.illinoisascd.org

IL ASCD Area Representatives Our “Area Reps” are a link to and from the various regions of our state. IL ASCD follows the same areas established by the Regional Offices of Education.

Denise Makowski

Chicago 618.203.3993 dmkowski224@gmail.com

Our Area Reps are led by a members of our IL ASCD Board of Directors, Denise Makowski.

Amie Corso Reed

O'Fallon School District 618.203.3993 amie.corso@gmail.com

Current Area Reps AREA 1: (Green)

AREA 2: (Dark Blue) AREA 3: (Yellow) AREA 4: (Pink) AREA 5: (Light Blue) AREA 6: (Gold)

April Jordan Jennifer Winters Stacy Stewart Jen Pollack Chad Dougherty Heather Bowman Jamie Bajer Mica Ike Vacant

Contact information for them can be found HERE.

The roles of the IL ASCD Area Representatives are: •

Encouraging IL ASCD membership to educators in their local areas;

•

Assisting with professional development;

•

Attend board meetings and the annual leadership retreat, when possible;

•

Disseminating information from IL ASCD board meetings or other sanctioned IL ASCD activities to local school districts or other regional members

•

Being a two-way communication vehicle between the local IL ASCD members regarding IL ASCD or any educational issues.

•

Keeping IL ASCD Board of Directors apprised of pertinent information regarding personnel issues (e.g., job vacancies, job promotions) and district program awards/recognition within the local area.

•

Communicating regularly with IL ASCD Executive Director and the Co-Leaders of the Membership and Partnerships Focus Area.

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Article From Gaps to Growth: How Tahlia’s Journey Reflects the Power of Illinois’ Numeracy Plan Sarah Murmann

When Tahlia entered my classroom as a freshman in high school, she carried more than just her backpack.

She had years of feeling like she “wasn’t a math person,” piles of unfinished homework, and a placement test score equivalent to that of a third-grader. Three years later, after a lot of hard work, time, and support, Tahlia looked at the score on her final exam with tears in her eyes: her first A in math. Her test score did not happen by accident, nor was it any singular change that pushed Tahlia to success. It was a strategic system of supports that included daily interweaving of number sense, lowfloor high-ceiling tasks, assessments to identify gaps in numeracy skills, and a classroom culture of perseverance.

Stories like Tahlia’s illustrate the need for Illinois to have a coherent vision for math instruction. The State Board of Education (ISBE) has taken up that call and is creating the Illinois Comprehensive Numeracy Plan, a framework designed to ensure every student has access to the kind of targeted, equitable supports that transformed Tahlia’s trajectory. As a working document, the plan offers a solid foundation with many of the elements that made Tahlia so successful. This article examines the Illinois 54

Another of the features of the Numeracy Plan is low-floor, high-ceiling tasks for students to engage in numeric and mathematical thinking. An example of such a task is to develop a formula for the number of blocks needed for a staircase where each step uses one more block than the previous step. Students can simply count the steps to start, but eventually they recognize patterns in the sums to create an equation to find the number

Comprehensive Numeracy Plan through the lens of secondary mathematics instruction, highlighting both its promising strategies and implementation challenges that the plan must address.

Key Strengths of the Numeracy Plan The central pillar of the Numeracy Plan is to increase students' numeracy skills.

At the secondary level, these skills are foundational for success in Algebra (Ronau et al, 2020), yet many students

In Tahlia’s class, each day began with warmup questions containing at least one number sense or proportional reasoning problem to help make incremental but impactful progress in students' numeracy skills. still struggle. Utilizing short numbersense routines is a simple way to increase number sense in all students, regardless of ability level. In Tahlia’s class, each day began with warm-up questions containing at least one number sense or proportional reasoning problem to help make incremental but impactful progress in students' numeracy skills. These helped to fill in gaps for Tahlia, but if elementary schools adopt these practices on a wide scale as the plan recommends, fewer students will enter high school with gaps like hers in the first place, and they will be better positioned for success.

of blocks for any number of steps. (See pg. 59) These tasks are supported by the work of Stanford Professor Jo Boaler, who argues that open-ended, visually rich, and discussion-based tasks engage students and help develop mathematical mindsets (Boaler, 2016). They allow students to access grade-level coursework while simultaneously reinforcing foundational numeracy skills to help address gaps. Tasks like these were a core reason Tahlia was able to succeed, and they should continue to be a pillar of the Numeracy Plan in the final draft.

55

From Gaps to Growth (cont.)

Numeracy Plan encourages diagnostic testing with larger in-depth assessments sparingly to address gaps and shorter, more frequent formatives to help address fundamental numeracy skills.

While students like Tahlia rarely enjoyed these assessments, they are critical for educators to find and address essential skills for success.

The importance of diagnostic assessments to identify gaps in students’ knowledge is also a key point in the Numeracy Plan. As the National Mathematics Advisory Panel found, gaps that begin in early education are exacerbated with age (National Mathematics Advisory Panel, 2008).

By the time students reach middle or high schools, deficiencies in numeracy and content knowledge compound and create additional frustrations for struggling students. For Tahlia, this frustration resulted in a daily struggle to engage in class, as she always felt defeated. If these gaps had been addressed earlier for Tahlia, her energy could have been spent building on new

Finally, one of the most important intervention systems for Talhia highlighted in the Numeracy Plan is creating an environment where productive failure is encouraged. Many teachers want to support students at the first signs of struggle, but to truly engage students in mathematical

The most crucial factor for Tahlia, and the most difficult to implement, is providing students enough time to bridge gaps in numeracy while succeeding in their gradelevel coursework. thinking, we must let them progress on their own before utilizing direct instruction. The deepest learning comes from productive failure and unproductive success (Kapur, 2016). In my classroom, I intentionally developed this mindset in a classroom filled with students who were used to avoiding challenges. Students were encouraged to explore, make

content rather than battling the lingering effects of unfinished learning.

It is critical for educators to identify gaps in foundational algebraic topics like fractions (Siegler et al, 2013) and equations (Knuth et al., 2006) as early as possible, as these are indicators of success in the upper grade levels. The 56

Success in advanced coursework and placement exams depends on students having solid foundations and recall in numeracy. conjectures, and revise their thinking before giving answers. Tahlia, who once shut down when faced with unfamiliar problems as a freshman, learned to lean into struggle and embrace it as a part of learning by her junior year.

When I worked with Tahlia, my school helped address this problem by providing her with a “double dose” intervention course, where I had Tahlia two class periods per day for three years. This was an amazing benefit to her and her classmates, as they had the time and space to engage with math in meaningful ways. However, access to this kind of intensive support varies widely among districts and schools, and not all districts have the funding, staffing, or structural flexibility required. Some schools use co-taught classes, targeted math intervention classes, or drop-in tutoring/ support for students. For the Numeracy Plan to truly support our struggling secondary students, ISBE should offer several possible concrete solutions to help districts provide support and then support these recommendations with resources to help underfunded districts build effective intervention systems.

Implementation Challenges at the Secondary Level While these critical elements are strengths of ISBE’s Numeracy Plan draft, other key elements are missing or will be difficult for districts to implement. The most crucial factor for Tahlia, and the most difficult to implement, is providing students enough time to bridge gaps in numeracy while succeeding in their grade-level coursework. To secondary teachers, it may seem like an impossible task to adopt new practices like lowfloor high-ceiling tasks, diagnostic testing, and foundational number sense routines while also covering the required course curriculum. Without adjustments to course pacing, teachers may feel overwhelmed and return to old habits.

The final draft of the Numeracy Plan should address how teachers can balance or prioritize different strategies and interventions during class time to best help students.

Finally, while the current version of the plan strongly emphasizes conceptual learning, it must be careful not to undervalue fluency in numeracy and number sense. High school students need procedural fluency and automaticity as well—the ability to utilize mental math 57

From Gaps to Growth (cont.)

• Low-floor, high-ceiling tasks provide access points for all students

facts. Success in advanced coursework and placement exams depends on students having solid foundations and recall in numeracy. As Tahlia once told me, “Math is easy when you don’t have to type everything into your calculator all the time!” The goal of the plan should be to integrate conceptual understanding with mathematical fluency to produce the best results for our students.

• Diagnostic assessments, in both the elementary and secondary levels, are essential for identifying and addressing gaps before they compound • Classroom cultures that embrace productive failure help students develop the perseverance needed for mathematical success

Recommendations for Moving Forward When the state’s vision and classroom practice align, students not only catch up; they flourish. And when students flourish, they exit high school as numerate citizens capable of solving problems, analyzing information, and contributing meaningfully to an increasingly data-driven world. The Illinois Comprehensive Numeracy Plan represents an opportunity to transform mathematics education for students across the state. Tahlia's story demonstrates what becomes possible when research-based strategies are implemented with fidelity and adequate support. As the plan continues to grow and develop, the following points are particularly important for the secondary level:

• Implementation requires creative scheduling solutions and additional supports • The plan must balance conceptual understanding with procedural fluency As ISBE continues to refine this framework, input from classroom teachers and building administrators will be essential to ensure the final plan is both ambitious and achievable. ISBE will have a second draft of the plan and hold a listening tour from February to March. The details can be found on ISBE’s webpage. Administrators and educators are strongly encouraged to participate and share their insights on what will make this plan work in real classrooms with real students. Your voice matters in shaping a framework that can help every student experience the kind of transformation Tahlia did.

• Daily number sense routines in secondary classrooms can help to address foundational gaps while students work on grade-level content 58

development. Psychological Review, 120(3), 559–588. https://doi. org/10.1037/a0032159

References Boaler, J. (2016). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages and innovative teaching. Jossey-Bass.

This is an image of the "low-floor highceiling task" described earlier.

Kapur, M. (2016). Examining productive failure, productive success, unproductive failure, and unproductive success in learning.

Educational Psychologist, 51(2), 289– 299. https://doi.org/10.1080/00461 520.2016.1155457 Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter?

Evidence from solving equations.

Journal for Research in Mathematics Education, 37(4), 297–312. https:// doi.org/10.2307/30034852

If we continue to add "steps" to these stairs, how many would we have we we get to Step 5?

National Mathematics Advisory Panel.

(2008). Foundations for success: The final report of the National Mathematics Advisory Panel. U.S. Department of Education.

Sarah Murmann is a dual-credit math teacher and Robotics coach at Crystal Lake South High School in Crystal Lake, Illinois. She is also a Senior Policy Fellow for Teach Plus Illinois, where she has helped to input teacher voice in AI legislation at the state level.

Ronau, R. N., Bay-Williams, J. M., & Van de Walle, J. A. (2020). Elementary and middle school mathematics: Teaching developmentally (10th ed.). Pearson.

Siegler, R. S., Thompson, C. A., & Schneider, M. (2013). An integrated theory of whole number and fractions 59

Article

Dr. Emily Wassell is an award-winning educator and holistic college coach with more

than 25 years of experience helping students thrive inside and outside the classroom.

She holds a BAS, MAT, and PhD in Educational Leadership, Research, and Policy from the University of Colorado Colorado Springs. A former teacher, principal, and visiting professor, Dr. Wassell is the founder of a global coaching practice that guides ambitious teens toward their dream colleges while prioritizing wellbeing, leadership, and long-term success.

Why Math Matters: Beyond Grades and Test Scores

Emily Wassell

In 2022, the United States recorded the steepest decline in math scores in three decades. According to the National Assessment of Educational Progress (NAEP), only 26% of eighth graders met proficiency standards, down from 34% in 2019 (National Center for Education Statistics [NCES], 2022). Internationally, American students continue to lag behind peers from countries such as Singapore, Japan, and Estonia on the Program for International Student Assessment (PISA) (Organisation for Economic Co-operation and Development [OECD], 2019).

For many parents and educators, these statistics are concerning primarily because of their implications for college admissions or standardized tests. However, math is far more than a set of numbers on a grade report.

Learning mathematics shapes how the brain develops, strengthens critical life skills, and builds confidence in problem-solving. If we reframe how we view math—less as a hurdle to clear and more as a language and way of seeing the world—we can help today’s students reclaim their mathematical potential.

The State of Math Achievement in America Declining math achievement is not simply an academic issue. Math proficiency is strongly correlated with college readiness, employability, and future earnings. In fact, 60

sulcus is central to numerical processing, while the prefrontal cortex supports logical reasoning and problemsolving (Ansari, 2008). Engaging these areas repeatedly strengthens neural connections, much like exercise

students with higher math achievement in high school are more likely to graduate college and secure stable, high-paying jobs, even if they pursue non-STEM careers (National Mathematics Advisory Panel [NMAP], 2008).

Students who regularly practice mathematics show better executive function, stronger attention control, and more effective decision-making (Park & Brannon, 2013).

The consequences extend beyond the individual. Economists warn that lagging numeracy skills weaken the U.S. workforce in a world increasingly shaped by data, algorithms, and quantitative reasoning (OECD, 2021). New studies using digital twins—AI models of brain activity—reveal the unique neural challenges faced by students with math learning disabilities and provide insights into tailoring instruction (Stanford University, 2025). Reversing the downward trend is essential not just for students’ futures, but for national competitiveness.

strengthens muscles. Stanislas Dehaene (2011) has described math as a kind of “mental gymnasium,” where working with numbers improves working memory, cognitive flexibility, and abstract thought. Importantly, these skills transfer. Students who regularly practice mathematics show better executive function, stronger attention control, and more effective decision-making (Park & Brannon, 2013).

Recent breakthroughs provide even more promising directions. Safe, non-invasive brain stimulation techniques, such as transcranial random noise stimulation (tRNS), have been shown to significantly improve math performance in young adults with weaker neural connectivity, suggesting that neuroscience-informed interventions may help struggling learners (University of Surrey, 2025). Similarly, Oxford researchers

What Happens in the Brain When Kids Learn Math Mathematics is one of the most cognitively demanding subjects we teach, and for good reason: it engages multiple brain regions at once. Neuroscientific research shows that the intraparietal 61

Why Math Matters (cont.) demonstrate that, unlike AI, the human brain learns by first stabilizing activity patterns, then adjusting connections— making math learning an especially powerful tool for cognitive resilience (University of Oxford, 2024).

More recent evidence underscores the importance of number sense for higherlevel thinking. A 2025 comparative study found that gifted students rely on more flexible, reasoning-based number sense strategies than their typically developing peers, highlighting the need to cultivate number sense not just for basic skills but for deeper problem-solving (Er & Dinç Artut, 2025). Unfortunately, as education experts note, number sense often receives less emphasis than early literacy in U.S. schools, despite its equal importance (Hechinger Report, 2025).

Number Sense as the Foundation At the heart of math learning is number sense—the intuitive ability to understand and manipulate quantities. Think of number sense as a child’s “feel” for how numbers work: recognizing that six is more than four, estimating how many candies are in a jar, or understanding that 12 can be broken into 7 and 5. When I work with students on SAT prep, I am astounded by how many students do not understand that dividing a number by a fraction will increase the number rather than decrease it. This type of numerical sensibility is critical for being able to solve problems and navigate patterns.

Math as a Language One of the most powerful shifts we can make is to help students see math as a language. Like spoken language, mathematics has symbols, grammar, and rules of syntax. For instance, an equation such as 3x + 2 = 11 is a concise way of communicating a relationship. Learning math, then, is not just about memorizing procedures but about expressing ideas, patterns, and relationships clearly and precisely (Sarnecka & Carey, 2008).

Research consistently shows that early number sense is one of the strongest predictors of later math success (Libertus, Feigenson, & Halberda, 2011).

Moreover, children with well-developed number sense are less likely to struggle with math disabilities such as dyscalculia (Butterworth, Varma, & Laurillard, 2011). David Geary (2013) emphasizes that preschool and early elementary years represent a critical window for strengthening these foundational skills.

Framing math as a language also changes how students respond to challenges.

Struggling to solve a problem becomes more like learning to conjugate a verb incorrectly at first—a natural step in mastering a new form of communication.

Jo Boaler (2015) argues that this mindset shift is essential for reducing 62

math anxiety and building persistence.

When students see math as a way to communicate ideas rather than as a test of intelligence, they are more likely to stay engaged and grow.

Moving Forward: How Parents and Educators Can Help The decline in math scores is reversible, but it requires collective effort. Recent educational psychology research emphasizes that a blend of conceptual understanding and timed practice builds both deep comprehension and automaticity—a three-step process of grounding, automating, and reflecting (McNeil et al., 2025). This approach builds flexible fluency without reducing math to rote memorization.

Seeing Math in the World Around Us For many teens, math feels disconnected from their daily lives. Yet math is everywhere: in the ratios of a recipe, the statistics of a favorite sports team, the angles of a skateboard ramp, or the symmetry of architecture. Nature itself is filled with mathematical beauty, from the spirals of sunflowers to the fractal patterns of coastlines.

In addition, neuroscience-driven programs are emerging as powerful supports. The MIND Research Institute’s ST Math platform, a visual, game-based system grounded in cognitive science, has shown significant improvements in student performance across diverse groups. Its new curriculum, InsightMath, continues this trend by integrating visual problem-solving with conceptual rigor (MIND Research Institute, 2025).

Helping teens notice these patterns makes math less abstract and more relevant. The OECD (2021) notes that numeracy is also a form of life literacy: individuals with stronger math skills demonstrate better financial decisionmaking, improved health outcomes, and greater adaptability in technologydriven fields. Parents can support this by pointing out real-world examples, encouraging budgeting exercises, or linking math to a teen’s personal interests. I love to have students budget for trips or events. To have limits on the spending, a goal in mind, and put together a realistic and feasible budget.

When students see math as part of their world—not just a school subject—they are more motivated to learn.

Practical strategies remain essential: 1. Encourage a growth mindset.

Students who believe math ability is expandable through effort and strategies outperform those who believe it is fixed (Boaler, 2015).

2. Emphasize conceptual understanding. Procedural fluency 63

Why Math Matters (cont.) matters, but research shows that deep understanding of why math works predicts long-term achievement (NCTM, 2020).

raise test scores—it is to cultivate mathematically literate citizens who see math as a tool for understanding and shaping their lives.

References

3. Supportive environments. Schools that provide tutoring, math labs, and collaborative teacher practices see stronger outcomes (NMAP, 2008).

Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4), 278–291.

4. Integrate real-world math. Connect math to areas teens already care about—music, sports, video games, or social media analytics.

Boaler, J. (2015). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages, and innovative teaching. Jossey-Bass.

Conclusion Math scores in the United States are declining, but the solution is not to double down on test prep. Mathematics is more than a school subject: it is brain training, a language, and a life skill.

Learning math strengthens neural networks, fosters logical reasoning, and builds resilience. It equips students not only to succeed academically but to thrive in a world where quantitative reasoning shapes everything from personal finance to public policy.

Butterworth, B., Varma, S., & Laurillard, D. (2011). Dyscalculia: From brain to education. Science, 332(6033), 1049–1053.

Dehaene, S. (2011). The number sense: How the mind creates mathematics (2nd ed.). Oxford University Press.

Er, Z., & Dinç Artut, P. (2025). Comparative analysis of number sense performance in gifted vs. typically developing students. Humanities and Social Sciences Communications, 12, 1016. https://doi.org/10.1057/s41599-02505403-9

Parents and educators play a crucial role in reshaping how teens view math. By nurturing number sense, framing math as communication, and highlighting its presence in the world, we can restore confidence and ignite curiosity.

Ultimately, the goal is not simply to

Geary, D. C. (2013). Early foundations for mathematics learning and their relations to learning disabilities.

64

change in high school mathematics: Initiating critical conversations. Author.

Current Directions in Psychological Science, 22(1), 23–27.

Hechinger Report. (2025). The building blocks of math students need to excel. https://hechingerreport.org/thebuilding-blocks-of-math-studentsneed-to-excel

National Mathematics Advisory Panel.

(2008). Foundations for success: The final report of the National Mathematics Advisory Panel. U.S. Department of Education.

Libertus, M. E., Feigenson, L., & Halberda, J. (2011). Preschool acuity of the approximate number system correlates with school math ability. Developmental Science, 14(6), 1292–1300.

Organisation for Economic Co-operation and Development. (2019). PISA 2018 results: What students know and can do. OECD Publishing.

Organisation for Economic Co-operation and Development. (2021). OECD skills outlook 2021: Learning for life. OECD Publishing.

McNeil, N., et al. (2025). What the science of learning teaches us about arithmetic fluency.

Psychological Science in the Public Interest, 26(1). https://doi. org/10.1177/1529100625123456

Park, J., & Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychological Science, 24(10), 2013–2019.

MIND Research Institute. (2025).

2024 Annual report: Neurosciencedriven math learning. https://2024. mindresearch.org/news/mindeducation-marks-strides-inneuroscience-driv en-mathlearning-in-2024-annual-report

Sarnecka, B. W., & Carey, S. (2008). How counting represents number: What children must learn and when they learn it. Cognition, 108(3), 662–674.

Stanford University. (2025). Digital twins offer insights into brains struggling with math. https://hai.stanford.edu/ news/digital-twins-offer-insightsinto-brains-struggling-with-math and-hope-for-students

National Center for Education Statistics.

(2022). The Nation’s Report Card: Mathematics 2022. U.S. Department of Education.

National Council of Teachers of Mathematics. (2020). Catalyzing

University of Oxford. (2024). New 65

Why Math Matters (cont.)

Dr. Emily Wassell is an award-winning educator and holistic college coach with more than 25 years of experience helping students thrive inside and outside the classroom. She holds a BAS, MAT, and PhD in Educational Leadership, Research, and Policy from the University of Colorado Colorado Springs. A former teacher, principal, and visiting professor, Dr. Wassell is the founder of a global coaching practice that guides ambitious teens toward their dream colleges while prioritizing wellbeing, leadership, and long-term success.

research shows the way the brain learns is different and better than AI. https://www.ox.ac.uk/news/202401-03-new-research-shows-waybrain-learns-different-and-b etterway-artificial-intelligence University of Surrey. (2025). Brain stimulation boosts math skills in struggling learners. PLOS Biology. https://phys.org/news/2025-06brain-boost-math-people-weaker. html

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Article From Students' Hearts to Brains – How Math Identity Improves Math Achievement

Liesl McConchie

Ask any teacher what’s getting in the way of students learning math today, and you’ll hear a variety of responses: lack of motivation, debates around explicit vs. inquiry-based instruction, or a general “checked-out” attitude that wasn’t nearly as common a decade ago.

We tend to respond with new strategies for instruction, curriculum, or assessment. But in my 25+ years as a classroom teacher, school leader, and translator of cognitive neuroscience, one truth keeps rising to the top: A student’s emotional relationship with math is foundational to their cognitive relationship with math.

Students don’t walk into our classrooms as blank slates.

They enter with years of experience, feelings, messages, and beliefs that shape how they see themselves as math learners. In neuroscience, we call this an “identity-shaping neural network.” It is a tapestry of past experiences, future expectations, sociocultural messages, and personal efficacy judgments. In schools, we simply call it their math identity.

And teachers don’t need a degree in neuroscience to leverage it. Below are four high-impact, low-prep activities you can use in any classroom to strengthen students’ math identities. Each activity is paired with a 67

Math Identity (cont.)

“Nugget of Neuroscience” to help you understand why these strategies work.

1. Mathland Every student carries a story about their past experiences with math— great teachers, discouraging moments, proud successes, bruised attempts, and everything in between. Those experiences shape how they show up academically today.

Figure 1: A depiction of Mathland that includes candy, flowers, sunshine, and a river of hearts as the line of symmetry.

To surface these stories, invite students to draw their version of Mathland—a fictitious place ruled by mathematics— and place themselves in it. It could be a faraway planet with non-human species, or a hidden civilization somewhere on Earth. Give students full creative license to draw their vision of this place where math rules everything. Their artwork will reveal their relationship with math more than any survey ever will. This can be the starting point of future conversations with each student as you journey with them through their own emotional landscape of Mathland.

Figure 2: A student who feels “lost in the forest” of math.

Figures 1, 2, and 3 show three different depictions of middle school students’ Mathland art. Ask yourself "If this is how they perceive themselves and math, how might that impact their ability to learn math?"

Figure 3: A depiction of Mathland that positions learning math in school, similar to a prison sentence.

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Once a week, introduce a Belonging Bio:

Nugget of Neuroscience Emotions and cognition are inseparable partners in learning. The brain systems we rely on in school—attention, motivation, memory, and decisionmaking—are all highly influenced by emotional states. When negative emotions like anxiety or uncertainty activate the amygdala, they block access to the prefrontal cortex, limiting students’ ability to think, plan, and learn.

In contrast, positive emotional states such as curiosity, confidence, and hope release hormones and neurotransmitters that strengthen memory formation and deeper learning (Ahmed et al., 2013). In short, how students feel directly shapes how well they can think.

• a math teacher who shares their family background • a mathematician who looks like them • a community member using STEM in meaningful ways Keep each bio short, just a few minutes.

Over time, patterns shift. Students begin thinking, “If they can do it, maybe I can too.”

Nugget of Neuroscience Feeling like part of the classroom “in-group” protects students against the neurological impact of chronic stress. When students feel excluded, the amygdala (the brain’s uncertainty detector) activates, pulling attention away from learning and toward social survival (Stanley & Adolphs, 2013). By diversifying who students see as successful math learners, we biologically reduce the stress placed on minoritized students.

2. Belonging Bios Students are quick to label themselves as a “math person” or “not a math person.”

These labels have lasting impacts on their brain and their capacity to learn mathematics. On a neurological level, belonging isn’t soft. It’s survival. When students feel excluded or unsure of their place in math environments, the brain is flooded with increased cortisol levels, which interfere with attention, working memory, and executive functioning (Quaedflieg & Schwabe, 2018).

3. Math Media Moments Students are swimming in messages about what it means to be “good at math” or who is good at math. Many of these messages come from media— TikTok videos joking about hating math, movies showing “genius” as rare and socially awkward, or influencers glorifying speed over depth.

Students need to see people like them being successful in math spaces.

These messages accumulate in the brain as unconscious beliefs.

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Math Identity (cont.)

• “Everyone understands this but you.”

Once a week, lead a Math Media Moment:

• “You’re doing it different than everyone else. That means you’re wrong.”

1. Show a 15–30 second clip: • a commercial • a line from a show • a meme • a screenshot of an online comment

These internal messages become part of students’ personal efficacy—their belief about what they can or cannot do in math spaces.

2. Ask students:

To interrupt this, invite students to draw their Math Gremlin—the little figure on their shoulder whispering discouraging thoughts.

• What message is being communicated?

• Is it true? Where do we see evidence?

3. Replace the message with an accurate one.

This takes a couple of minutes but can undo years of internalized stereotypes.

Nugget of Neuroscience The brain strengthens neural pathways that fire frequently and with emotional intensity. This is Hebb’s Law, often summarized as “neurons that fire together, wire together” (Langille & Brown, 2018).

Media messages, especially humorous or emotionally charged ones, “fire” often, making them neurologically sticky. Talking about them interrupts automatic wiring and rewires healthier beliefs.

Figure 4: A Math Gremlin drawn by an elementary-aged student.

Giving your Math Gremlin its own shape and color helps externalize these unhelpful thoughts, creating distance from the student’s identity.

4. Math Gremlins Every student has an inner voice that whispers unhelpful things. For students learning math, it could sound like:

Once students have separated themselves from this invisible gremlin,

• “You’re slower than everyone else.”

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invite them to create a comeback phrase: Gremlin: “You’re not smart enough.”

Response: “I’m learning. My brain changes every day.”

4. Personal efficacy, one’s level of confidence and competence with math (Math Gremlins) For more activities and a deeper understanding of the brain science behind our math identities, check out my newest book, Building a Positive Math Identity: A Brain Science Approach.

When you see a student shutting down, a quiet “What’s your gremlin saying today?

And what can you say back?” can shift a student’s beliefs about their math ability.

Building strong math learners requires strengthening the relationship students have with math itself. When students heal from their past, believe they belong, and rewire unhelpful messages, the academic gains follow organically. In other words, every micro-interaction in the classroom influences whether a student moves toward or away from a stronger math identity.

Nugget of Neuroscience A student’s emotional state directly influences whether the learning regions of the brain “turn on” or “shut down.” Negative states like anxiety or hopelessness activate the amygdala, which blocks the prefrontal cortex—the center of complex thinking, planning, and problem-solving (McGarry & Carter, 2016). Externalizing the negative voice reduces its emotional power and reopens cognitive functioning.

This isn’t extra work.

This is the work that makes the rest achievable.

Putting It All Together These four activities align with the four main variables that build one’s math identity:

References

1. Past experiences with math (Mathland)

Ahmed, W., Van der Werf, G., Kuyper, H., & Minnaert, A. (2013). Emotions, selfregulated learning, and achievement in mathematics: a growth curve analysis. Journal of educational psychology, 105(1), 150.

2. Future vision of self in math spaces (Belonging Bios) 3. Socio-cultural influences regarding who is good at math, and what it means to be a “math person” (Math Media Moments)

Langille, J. J., & Brown, R. E. (2018).

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Math Identity (cont.) a Positive Math Identity: A Brain Science Approach, and co-author of the bestselling book Brain-Based Learning with Dr. Eric Jensen. She has been published in multiple education journals, including ASCD's Educational Leadership journal and NCTM’s Mathematics Teacher. With over 25 years of experience in education, Liesl bridges her knowledge of how the brain best learns with her experience of teaching across the K-12 spectrum to create tangible strategies to support teachers and schools across the globe. She has a rich background in education that includes creating new schools, leading wholeschool reforms, delivering workshops to educators, and speaking at conferences.

Liesl brings the highest quality of research, professionalism, and engagement to all her contributions to the field of education.

The synaptic theory of memory: a historical survey and reconciliation of recent opposition. Frontiers in systems neuroscience, 12, 52.

McGarry, L. M., & Carter, A. G. (2016).

Inhibitory gating of basolateral amygdala inputs to the prefrontal cortex. Journal of Neuroscience, 36(36), 9391-9406.

Quaedflieg, C. W., & Schwabe, L. (2018).

Memory dynamics under stress.

Memory, 26(3), 364-376.

Stanley, D. A., & Adolphs, R. (2013).

Toward a neural basis for social behavior. Neuron, 80(3), 816-826.

Liesl McConchie is an international expert on how the brain learns, author of Building

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Article The Skills-Based Classroom: Rethinking Assessments to Refocus Learning

Keenan Clark

Jake Towers

Introduction In our high school mathematics classrooms, we began to notice patterns that didn’t sit right with us. Students with solid conceptual understanding weren’t always earning the grades they deserved, while others with significant gaps were still walking away with A’s or B’s. Homework was losing its value—students copied, skipped it entirely, or increasingly turned to apps like Photomath and AI tools to generate answers. Makeup work consumed hours each week, and students who needed more time to learn rarely had meaningful chances to show improvement.

We knew these were not isolated challenges but symptoms of outdated assessment practices. During the summer of 2022, we committed to rethinking our approach. What emerged was a hybrid model we now call The Skills-Based Classroom. This is a system that blends the core ideas of Standards-Based Grading with our district’s traditional 100-point scale. It’s not radical, but it is transformative. And more importantly, it works.

Identifying the Problems 1. Unreliable Grades Our grading system was skewed by compliance.

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Skills-Based Classroom (cont.)

Completed homework, extra credit, and effort-based tasks often outweighed actual understanding.

Grades were misleading and did not tell an accurate story of what students knew.

The Skills-Based Classroom To confront these challenges, we redesigned nearly every aspect of our instructional and assessment system.

At the heart of this model is performance-based communication on a 1–4 scale:

2. The Homework Dilemma Math has long been synonymous with homework, but many students were no longer engaging authentically with it. Copying from peers or apps inflated grades but left gaps in learning, and homework checks consumed precious instructional time.

1 – Insufficient Evidence 2 – Basic Understanding 3 – Strong Understanding 4 – Mastery These levels communicate learning more clearly than points or percentages ever could.

3. Makeup Work Overload Daily assignments, weekly quizzes, and chapter tests created a maze of deadlines and makeups. Students with absences (excused or not) found themselves in a perpetual cycle of catching up, and teachers had to choose between hours of managing the logistics or disregarding antiquated school policies.

The biggest structural change, however, is our weekly routine. Every student meets with us individually to review progress, discuss misconceptions, and set goals. These short conversations have become one of the most powerful tools we use. They create accountability, build relationships, and shift the classroom culture from “What’s my grade?” to “Where am I at right now?”

4. Student Learning Variability Our pacing was guided by isolated instructional units and left some students racing to keep up and others bored, unchallenged, or unmotivated.

The structure offered little room for remediation or evidence of growth once an assessment window closed.

We still track and calculate a traditional percentage at semester’s end, but compliance and learning are separated, allowing us to see a clearer picture of true mathematical proficiency.

Surprisingly, our workload has decreased, and student ownership has skyrocketed.

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related to the current learning unit.

The Skills Assessment Central to our model is a reimagined approach to assessment. Traditional vehicles such as homework for practice, quizzes for checks, and tests for summative grading often blurred together in confusing and inequitable ways. We combined them into one tool: The Skills Assessment.

Multiple Attempts Without Penalty No two assessments are identical, but each version samples the same breadth of content. Students must take at least four assessments per skill, and we always average a student’s best four scores. This approach: • encourages persistence

Structure and Frequency A Skills Assessment:

• reduces anxiety • allows students to demonstrate growth

• includes approximately four test-like questions

• avoids grade inflation because rigor remains consistent

• is given about twice per week • takes 8–12 minutes

Instruction still moves forward traditionally from unit to unit, but students can request reassessments on any prior skill at any time. When a student demonstrates mastery, they shift their focus to the next skill.

• focuses on a tightly aligned set of skills that summarizes a unit These brief, targeted assessments allow us to monitor learning in real time instead of waiting until the end of a chapter. They serve as both formative checks and summative evidence.

Measuring Impact To understand whether this new system truly improved learning, we compared outcomes from our Algebra II classes from 2014–2019 to those from 2022– 2024. The results were striking.

Feedback and Revision Students receive written and verbal feedback every week. During one class period, we conduct one-on-one feedback conferences that rely on a discussion between the teacher and student. These conversations help students identify errors, revisit rules, and see patterns in their thinking. Concurrently, the rest of the class works on independent practice

Keep in mind, the same curriculum was used both before and after the switch to the Skills-Based Classroom strategy.

In fact, the final exam covered the same topics and was written to be almost 75

Skills-Based Classroom (cont.)

Statewide Recognition For the fourth consecutive year, our high school earned an Exemplary designation for the 2024–2025 school year. Not only was Carterville High School Exemplary, but its raw score has it currently placed as the 6th highest rated high school in the state of Illinois

identical to exams prior to the change.

• Semester exam grades improved proportionally to final semester averages.

• Students earning a final semester average of an A increased from 17% to 49%.

• Over 80% of students earned an 80% or higher class average.

Advanced Placement Success Initially uncertain about applying this approach to advanced-track students, we piloted the Skills-Based Classroom in AP Calculus during the 2023–2024 school year. Homework and quizzes were eliminated; students relied solely on skills assessments and retakes to demonstrate mastery. AP Calculus enrollment typically ranges from 22 to 28 students.

• Students earning a final semester failing grade dropped from 5% to 0%.

Yes, not one student has failed one of our classes in the past 3 years.

• Students displayed stronger confidence, fewer gaps, and far more ownership over their progress.

We also examined broader school-wide data.

Results spoke for themselves:

State Performance Beginning in 2022, the majority of our juniors, which includes the non-advancedtrack students, entered skills-based math classrooms. In 2023, our school’s SAT average exceeded the state average by 27.3 points, compared to 25.2 and 19.5 in the two years prior to implementation.

• Before implementation (2022 - 2023): 43% scored a 3 or higher.

• After implementation (2023 - 2024): 81% scored a 3 or higher. This exceeded both the state average (64.8%) and the global average (64.3%).

• More than 60% of our students scored a 4 or higher.

In 2024-2025, when Illinois transitioned from SAT to ACT, our students continued to outperform state averages by a large margin. With the ACT only being in effect for one year, longitudinal data does not yet exist.

• In 2024 – 2025, an incredible 89.3% of AP Calculus students scored a 3 or higher and once again obliterated the state and global average.

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Conclusion The Skills-Based Classroom is not a departure from sound mathematics instruction; we have simply refined our approach to assessments. If you walk into our classroom on any random school day, what you will likely see is the same as in any other math classroom. We still rely on daily lessons, independent practice, group work, and meaningful teacher-student interactions. What has changed is the lens through which we view assessment.

Returning to Our Original Problems Unreliable Grades By removing homework and other compliance tasks from grading, our assessments now reflect only the knowledge students demonstrate in supervised settings.

Homework Dilemmas Practice remains essential, but we no longer collect or grade it. Students quickly realized that their success on skills assessments, not points from worksheets, determined their grade.

By focusing on skills, feedback, and growth, we have witnessed students take

Grades now reflect knowledge rather than compliance, and students who once felt left behind are finding pathways to mastery.

Makeup Assignments With fewer traditional assessments, the burden of late work disappeared.

Skills assessments offer flexible, lowstakes opportunities for students to demonstrate learning, eliminating the need for extensive makeup policies.

greater responsibility for their learning, engage more deeply with mathematics, and experience more equitable opportunities to succeed. Grades now reflect knowledge rather than compliance, and students who once felt left behind are finding pathways to mastery.

Student Learning Variations Students can reassess at any time, allowing those who need more time to learn deeply while enabling advanced learners to move forward at an appropriate pace. Growth is built into the structure, not treated as an exception.

Most importantly, the Skills-Based Classroom doesn’t require a new curriculum, expensive software, or permission to overhaul the grading system. It simply requires a willingness to rethink assessment in the service of student learning.

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Skills-Based Classroom (cont.) of mathematical concepts, moving beyond traditional chapter-based instruction. At CHS, Keenan is also a longtime coach, and he shares his commitment to education with his wife, Kaci, who serves as the Social Studies Department Chair at CHS. They are the parents of four children.

Keenan Clark has been a dedicated educator in the Carterville school district since 1998. His career journey includes teaching junior high (1998–2003), followed by nearly two decades as a high school teacher (2003–2021). He also served as an Assistant Principal at the 4-6 Intermediate School (2020–2022) before returning to Carterville High School in 2022 to focus on Algebra II instruction.

Jake Towers has been teaching mathematics at Carterville High School for eight years. He graduated from Southern Illinois University Carbondale in 2018 with a bachelor's degree in mathematics education, and Iater earned his master's degree in educational leadership from Eastern Illinois University in 2022. In addition to teaching, he also coaches football and basketball within the district.

He is a proud co-creator of the Skills Based Classroom (SBC) teaching strategy (www.skillsbasedclassroom.com), a framework dedicated to improving student mastery through focused, transparent skill development and assessment.

His instructional work prioritizes deep understanding and practical application

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Article What's the Story?

Kathleen Meyer

When thinking about math instruction, the thought of infusing stories and literacy skills with different mathematical topics is often something not considered.

However, the demands of the state-level tests and other tests that students regularly take require a strong literacy background. Schmidtke et al. (2025) shared that when students have poor levels of reading fluency, these students generally become frustrated and tend to avoid tasks that involve reading (Schmidtke et al., 2025). What happens when students have the skills in math but cannot solve the problems that stare back at them? What can be done to support the linguistic needs of these students in a math class while moving forward with the requirements of a math curriculum?

A few summers ago, I found myself with a bunch of other educators from around the country at a STEAM in the PARK camp in the New River Gorge National Park and Preserve. Our evening conversation topics ranged from the beauty of the New River flowing right outside of the lodge at Camp Brookside to grant writing. Our conversation eventually drifted to some of the new Artificial Intelligence (AI) programs that were emerging and changing the landscape of education.

As a long-time special education teacher with stops along the way to teach math, STEM, and language arts, while 79

What's the Story (cont.) supporting a group of students who were also English language learners, I knew that a lot of my students not only struggled with the math but also with working through lengthy word problems where the purpose of the problem was often unclear. When a student is reading several grade levels below and then needs to work through math word problems, the situation becomes daunting. The question becomes, how can math become more accessible to all students while supporting the linguistic needs of these students?

2024). AI provides the ability to quickly create the skeletons of a lesson that can be fleshed out to meet the needs of many different types of learners in a matter of minutes instead of the hours the same task once took. These tools also allow for creative ways to embed literacy, problem-solving, and interest into various math topics.

Readers’ Theatre Finding ways to introduce a math topic can be a challenge. What happens when the topic is introduced by an assortment of characters that the students came together to name and to adopt as a chapter mascot? Suddenly, students have materials to work with when working through new math concepts that are not as intimidating. Jones (2025) also shared that there is a wide range of

The Main Tools - MagicSchool.ai and ChatGPT The environmental implications of using AI tools are immense, and this needs to be acknowledged. However, as a teacher who is constantly trying to adapt lessons

These tools also allow for creative ways to embed literacy, problem-solving, and interest into various math topics. to meet the needs of my students, creating several assignments that meet the various needs of my students each week was just not feasible. Handley and Donnelly (2024) explained that if meaningful and sustainable change is to happen, educators need to be equipped with the tools necessary to take tasks off their plates (Handley and Donnelly,

benefits of students using readers’ theatre in class, including improved fluency, increased comprehension through text engagement, oral language skills, increased vocabulary, and creating a collaborative learning environment (Jones, 2025). Students are working together and experiencing the math lesson through a story using characters 80

that may experience math in real-world settings. Through an engaging lesson, student participation increases, and the students also learn how to talk about math through a script that they can use later to explain what they have learned.

memorable (Frommert, 2023). By asking one of the AI tools to create a story about a given math topic that includes key vocabulary, real-life examples, set in a certain location, with specific characters, and practice problems, students are

Developing language-rich supplemental activities becomes increasingly important for all levels of students, especially students who are struggling with the academic language in a course. more engaged with the paths that the characters take, and helping the characters to successfully navigate the math. When math concepts become less intimidating, they also become more accessible to students.

Stories How long does it take to write a story that is mathematically accurate, interesting, and ready to use? A few hours, if everything goes as planned. This task can be done using an AI tool like ChatGPT or MagicSchool in a matter of minutes. Is it perfect? No. However, often the elements and details are created, and it takes the expertise of the teacher to make it something special for the class.

Vocabulary and Academic Language Students need to be able to understand and apply the math vocabulary for a given unit to effectively convey their understanding of a topic. Espinas and Fuchs (2022) explained that when the academic language in a content area, such as math, is limited, the student will often struggle to solve word problems (Espinas and Fuchs, 2022). Developing language-rich supplemental activities becomes increasingly important for all levels of students, especially students who are struggling with the academic language in a course. AI

Stories can be used to introduce a unit or as a review for a test. Frommert (2023) shared that storytelling has been embedded in the humanities subjects as it captures the attention of the learners and allows the learners to see how different concepts are interconnected.

Stories have been shared for generations because they are meaningful and 81

What's the Story (cont.) provides anything from vocabulary lists, vocabulary games, and strategies to interject vocabulary development activities into lessons. If a student can practice the vocabulary consistently and then apply the vocabulary to different situations, when it comes time for the extended response type questions, not only will the students be confident in answering the questions, but the students will also have the mathematical terminology to answer the questions accurately.

References Espinas, D. R., & Fuchs, L. S. (2022). The effects of language instruction on math development. Child development perspectives, 16(2), 69–75. https:// doi.org/10.1111/cdep.12444 Frommert, C. (2023). Using stories beyond word problems to teach math: Stories can help students recall key math concepts and make the subject more relevant to them. Edutopia. https:// www.edutopia.org/article/mathclass-using-storytelling/

Conclusion There is no perfect way to teach math.

Some students thrive on the routines of algorithms. Other students require creativity. Some students simply need a reason to be engaged with the topic.

When the students and the teacher can come together to create something unique to the class that covers the topic, not only does math get taught, but the classroom community becomes stronger.

Peanut the Squirrel and Waddles the Duck may mean nothing to students outside of my classroom, but to my students, they are the characters who are making math meaningful and accessible.

Handley, J. & Donnelly, L. (2024). What Can I Take Off Your Plate? A Structural-and Sustainable-- Approach to Countering Teacher Burnout. ASCD. Jones, S. (2025). Bringing readers’ theatre to life: The power of readers’ theatre.

Town End Research School. https:// researchschool.org.uk/town-end/ news/bringing-reading-to-life-thepower-of-readers-theatre Schmidtke, D., Yamada, S. & Moro, A.L. Bridging to academic success: The impact of reading gains in an English bridging program on GPAs. Read Writ 38, 195–224 (2025). https://doi. org/10.1007/s11145-024-10514-x

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The concept of being a lifelong learner is something that Kathleen takes seriously.

She earned her bachelor’s degree from Butler University, where she studied history, education, music, and geography.

She then completed a master’s degree in effective teaching with a concentration in special education at Butler University.

She continued her graduate education at Concordia University and earned a second master’s degree in curriculum and instruction with a focus on supporting English language learners. Just to keep things exciting, she also earned her bilingual certification in Spanish. She is pursuing another degree through the American College of Education in curriculum and instruction.

Kathleen Meyer is currently a sixth-grade general education mathematics teacher and an eighth-grade special education resource teacher at Indian Trail Junior High School in Addison, Illinois. She has been in the Addison School District #4 for almost two decades. She has taught a wide range of subjects, including STEM, language arts, math intervention, instructional math, instructional language arts, and has cotaught math, language arts, science, and social science. Kathleen is also a regular participant in the STEAM in the PARK program through Expeditions in Education, which allows her to collaborate with educators from all over the country while exploring different National Parks.

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Article Everyone's a Math Person

Emmie Pawlak

It is common to hear someone say, “I’m not a math person.” Many people go through life thinking they are consigned to not being able to make sense of math. In fact, there’s the old story from the 1990’s when A&W Restaurants offered a ⅓ pound burger for the same price as most fast food restaurants were charging for a ¼ pound burger. The “Third is the Word” campaign failed terribly because most Americans did not understand that ⅓ pound is actually larger than ¼ pound (Green, 2014). Many Americans were taught that being good at math meant being good at memorizing math facts and the order in which to perform a procedure. If that was difficult, there was no way around it and no hope for becoming better at math. Using a cognitive science lens on the teaching and learning of math shows that no one should think they are unable to become a math person.

Using a lens of cognitive science means making instructional decisions based on how the brain learns.

It begins with having a foundational understanding of the architecture of what is happening when the brain is exposed to new information and what needs to happen in order for that information to be retained in a useful way.

Key attributes of lessons that cognitive science show maximize the learning include: 84

This type of classroom scenario has been in play for decades, aiding and abetting the conventional wisdom that most Americans are not “math people.” In fact, American students have lagged behind their international peers for decades; the country’s current 8th-grade Math NAEP scores are only 5 points (out of a 500-point scale) higher than they were in the 1970s (Petrilli, 2024).

• Directing the learner’s attention • Connecting new learning to prior learning • Managing the amount of new information, and • Providing time and opportunities to think deeply about the new information.

The conventional picture of most math classes is one where the teacher is at the board, demonstrating a problem stepby-step while the students are frantically trying to write down all of the things the teacher is doing. The teacher is doing all the talking, and many students may not know what question to ask in the moment if they missed a step in the procedure. If a student missed copying down a step, that student may not know what to do, especially if they had to do the homework after class, on their own. In that “typical” setting, there are multiple daily opportunities for a student to fall behind, each time reinforcing the

Paying attention to cognitive science in the design and implementation of any lesson, but especially in a math lesson, will increase the likelihood that the information transmitted will not only be retained but will also be used in connecting more knowledge. The key instructional moves missing in the traditional math lesson are small but important and, unfortunately, easy to overlook.

When thinking of the tenets of cognitive science, key instructional moves a teacher will need to specifically plan for

Processing can look like students reflecting on what was just explained, restating the information, comparing with their peers, or examining how this new concept compares to their current understanding. are: “Who is doing the thinking?” and “How often is that person getting the

idea that the student will never be able to be proficient at math.

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Everyone's a Math Person (cont.) opportunity to do that thinking?” When a teacher is explaining a new concept or a new procedure, and students are copying down the information from the board,

typically is (Brown, Roediger III, McDaniel, 2014). This simple change in the daily work of a mathematics classroom can go a long way towards increasing student

These connections are important for students to see explicitly.. the teacher needs to stop often—twenty to thirty seconds after new information is given—to allow students time to process that information. Processing can look like students reflecting on what was just explained, restating the information, comparing with their peers, or examining how this new concept compares to their current understanding. The key is the frequency and depth of this processing.

If the teacher asks one deep question every ten minutes, there has not been sufficient processing time for new knowledge to stick.

retention of materials, regardless of whether the level of mathematics instruction is primary or advanced high school coursework.

The practice of regular reflection and practice in the classroom is a small tweak with big benefits. Additionally, there are other teacher moves that can increase the effectiveness of the lesson. Math concepts build upon each other. Teachers are very familiar with the concepts that they are teaching and see the connections between individual concepts. As teachers, our mathematical knowledge has been connected and solidified to the point that the connections between strategies or procedures are obvious to us.

Oftentimes, teachers forget to make these clear to the students because they are already clear to the teacher.

These connections are important for students to see explicitly—to connect the new learning to previously built understanding. The teacher needs to lead students from where they started

In math classes, whether they are utilizing “traditional” or “new math” philosophies, every student needs to be thinking deeply about the concepts, spurred by regular, frequent questions specifically designed to help students see the connections between their current understanding and the new understanding of the teacher’s lesson.

In order to make these lessons stickier in students’ brains, the material needs to be practiced significantly more often than it 86

in their previous learning to the day’s new learning, making sure that students are able to make those connections and build upon the math foundation that has already been laid.

Moving to a framework for teaching mathematics. Teaching Children Mathematics, 25(3), 133-136.

Kirschner, P., Hendrick, C., & Heal, J. (2022). How teaching happens: Seminal works in teaching and teacher effectiveness and what they mean in practice. Routledge.

Instructional moves are critical to the teaching of math. However, encouraging enough practice for work to become automatic and memorized is still a critical component. Good instructional strategies will help students develop conceptual fluency, leading to a strong number sense that will help students gain more access to increasingly difficult concepts and procedures (Huinker, 2018). As teachers plan their lessions, they need to ensure that they are creating opportunities for students to develop and build fluency. Having good conceptual fluency will allow students to have more cognitive space.

Petrilli, M. (2024, July 2). When was the golden age of American K-12 education? and how can we tell?

– The 74. The 74. https://www. the74million.org/article/when-wasthe-golden-age-of-american-k-12education-and-how-can-we-tell/

Dr. Emmie Pawlak is the Director of Math, Science, and Accelerated Pathways in Cicero School District 99. Her professional work is creating and supporting systems that elevate instructional practices, including helping staff measure their impact quantitatively and qualitatively and use those measurements to further student growth and achievement. Dr. Pawlak is also a language learner. Learning a second (or third) language has helped her support dual language learning environments. A core value of hers is that students should be not just biliterate but also "bi-numerate" and be able to use their whole linguistic repertoire to explain their math thinking!

References Brown, P. C., Roediger III, H. L., & McDaniel, M. A. (2014). Make it stick: The science of successful learning.

Harvard University Press.

Green, E. (2014). Why do Americans stink at math? The New York Times MM22, July 27.

Huinker, D. (2018). Principles to Actions: 87

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19Upcoming Events Empowering Visionary Curriculum Leadership Cohort Jan.-May | 9:00am - 3:00pm 10701 S. Kilpatrick Ave Explore learning with education leaders who deliver valid research-based learning approaches.

My Kids Can't Write presented by Paul Emerich France Feb. 10 | 9:00am - 12:00pm NIU Naperville or Online Learn to use cognitive writing as a means for writing across the disciplines, building students' stamina for on-demand writing tasks, and generating studentdriven evidence of learning.

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AI with Intention - Catch Them Learning: Supporting Academic Integrity in an ERA of AI presented by Tony Frontier Jan. 27 | 8:30am - 3:00pm Medinah Shrine Banquets or Online Explore practical, research-based solutions to support academic integrity, deter cheating, and help students take ownership for their learning.

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Decision Science as a School Leader presented by Jason Major Feb. 18 | 9:00am - 3:00pm NIU Naperville In this interactive workshop, Major will increase awareness of four domains from The Alliance for Decision Education: Valuing and Applying Rationality, Thinking Probabilistically, Structuring

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to equip educators, administrators, and support staff with the skills and confidence needed to navigate the Individualized Education Program (IEP) process.

Decisions, and Recognizing and Resisting Cognitive Biases.

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Next Generation Science presented by Jeff Spencer Feb. 19th - Champaign March 16th - Oak Lawn 9:00am - 3:00pm In-person Learn what the Next Generation Science Standards are and what an NGSS-aligned classroom looks like.

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Pump Up Primary Conference - PreK thru 2nd March 4 - 6 Renaissance Hotel 45th annual Pre-K, Kindergarten, 1st and 2nd grade conference.

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Every Graduate Future Ready: Delivering Employability Skills Presented by Chapman & Simons April 14 | 9:00am - 3:00pm Oak Lawn, Online or On-Demand School-based teams will design a grades 6–12 scope and sequence that builds college, career, and civic readiness for all learners.

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IEP Toolkit: Mastering Writing, Accommodations, Data Collection, and Understanding Behavior presented by Shelley Kenow March 11 | 9:00am - 12:00pm Live Online or On-Demand This comprehensive webinar is designed

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Empowering Small Group Instruction in Reading and Writing presented by Jennifer Serravallo April 15 | 9:00am - 3:00pm Online or On-Demand Regardless of your literacy curriculum or approach, you will be empowered to bring truly responsive small group teaching to your classroom for better outcomes in both reading and writing.

MATH THERAPY Featuring Vanessa Vakharia April 22 | 9:00am - 3:00pm Medinah Shrine Center, Online or OnDemand You’ll leave this session with practical, no-nonsense tools to turn those “I can’t do math” students into “I can do this” students!

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Building School-Wide Systems of Care and Belonging presented by Ricky Robertson April 21 & May 5 | 8:30am - 3:30pm Medinah Shrine Center, Online or OnDemand Through guided reflection and actionable strategies, you will leave equipped to foster a culture where you and staff will feel valued, safe, and supported in your essential work.

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