15 minute read
Improving Equity and Mathematics
Carol Larson
Eric Sinclair
Article
Introduction
The onset of the 2020 pandemic was an eye-opening experience for many educators. As curriculum administrators who work for a charter school network that serves traditionally marginalized students, the consequences and the severity of the digital divide were clear to us. Our local assessment data showed that we experienced low growth in mathematics from the spring to fall in 2020. Several testing organizations echoed those observations and reported that students across the nation started the 2020-21 school year further behind in mathematics than previous cohorts and that this gap was greater for marginalized students (Brody & Koh, 2020; Kuhfeld et al., 2020).
Throughout the 2020-21 school year, our educators engaged in discussions about how we could address unfinished learning in mathematics. We discussed the need to create a shared understanding of what high quality digital learning in mathematics looks like so that our instructional leaders can promote consistent practices across our network. As a result, we reviewed numerous eLessons, articles, and webinars to synthesize what we learned into a tool that identifies recommended
practices for stronger virtual instruction. Although our final document includes additional guidance on community building, workload management, student engagement, and norms and routines; the following four principles can be used as an initial framework for improving mathematics instruction in virtual settings.
Principle 1: Design the virtual environment for accessible mathematics instruction.
To be effective in virtual environments, math teachers not only have to be knowledgeable about content and pedagogy, but they also need to understand the fundamentals of how accessing content or engaging with the lesson, such as the onset of computer vision syndrome (Gowrisankaran & Sheedy, 2015) or reading comprehension challenges that may result from longer passages (Singer & Alexander, 2017). For these reasons, the design of visual presentations and web-based interfaces should include the thoughtful use of attentional cues, white space, font size, and media. (The University of Minnesota posted an academic slide design webinar that covers several of these design fundamentals). Lessons should also include high quality and developmentally appropriate media, lighting, and audio; expository, active,
to design e-learning. It has been found that students interact with virtual environments differently than they do with face-to-face environments, so direct translations of lessons from traditional in-person learning to e-learning may not work. For instance, students can experience unique barriers in virtual environments that prevent them from and interactive activities; assistive technologies; and intuitive course navigation routines that result in having to make the fewest number of transitions or use the fewest number of links. In addition, there should be a balance between onscreen and offscreen activities, while chunking longer lessons into smaller segments at their natural
breaks to provide opportunities for screen breaks and movement.
For virtual environments, math teachers will need to consider how to integrate technology into lessons. One of the problems that we witnessed as administrators is that some teachers appeared to start with technology choices before considering what students need to be able to learn and do in the lesson. A better practice is to begin by considering the learning goals first and then to choose the tools that will best help students to meet those goals. This process requires teachers to ask two questions: What will students need to be able to do during the lesson? In what ways can the lesson be modified to increase student participation and improve equity and access to the mathematical content?
Here is an example of a kindergarten Eureka math lesson (see figure 1). This lesson requires students to observe the
Figure 1
This is an excerpt taken from Eureka Math kindergarten module 2, lesson 1. To view the full lesson, please visit: www.engageny.org.
properties of shapes and to be able to categorize them accordingly. Using the .pdf copy as a visual for the presentation would not be developmentally appropriate for kindergarten students, because the teacher would only be able to show part of the .pdf at a time or the font size would be small if the entire worksheet were displayed at once. A teacher could write or draw directly onto the .pdf, but that could lead to visual clutter. A document camera could be used for the teacher to demonstrate the sorting of shapes, but then the students would not be able to actively participate in the lesson unless they had access to their own materials. Many of our students do not have printers at home, so unless the worksheet was made available to them ahead of the lesson, it would be difficult for those students to complete the assignment.
Figure 2
This drag and drop activity was created as a virtual alternative to the downloadable .pdf worksheet included in the kindergarten module 2, lesson 1 activity. There are many online video tutorials on how to create drag and drop activities, including this one.
One way to address these problems and to promote equity is to create an interactive virtual version of this activity that all students can access. For example, the teacher could create a set of Google slides that would enable students to drag and drop shapes into predefined categories (see figure 2). Slides like this can be used to lead classroom discussions in-person or virtually, and copies of slides
can be made for individual students so that they could sort their own shapes online. Finally, a slide like this can be easily revised for new categories, such as asking students to categorize shapes that are triangles and shapes that are not triangles.
Aside from considering how to transform activities for virtual spaces, teachers will also need to consider how to improve student access to support multilingual students. In an asynchronous environment where some students may not be able to read directions independently, teachers can record them with an audio application like Vocaroo and insert those files into lesson materials or assignment portals. Students can be taught how to use browser extensions that offer text-tospeech and speech-to-text functions, such as Read&Write or translations
mathematical content and activities in order to improve equity and access. For instance, students who experienced unfinished learning during the pandemic may need to access specific topics in mathematics via concrete experiences and representations, and digital manipulatives could be used to provide multiple representations of a concept.
Additionally, the use of assistive technologies can eliminate or minimize barriers to learning. For instance, activating closed captions during lesson presentations not only help the hard of hearing, but they also support, such as Google translate. Some lesson presentation tools, such as Nearpod, provide students with the opportunity to submit drawn, audio, or video responses within a single platform. Additionally, Nearpod integrates with some mathematical applications, such as Desmos and Phet Interactive Simulations. This integration minimizes the number of transitions that students will need to make during a lesson, which improves user experience.
Before integrating assistive technologies and digital applications into lessons, it is important to provide students with time to practice them. For instance,
kindergarteners may need to practice dragging and dropping items, activating sound files, and using text-to-speech technologies before they can use these tools independently. Because learning how to use new tools can supplant instructional and planning time, it is recommended that school systems adopt and use consistent tools across grade levels and content areas when possible so that students can make seamless transitions between classrooms.
Principle 2: Design asynchronous and synchronous instructional plans that maximize time and optimize learning
At the beginning of 2020, much of our e-learning in mathematics consisted of live lessons or recordings of lessons that were accompanied by digital copies of worksheets. Observations of these lessons revealed limited student engagement and a significant number of missing assignments.
As we learn more about e-learning, we are discovering that long lectures may be an inefficient and ineffective way to teach in virtual environments (Gallagher & Cottingham, 2020). Because time for human interaction can be limited in eLearning, it is important for teachers to strategically prepare synchronous lessons by considering which experiences or tasks would be best suited for realtime interactions. Synchronous sessions should be designed to optimize student engagement and include active student experiences, such as opportunities for student discussions, Socratic seminars, and collaborative problem-solving. Additionally, teachers may be able to improve engagement by segmenting these sessions into manageable, more digestible interval chunks (see Ringel, Tarallo, & Green, 2020 for an example). Finally, including some open-ended, low floor/high ceiling activities that promote inclusivity and increasing a student’s ability to meaningfully contribute to the discussion may also improve student participation rates, diminish the potential for math anxiety or embarrassment, and increase selfefficacy during synchronous sessions.
Quality asynchronous mathematics lessons also require intentional planning with an understanding that students should be able to complete asynchronous work independently or with limited support. In asynchronous-only environments, students will complete a series of self-paced lessons that support learning goals. When used as a support for face-to-face or synchronous lessons, asynchronous activities should be designed to maximize synchronous time and help teachers plan for targeted instruction. For example, asynchronous coursework can be used to activate background knowledge, facilitate
project completion, demonstrate how to solve a problem, collect assessment data, strengthen fluency work, engage in explorations, solve open-ended problems, provide peer feedback, offer student collaborations, or individuate instruction.
Designing asynchronous and synchronous sessions to align to the same learning goals and optimize instruction requires teachers to ask, what do digital technologies do best and what do humans do best? Tasks that require greater support and real-time interaction between teachers and peers should be reserved for live sessions whereas tasks who need intervention support ahead of a new topic. The benefit of these types of applications is that they can provide students with immediate feedback and individuate instruction by adapting problem sets to a student’s zone of proximal development.
In another example, a teacher may design an asynchronous activity to support a synchronous session. For instance, this video could be used as an asynchronous notice and wonder activity to launch a lesson on parabolas. In this video, students observe the bounce pattern of a tennis ball over time. Students can record three things that they notice and
three things that they wonder about the bouncing tennis ball into a document or note catcher. This asynchronous activity would provide students time to process the visualization of the bouncing ball internally before they meet with their classmates to discuss it either in small groups or as a class. Because students had an opportunity to become familiar with the video and process their initial
that can be completed independently or more effectively or efficiently with digital technologies may be better suited for asynchronous learning. For instance, some mathematics applications (e.g., Dreambox, Aleks, IXL, etc.) can be used to strengthen fluency work during asynchronous time or can be used to provide “just in time” co-requisite development (Martin, 2020) for students
thoughts, the teacher does not have to spend as much time introducing the video during the synchronous session. Additionally, the teacher can also use the asynchronous student responses to plan for the synchronous lesson, which may be more meaningful to the students. For instance, the teacher may note that some students notice a decrease in the height of the bounce with each bounce or wonder if they would observe similar outcomes with different types of balls. Using that information, the teacher could design the lesson to build concepts and make connections to these notices and wonderings.
Principle 3: Integrate effective assessments and feedback practices.
Teacher responsiveness is important to learning, and this includes providing direct and indirect student feedback. This feedback should be timely, tied directly to learning goals, and communicate how students can improve performance. Student expectations should be clearly and consistently communicated to students, and when applicable, students should be able to create learning goals for themselves. In a virtual environment, teachers can share exemplars of what meeting and not meeting expectations look like, provide video presentations on expectations, post the criteria that will be used to evaluate student work using checklists or rubrics, and more. There are many applications that can be used for feedback, such as features that are embedded in Google suite applications, Vocaroo, Jamboard, Padlet, and Flipgrid. Teachers can use these tools to draw, add written or audio anecdotal notes, or post video files that show students how to improve their work (see an example). Some tools, such as Nearpod, Google slides, and Pear Deck, can be used to efficiently collect real-time student response data. Digital mathematics programs, such as Dreambox or IXL, provide students immediate feedback to students and offer teachers student progress reports and analytics.
In virtual environments, adjustments may need to be made in how students’ responses are collected for assessment purposes. Although multiple choice problems are a fast and easy way to collect information in digital spaces, they generally do not reveal how students approach and process the mathematics. One way to address these problems is to include assessment items that are designed to reveal student thinking. For instance, the chart in figure 3 on the following page can be posted as an asynchronous pre-assessment. Prior to a lesson on using pictograph data, the teacher can post this chart to observe what students already know by asking them how many more students voted
Figure 3
A pre-assessment item like this could be used in an asynchronous setting to gather information about what students know ahead of a synchronous session.
for chocolate than for strawberry and to explain their thinking. Some students may count the total number of cones on the chart, some may count the number of cones in each flavor category using one-to-one correspondence, some may count each cone as two votes, and some may successfully solve for the “how many more” question. The teacher can use the student responses from the asynchronous pre-assessment to inform instruction and determine a strategic pathway for developing the important ideas of the lesson. For instance, if responses reveal that most students can distinguish between the different levels of flavor but interpret each cone as = 1, then an important objective will be to teach students how to use a pictograph key and skip counting to interpret the graph. One of the most important teaching practices is to conduct checks for student understanding. Checks for understanding are a type of formative assessment that help teachers gauge the effectiveness of their teaching and to determine whether instructional adjustments need to be made. This information also helps teachers to identify which students require additional support. Prior to the pandemic, the most common forms of checks for understanding among our teachers included scanning student responses on individual dry-erase boards, collecting exit slips, or asking students to provide quick self-assessments. One positive outcome from the transition to e-learning during the pandemic is that teachers now have access to more tools that are better suited for collecting this
information during in-person and digital learning as well. For instance, reverting back to our Kindergarten sorting of shapes activity, the teachers can use the Google slide “grid view” option to observe students simultaneously solving the same problem (see figure 4). This provides the teacher with immediate information about how students are approaching the problem and what misconceptions or errors some may have. Additionally, tools like Nearpod and Pear Deck provide teachers with the ability to access grid view or scrollable student responses during a lesson (see figure 5 on the following page). Some tools also provide opportunities for students to provide peer-to-peer feedback.
Conclusion
Overall, improving equity and access to mathematics in virtual spaces will require time, resources, and perceptional shifts that ask us to reimagine how to effectively use digital tools to optimize learning in any learning environment. This will require a commitment to integrate technology into the classroom in meaningful ways while engaging in cycles of continuous innovation and improvement. For those who are at the beginning stages of this work, these five principles are one way that we can start addressing the digital divide in mathematics.
Figure 4
Some applications, like Google slides, provide teachers with the option of viewing students’ work on one screen in real-time.
Figure 5
Scrollable student responses like this one in Pear Deck provide real-time student responses that can be used to check for understanding.
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When this article was written, Carol Larson was the Head of Academics for Christel House Indianapolis. She is currently the Executive Director for Indiana Connections Academies, which are part of the Pearson Virtual Schools network.
Eric Sinclair has been a public school educator for ten years and has worked in urban charter schools for four. He earned his Master’s degree in education from Eastern Illinois University in 2013 and his Ph.D. in Curriculum & Instruction from Indiana State University in 2017. Eric is the Humanities Director for Christel House Indianapolis.
