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Differentiation in the Mathematics Classroom NCCTM October 11-12 Future Ready Schools


“There is no magic set of instructional strategies that will solve our problems. There is no behavior management program that can begin to substitute for building relationships of trust and respect with individual human beings. We simply have to decide the shape we want our teaching careers to take, and begin moving in that direction.� (Tomlinson, p91)

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Objectives • Define

differentiation

Design Activities from clear learning targets

• Examine

role of Assessments and Feedback Future Ready Schools


What is Differentiation? Responsive instruction • An extension of, but not a replacement for high quality instruction •

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What is differentiation guided by? • Guiding

Principles:

Respectful tasks Flexible grouping Ongoing assessment Adjustment Future Ready Schools


Differentiation- a multidimensional task • Considerations:

student needs curriculum knowledge and skills data Future Ready Schools


Students seek. . . Affirmation

Challenge

Purpose

Contribution Power Future Ready Schools


Teacher responds . . . Investment

Invitation

Persistence

Reflection

Opportunity

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Curriculum and Instruction‌ Scaffold

Important

Demanding

Focused Engaging Future Ready Schools


What do you see? 1.

Which animal represents where you are with the differentiation of instruction? Why?

2.

What are some things you have seen or should see in a classroom where teachers differentiate?

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Why is it so difficult? Assess the child; analyze the data; plan the lessons; complete this 20 or more times per child; plan whole group instruction and four to six small groups; provide three to ten centers; differentiate each center; monitor twenty plus students and adjust instruction on a daily basis; reassess the child; analyze the data; plan the lessons, etc.

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Classroom Environment Activity: Discuss the following: How do students transition into: • Small group rotation in a timely manner • Centers (List each response on chart paper.) Future Ready Schools


Clear and Appropriate Learning Targets DECONSTRUCTING STANDARDS

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Deconstructing Complex Standards 1.

Determine ultimate type: knowledge, reasoning, skill, or product

2.

Identify its underpinning learning targets Future Ready Schools


6th Grade Standard/Benchmark:

Type:

x

Knowledge

3.03 Transform figures in the coordinate plane and describe the transformation.

Reasoning

x

Skill

Product

Learning Targets What are the knowledge, reasoning, skill, or product targets underpinning the standard or benchmark? Knowledge

Reasoning

Skill

Product

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6th Grade Standard/Benchmark: 3.03 Transform figures in the coordinate plane and describe the transformation. Type: X Knowledge

Reasoning

X Skill

Product

Learning Targets What are the knowledge, reasoning, skill, or product targets underpinning the standard or benchmark? Knowledge

Reasoning

Skill

Know the types of transformation s Definition Movement Directional vocabulary Identify coordinates of images

Distinguish between the types of transformation using rules and images

Describe location of coordinates Use words to describe transformations Reflect a figure over a line Translate a figure in a plane

Compare transformation movements

Product

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Assessments for Learning Formative • For learning • Frequently • Use results to determine next steps • Descriptive feedback

Summative • Of learning • Less frequent • Evaluative/grade • Referrals

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Assessment methods are legitimate options when their use correlates highly with the learning target and the intended use of the information.

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Assessment Methods: 1.Selected response and short answer 2.Extended written response 3.Performance assessment 4.Personal communication

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Classroom Communication •Must connect to learning. •Everyone must understand the meaning of the achievement target. •Everyone must understand the symbols being used to convey information. •The communication must be tailored to the intended audience. Future Ready Schools


“The most powerful single modification that enhances achievement is feedback. The simplest prescription for improving education must be ‘dollops of feedback’ ” -Robert Marzano

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Effect of Feedback Characteristics of Feedback from Classroom Assessment

% Gain or Loss in Student Achievement

Example

Right/Wrong

-3

× √

Provide correct answer

8.5

“b” is the correct answer

Criteria understood by students

16

Clarity regarding scoring

Explain

20

Why correct or incorrect

Repeat until correct

20

Can’t move on until mastered

Displaying results 26 graphically

Data logs in notebook, students/class track data, data wall

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Types of Feedback •

Evaluative –

Sums up achievement and assigns a label, expresses a judgment

Descriptive -offers information about the work, product, or performance relative to intended learning

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Evaluative – – – – – – –

Grades (A,B,C,D,F) Letters (P for proficient, D for developing, B for beginning) Numbers (4 for exceeds standard, 3 for meets standard, etc) Words (Excellent, Good, Fair, Poor) Other symbols (smiley faces, stars, pluses, checks, minuses, etc.) Written comments (good work, needs work) Stickers (Great job! Awesome! Super!

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Descriptive Value neutral (avoids praise or blame) • Focuses on the intended learning • Shows where the work is right or wrong and why • Pinpoints strengths and identifies areas of improvement in terms of the intended learning •

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Descriptive cont…

Takes in account the amount of corrective information the learner can act on at one time • Models the kind of thinking students will engage in when they self-assess • Can be used by students to take action to improve • Does not cause the learner to shut down •

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Communication Used in the Classroom You made simple mistakes with translating the triangle. Next time take a few minutes to check your work. Evaluative

Descriptive Evaluative

√ Evaluative

Try harder next time.

+ Evaluative

Evaluative Future Ready Schools


Activity: 1. Identify an activity for students (below average, average, above average) for your learning target. 2. List at least 2 formative and 1 summative assessments you will use to provide feedback. 3. For each assessment identify the type of feedback you will provide (Descriptive/Evaluative).

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Resources Fulfilling the Promise of the Differentiated Classroom, 2003, Carol Ann Tomlinson Advancing Reading Achievement, 2003, David and Ann Collins, Serve Classroom Assessment for Student Learning: Doing It Right-Using It Well, 2006, Richard Stiggins, Judith Arter, Jan Chappuis, and Stephen Chappuis

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Contact Information Middle Mathematics Consultant: Mary Russell mrussell@dpi.state.nc.us Middle/Secondary Mathematics Section Chief: Everly Broadway ebroadway@dpi.state.nc.us

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differentiation: community.learnnc.org  

Handout from ncctm07 conference

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