The Use of Student Work as a Context for Promoting Student Understanding and Reasoning Yvonne Grant Portland MI Public Schools Michigan State University Elizabeth Phillips Michigan State University 2015 Leadership Seminar on Mathematics Professional Development Teacher Development Group March 18-21,

Current Projects  Arc of Learning  Classic Problems  Modeling in the CMP Curriculum  Deeply Digital CMPX  Teacher Support  Formative Assessment  Student Work as a Context for Student Learning 2

Overview Student Work as a Context for Learning  What opportunities exist for students to engage in problems involving student work?  What is the nature of the student work?  What are the intended mathematical purposes of the student work?  What is the role of the teacher in using student work as a context for learning? 3

Discussion  How do you use student work? 4

Emerging Criteria for what counts as student work:  Mentions a person (not necessarily a name)  Mentions how that person thought about the embedded mathematics: mathematical claim, idea, conjecture, reasoning about something, student reflections, report some observations/measurements  Has an expected student activity: analyze, critique, or reflect on mathematical thinking of another, E.G: Is this thinking correct? Why? How does this compare to what you thought? Does this make sense to you? Explain. Compare and contrast? Will this strategy work? 5

One of these things is not like the others… Which of these is an example of student work? 6

Examples of Student Work  Classroom generated  Teacher generated  Curriculum generated 7

Discussion  How do you use student work? 8

Working Premise Understanding and reasoning emerge as students and teachers interact around a sequence of rich problems to discuss, conjecture, validate, generalize, extend, connect and communicate.  What is the role of student work to produce understanding and reasoning? 9

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Classroom Generated Classroom (student) generated student work refers to what is written or spoken by students that arises from the task the students are thinking about in class.  What does this look like in a classroom?  What is the role of the student? The teacher? Curriculum? 11

Classroom Example: Finding an algorithm for multiplying proper fractions As you look at the problem  Describe the mathematical understandings. Anticipate student responses. 12

CMP3: Let’s Be Rational, Problem

Classroom Video The teacher is conducting a summary of the problem. She added two problems 2/7 x 1/3 and 9/10 x 1/6 which are also shown in the video. Problem 2.1Focus: How does the area model relate to multiplying fractions?  How does the teacher use the student work to promote the goals of the problem? 14

How does the teacher use the student work to promote the goals of the problem? Take notes on  The student work  How the student work is being used? 15

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CMP3: Let’s Be Rational, Problem 2.2 What are the mathematical goals? How does student work promote these understandings? 17

We have seen an example of classroom generated student work. 18

Curriculum Generated Student Work a reference within the student text to how a person thought about a mathematical context or problem and requires students to analyze, evaluate, generalize, critique, and/or reflect on one or more persons’ mathematical thinking.

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Another Example What strategies can you use to multiply any two fractions?  Anticipate how students might do Part A.3. 21

CMP3: Let’s Be Rational, Problem

Classroom Video Problem 2.2 Focus: What strategies can you use to multiply any two fractions? In the video the class is summarizing the strategies used to solve part A. 3. How does the teacher use the student work to promote the goals of the problem? 23

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Student Strategies 25

Video Reflection  What mathematical understandings emerged?  What was the role of the student work?  Why did the teacher impose a piece of student work? 26

Why is…? What’s the mathematical understanding? Student or teacher generated? 27

Curriculum Generated Curriculum generated student work refers to student work the authors use as a context for learning within the student materials.  What is the role of the student work?  Why did the authors impose the student work? 28

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Homework 30

Challenges of Interpreting Student Work Questions:  What type of cognitive demand is involved in analyzing the work of another person?  What happens if all students are not at a place to access the work? How does a teacher know when to pose the work? What does the teacher do? 31

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In Classrooms Using the Mathematical Practices – Students expect to make sense of the mathematics. 33

Mathematical Practices  Make sense of problems and persevere in solving them  Reason abstractly and quantitatively  Construct viable arguments and critique the reasoning of others  Model with mathematics  Use appropriate tools strategically  Attend to precision  Look for and make use of structure  Look for and express regularity in repeated reasoning 34

NCTM Principles for Teaching and Learning  Establish mathematics goals to focus learning  Implement tasks that promote reasoning and problem solving  Use and connect mathematical representations  Facilitate meaningful mathematical discourse  Pose purposeful questions  Build procedural fluency from conceptual understanding  Support productive struggle in learning mathematics  Elicit and use evidence of student thinking 35

Teacher Generated Teacher generated student work refers to student work the teacher generates for particular purposes, usually to highlight a strategy or an important aspect of the concept being studied  What is the role of the student work?  Why did the teacher impose the student work? 36

Student work as Artifacts 37

Student Work for Planning  What issues does a teacher attend to in planning?  How might examples of student work be useful?  Would any of the following examples of student work be useful as teacher imposed? Why 38

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Student Work for Planning  What issues does a teacher attend to in planning?  How might examples of student work be useful?  Would any of the preceding examples of student work be useful as teacher imposed? Why 45

Back to Curriculum Generated Student Work  What are potential affordances of using student work as a context for learning in written curriculum materials? 46

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48 CCSSM 7.N.S.A.2a

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Student Work Reflection  What potential do these problems have for promoting learning? What kind of learning? 53

Discussion  In what ways can student work be used as a context for developing understanding and reasoning? for the student? for the teacher?  What role does student work play in planning? Teaching? Assessing? Reflecting?  What classroom norms are needed to make this possible? 54

Roles of Curriculum Generated Student Work Research Questions:  What opportunities exist for students to engage in problems involving student work?  What is the nature of the student work?  What is the intended mathematical purpose of the student work? Refine strategies Attend to nuances Introduce strategies and argumentation ? 55

“Knowing mathematics, really knowing it, means understanding it. When we memorize rules for moving symbols around on paper we may be learning something, but we are not learning mathematics. When we memorize names and dates we are not learning history; when we memorize titles of books, we are not learning literature. Knowing a subject means getting inside it and seeing how things work, how things are related to each other, and why they work like they do.” Making Sense, James Hiebert, et al p. 2 56

If you have any thoughts concerning this research project, please share them with us. Thank you for your contributions. Betty Yvonne 57