The Use of Student Work as a Context for Promoting Student Understanding and Reasoning

Yvonne GrantPortland MI Public SchoolsMichigan State University

Elizabeth PhillipsMichigan State University

2015 Leadership Seminar on Mathematics Professional DevelopmentTeacher Development GroupMarch 18-21, 2015

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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

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OverviewStudent 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?

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Discussion

How do you use student work?

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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?

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One of these things is not like the others…Which of these is an example of

student work?

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Examples of Student Work

Classroom generated

Teacher generated

Curriculum generated

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Discussion

How do you use student work?

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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?

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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?

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Classroom Example: Finding an algorithm for multiplying proper fractions

As you look at the problem Describe the mathematical

understandings.

• Anticipate student responses.

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CMP3: Let’s Be Rational, Problem 2.2 13

Classroom VideoThe 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?

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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?

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CMP3: Let’s Be Rational, Problem 2.2

What are the mathematical

goals?

How does student work

promote these understandings?

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We have seen an example of classroom generated student work.

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Curriculum Generated Student Work

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-- 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 ExampleWhat strategies can you use to multiply any two fractions?

Anticipate how students might do Part A.3.

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CMP3: Let’s Be Rational, Problem 2.2 22

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?

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Student Strategies

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Video Reflection

What mathematical understandings emerged?

What was the role of the student work?

Why did the teacher impose a piece of student work?

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Why is…?

What’s the mathematical understanding?

Student or teacher generated?

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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?

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Homework

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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?

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

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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

reasoning34

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 thinking35

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?

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Student work as Artifacts

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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 following examples of student work be useful as teacher imposed? Why

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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

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Back to Curriculum Generated Student Work

What are potential affordances of using student work as a context for learning in written curriculum materials?

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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?

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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?

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Roles of Curriculum Generated Student WorkResearch 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 strategiesAttend to nuances Introduce strategies and argumentation?

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“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

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If you have any thoughts concerning this research project, please share them with us.

Thank you for your contributions.

BettyYvonne

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