Strategies to Promote Motivation in the Mathematics Classroom TASEL-M August Institute 2006

Motivation in the Math Classroom In pairs discuss: What, ideally, does student involvement in learning mathematics look and feel like from… your perspective as a teacher? the perspective of your students?

Research on Motivation Guiding question: What factors promote (or discourage) students’ involvement in thinking about and developing an understanding of math? “Involvement” is more than being physically on-task Focused concentration and care about things making sense Intrinsically motivated to persist Cognitively engaged and challenged Two areas of focus: Cognitive Demand of Mathematical Tasks Discourse Strategies References Henningsen & Stein (1997). Mathematical tasks and student cognition. Journal for Research in Mathematics Education, 28(5), 524-549. Turner et al. (1998). Creating contexts for involvement in mathematics. Journal of Educational Psychology, 90(4), 730-745.

Mathematical Tasks What is cognitive demand? Focus is on the sort of student thinking required. Kinds of thinking required: Memorization Procedures without Connections Requires little or no understanding of concepts or relationships. Procedures with Connections Requires some understanding of the “how” or “why” of the procedure. Doing Mathematics Lower level Higher level

Examples of Mathematical Tasks (1) Memorization Which of these shows the identity property of multiplication? A) a x b = b x a B) a x 1 = a C) a + 0 = a Procedures without Connections Write and solve a proportion for each of these: A) 17 is what percent of 68? B) 21 is 30% of what number? Too much of a focus on lower level tasks discourages student “involvement” in learning mathematics.

Examples of Mathematical Tasks (2) Procedures with Connections Solve by factoring: x2 – 7x + 12 = 0 Explain how the factors of the equation relate to the roots of the equation. Use this information to draw a sketch of the graph of the function f(x) = x2 – 7x + 12. Doing Mathematics Describe a situation that could be modeled with the equation y = 2x + 5, then make a graph to represent the model. Explain how the situation, equation, and graph are interrelated. Higher level tasks, when well-implemented, promote “involvement” in learning mathematics.

Characteristics of Higher-Level Mathematical Tasks Higher-level tasks require students to… do more than computation. extend prior knowledge to explore unfamiliar tasks and situations. use a variety of means (models, drawings, graphs, concrete materials, etc…) to represent phenomena. look for patterns and relationships and check their results against existing knowledge. make predictions, estimations and/or hypotheses and devise means for testing them. demonstrate and deepen their understanding of mathematical concepts and relationships.

The Border Problem Without counting 1-by-1 and without writing anything down, calculate the number of shaded squares in the 10 by 10 grid shown. Determine a general rule for finding the number of shaded squares in any similar n by n grid.  

Video Case: Building on Student Ideas The Border Problem What might be the lesson’s goals and objectives? What is the cognitive demand of the task (as designed)? As you watch, consider: Who is doing most of the thinking? How does the teacher support student “involvement”? After watching, think about: What sort of planning would this lesson require? From: Boaler & Humphreys (2006). Connecting mathematical ideas. Portsmouth, NH: Heinemann.

Discourse Strategies (less involvement): I-R-E Initiation-Response-Evaluation (I-R-E) Ask a known-answer question Evaluate a student response as right or wrong Minimize student interaction through prescribed “turn taking” Establish the authority of the text and teacher Examples What is the answer to #5? What are you supposed to do next? What is the reciprocal of 3/5? 5/3. Very good! That is exactly what the book says.

Discourse Strategies (less involvement): Procedures Give directions Implement procedures Tell students how to think and act Examples Listen to what I say and write it down. Take out your books and turn to page 45.

Discourse Strategies (less involvement): Extrinsic Support Superficial statements of praise (focus is not on the learning goals and objectives) Threats to gain compliance Examples You have such neat handwriting. These scores are terrible. I was really shocked. If you don’t finish up you will stay after class.

Discourse Strategies (more involvement): Intrinsic Support View challenge/risk taking as desirable Respond to errors constructively Comment on students’ progress toward the learning goals and objectives Evoke students’ curiosity and interest Examples That's great! Do you see what she did for #5? This may seem difficult, but if you stay with it you'll figure it out. Good. You figured out the y-intercept. How might we determine the slope here?

Discourse Strategies (more involvement): Negotiation Adjust instruction in response to students Model strategies students might use Guide students to deeper understanding Examples What information is needed to solve this problem? Try to break the problem into smaller parts. Here is an example of how I might approach a similar problem.

Discourse Strategies (more involvement): Transfer Responsibility Support development of strategic thinking Encourage autonomous learning Hold students accountable for understanding Examples Explain the strategy you used to get that answer. You need to have a rule to justify your statement. Why does Norma’s method work?

Reflecting on Instructional Practices: Creating a Self-Inventory Rubric How you can strengthen the ways student involvement and motivation are promoted and supported in your classes? Write 3-5 statements about specific strategies you’d like to work to improve this year. Draw ideas from On Common Ground, TARGET TiPS, motivation data, and Motivation in the Classroom presentation Examples: “I give students tasks that require them to think about mathematical relationships and concepts.” “I provide feedback to students that promotes further thinking and improved understanding.” “I allow opportunities for students to be an authority in mathematics.” Identify where you are now and where you want to be.