Strategies to Promote Motivation in the Mathematics Classroom

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

2. 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?

3. 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.

4. 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

5. 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.

6. 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.

7. Characteristics ofHigher-Level Mathematical Tasks

8. 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.

9. 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.

10. 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.

11. Discourse Strategies (less involvement): Procedures • 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.

12. Discourse Strategies (less involvement): Extrinsic Support • 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.

13. Discourse Strategies (more involvement): Intrinsic Support • 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?

14. Discourse Strategies (more involvement): Negotiation • 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.

15. Discourse Strategies (more involvement): Transfer Responsibility • 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?

16. 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.