Overview Mini-problem Analyzing teacher questions Observing student thinking Wrap up

A student solved the problem 92 - 37 in the following way: I know that 92 – 40 = 52. Since 37 is 3 less than 40, I need to take 3 away from 52. So the answer is 49. Analyze the student’s method, and explain why it gives the incorrect answer. Why might a student think this method would work? How could you modify this method to make it work? (That is, how can you start with 92-40=52, and arrive at the correct answer?) What are some other erroneous subtraction methods that students might come up with?

Purposes for Teacher Questions Initial eliciting of students’ thinking Probing students’ answers Trying to figure out what a student means or is thinking when you don’t understand what they are saying Checking whether right answers are supported by correct understanding Probing wrong answers to understand student thinking Focusing students to listen and respond to others’ ideas Supporting students to make connections (e.g., between a model and a mathematical idea or a specific notation) Guiding students to reason mathematically (e.g., make conjectures, state definitions, generalize, prove) Extending students’ current thinking, and assessing how far they can be stretched

Developing Question Shells Work in groups to develop “question shells” for each purpose. Examples: Initial eliciting of student thinking (Purpose #1 ): What did you come up with? What have you found so far? Focusing students to listen and respond to other’s ideas (Purpose #3) What do people think about what Patty said? How does that relate to what Derek said? Record your ideas on a separate piece of paper. We will collect these and then compile them into one document to develop a beginning repertoire of questions.

Observing Student Thinking Solve the problems. What is the same and different about these problems? How do you think young children might solve them?

Observing Students’ Strategies Watch the student solve the problem. Make a record of the student’s approach. What next question would you ask the student to probe his or her thinking?

Why we are working on this… Increase awareness that there are different types of word problems and that the structure of a problem can influence how students solve it Recognize the variety of strategies that students can use to solve problems Develop skills at observing and interpreting students’ thinking Develop skills for asking questions to probe students’ thinking

Wrap Up Assignments: Read through mini-problem description. Work with CT to choose problem. Send us an email with your problem by Wednesday, Sept. 28, at 8pm. Reading and related tasks Please leave notebook --- pick up tomorrow outside of Suite 2400 Comment cards