1. Teacher Quality Workshops for Fall 2010 & Spring 2011

2. Year-long Objectives Improve our capacity to teach in a manner that fosters conceptual understanding and mathematical thinking Strengthen our mathematical knowledge and pedagogical content knowledge Improve student achievement (TAKS, STARR)

3. To Achieve Those Objectives Attend workshops with an active mind Complete 2 “lesson study” projects each semester  Identify a topic and its related important key ideas  Discuss and formulate learning goals (e.g. address common misconceptions)  Plan a classroom lesson (search for good ideas/problems)  Teach/observe the lesson  Collect and analyze student work  Reflect and write-up

4. To Achieve Those Objectives Attend workshops with an active mind Complete 2 “lesson study” projects each semester Use http://thinkmaththink.wikispaces.com to share documents (lesson plan, student work, write-up)http://thinkmaththink.wikispaces.com Be prepared for each workshop Connect workshop ideas to your classroom practices Partner with a fellow teacher and try to observe each other’s implementation of the designed lessons

5. Workshop Structure (in general) 4:30 – 5:00pmDinner 5:00 – 5:15pm ThinkMathThink Comments Establish Objectives 5:15– 6:25pmActivity 1 6:25 – 6:35pmBreak 6:30 – 7:45pm Activity 2 7:45 – 8:00pmRecapitulate Main Points Preparations for the Next Workshop

6. Workshop #1 (Aug 19) 6:30 – 7:00pmActivity 1: Teaching for Conceptual Understanding & Mathematical Thinking 7:00 – 7:30pm Activity 2: Group work on “Lesson Study” Project 7:30 – 7:50pmPresentation of Topics & Goals 7:50 – 8:00pmPreparations for the Next Workshop

7. Fostering Conceptual Understanding and Mathematical Thinking

8. Why is Understanding Mathematics so Important? One’s knowledge are interconnected and one can reconstruct them when needed. One can flexibly apply those ideas to new situations. One can flexibly apply those ideas to new situations. One feels great! One feels great!

9. How Can Classrooms be Designed to Promote Understanding?

10. Why Use a Problem-based Approach? Students must experience the intellectual need for the concept to be learned “For students to learn what we intend to teach them, they must have a need for it, where by ‘need’ is meant intellectual need, not social or economic need.” (Harel, 2007)

11. Why Use a Problem-based Approach? “The process of knowing is developmental in the sense that it proceeds through a continual tension between accommodation and assimilation.” (Harel, 2007, p. 265) Students must experience the intellectual need for the concept to be learned Understanding involves grappling and resolving the inconsistency between one’s existing conception and a problem situation

12. Why Use a Problem-based Approach? Students must experience the intellectual need for the concept to be learned Understanding involves grappling and resolving the inconsistency between one’s existing conception and a problem situation Problems are the means to experience the limitation of their existing knowledge and the need for a new piece of knowledge

13. How Can Classrooms be Designed to Promote Understanding? 1.Allowing mathematics to be problematic for students Pose challenging problems within students reach Challenge students to use what they know for a simpler problem (e.g. ¾ + ½) to solve a more complex problem (e.g. 5¾ + 1½) “Refrain from stepping in and doing too much of the mathematical work too quickly” (Hiebert & Wearne, 2003)

14. How Can Classrooms be Designed to Promote Understanding? 1.Allowing mathematics to be problematic for students (Hiebert & Wearne, 2003) In comparing 8 th grade lessons in the TIMSS study among U.S., Germany, and Japan, “U.S. teachers almost always stepped in to show students how to solve the problems; the mathematics they left for students to think about and do was rather trivial. Teachers in the other two countries allowed students more opportunities to wrestle with the challenging aspects of the problems.” (p. 6-7)

15. How Can Classrooms be Designed to Promote Understanding? 1.Allowing mathematics to be problematic for students (Hiebert & Wearne, 2003) 2.Examining increasingly better solution methods Allow students to use their own methods but commit them to search for better ones (more efficient, flexible, understandable) Provide opportunities for students to share their methods, to hear others’ methods, and to examine the strengths and weaknesses of various methods “Examining methods encourage students to construct mathematical relationships, and constructing relationships is at the heart of understanding” (p. 9)

16. How Can Classrooms be Designed to Promote Understanding? 1.Allowing mathematics to be problematic for students (Hiebert & Wearne, 2003) 2.Examining increasingly better solution methods What information to be shared? Conventions such as order of operations, exponents, function notation Key ideas embedded in students’ solution methods Alternative solutions not presented by students When to share information? When students see the need 3.Providing appropriate information at the right time

17. How Can Classrooms be Designed to Promote Understanding? 1.Allowing mathematics to be problematic for students (Hiebert & Wearne, 2003) 2.Examining increasingly better solution methods Hiebert, J., & Wearne, D. (2003). Developing understanding through problem solving. In H. L. Schoen (Ed.), Teaching mathematics through problem solving: Grade 6-12 (pp. 3-13). Reston, VA: National Council of Teachers of Mathematics. 3.Providing appropriate information at the right time

19. “Lesson Study” Project

20. Why “Lesson Study” Project? Apply what you have learned from the last three series of workshops into your own classrooms  Quantitative reasoning (e.g., ratios & proportions)  Algebraic reasoning (e.g., change & graphs)  Measurement (e.g., formulas for pyramids & cylinders)  Issues on teaching & learning via analysis of video cases and student work (e.g., questioning techniques, common misconceptions)

21. Why “Lesson Study” Project? Apply what you have learned from the last three series of workshops into your own classrooms Improve our teaching Experience the process of designing, planning, and teaching lessons Build a professional learning community

22. What does a “Lesson Study” Project entail? Step 1: Identify a topic and its related key ideas Topics that you said you like to conduct classroom research Measurement (6) Proportions (5) Probability: Dependent Events (5) Formulas for Areas and Volumes (5) Fractions & Percents (4) Scale Factors (3) Equation Solving (2)

23. What does a “Lesson Study” Project entail? Step 2: Formula learning goals Step 3:Design activities and plan a classroom lesson Present your lesson and get inputs from the other groups Step 1: Identify a topic and its related key ideas Try out your activities during a workshop session

24. What does a “Lesson Study” Project entail? Step 4:Implement/observe the lesson Collect student work Step 5:Analyze student work Step 6: Reflect and report the results (relate to goals) Refine the lesson for future use Write up a brief report Step 1: Identify a topic and its related key ideas Step 2: Formula learning goals Step 3:Design activities and plan a classroom lesson

25. Tentative Schedule 1.Aug 19 S1, S2S1, S2 2.Sep 16 S3S2, S3 3.Sep 30 S5, S6S3 4.Oct 14S1, S2S5, S6 5.Nov 4S3S1, S2 6.Nov 18S5, S6S3 7.Dec 2S5, S6 Groups A & B Groups C & D Project 1Project 2Project 1Project 2 Teach & Observe Lesson #1 Teach & Observe Lesson #2

26. Activities Get into Groups (based on grade level) Select a Topic that you will teach  Consider topics that students have difficulty understanding  Consider topics that you find it challenging to engage your students to think actively  Consider topics that you are excited to try new ideas Identify the Key Ideas  Think about TEKS and TAKS  Think about students’ common misconceptions Discuss and Formulate Learning Goals  Think about mathematical habits of mind you want to foster  Find out what it takes for students to develop the conceptual understanding

27. Step 1: Identify Topic Step 2: Discuss Learning Goals

28. Preparation for Workshop 2 (Sep 16) Read the article on “Developing Understanding through Problem Solving” Hiebert, J., & Wearne, D. (2003). Developing understanding through problem solving. In H. L. Schoen (Ed.), Teaching mathematics through problem solving: Grade 6-12 (pp. 3-13). Reston, VA: National Council of Teachers of Mathematics.

29. Preparation for Workshop 2 (Sep 16) Read the article on “Developing Understanding through Problem Solving” Search for activities/problems for your topic that are likely to help you achieve your agreed learning objectives Think about the lesson for your topic (2 groups will present your lesson in the next workshop) Share resources/notes/reflections and post your questions/comments/ideas at http://thinkmaththink.wikispaces.com/ (Note: there is a discussion tab for each page/group) http://thinkmaththink.wikispaces.com/