Developing the TechMath Instructional Module

1. Developing the TechMath Instructional Module

2. “Imagine a classroom, … NCTM, 2000. PSSM, p.3.

3. where all students have access to high-quality, engaging …instruction.”

4. “[where] there are ambitious expectations for all, with accommodation for those who need it.”NCTM, 2000. PSSM, p.3.

5. “…[where students] learn important mathematic[s] with understanding.”NCTM, 2000. PSSM, p.3.

6. “Technology is an essential component of the environment.” NCTM, 2000. PSSM, p.3.

7. “Students confidently engage in complex mathematical tasks…” NCTM, 2000. PSSM, p.3.

8. “…[and] draw on knowledge from a …variety of mathematical topics,

9. [and] approach… the same problem… in different ways…” NCTM, 2000. PSSM, p.3.

10. “…students make, refine, and explore conjectures …

11. and use a variety of reasoning and proof …to confirm or disprove [their]… conjectures.” NCTM, 2000. PSSM, p.3.

12. NCTM, 2000. PSSM, p.3. “Students are flexible and resourceful problem solvers.”

13. “Alone or in groups and with access to technology, NCTM, 2000. PSSM, p.3.

14. [students] work productively and reflectively,

15. with the skilled guidance of their teachers.”

16. “Orally and in writing, students communicate their ideas and results effectively.”NCTM, 2000. PSSM, p.3.

17. “Students value mathematics and engage actively in learning it.” NCTM, 2000. PSSM, p.3.

18. Imagine.

19. Imagine your TechMath module as the curriculum for the classroom in our vision.

20. Central to the module and the key to module development is the essential question.

21. The essential question--- A problem…

22. …a “puzzlement.” Something that is not obvious, not clear, that is challenging, engaging, something that the student wants to know.

23. But is the problem instructionally rich?

24. Does it engage students in important mathematics? enable students to make connections? promote communication? support different entry levels & different approaches?

25. Example of NCTM “Instructionally Rich Task” is generalizing a geometric pattern.

26. How do we pose the problem? Tell a story of the business; show a video; project pictures; share some quotes from your business partner. Engage the students. Pose the question. Use Polya’s advice—don’t say too much.

27. Developing Instruction • Use Polya’s stages or • 5E Lesson Structure or • a curriculum approach of posing the question, exploring some mathematics, and then returning to the question.

28. Don’t forget closure. How can we ensure our students’ reflections—their “looking back,” making sense of new knowledge? Ask students to write a business report, create and share similar problems, construct a concept map…

29. If mini-unit Daily Lesson Plans Assessment of Student Learning If student project Teacher Notes Task Description Sample Solutions Rubric for Evaluation TechMath ModuleI. Title PageII. Overview/prefaceIII. Table of Contents

30. Lesson Plans Write your lesson plans for novice teachers. Title your lesson plans. Write clear statements of learning objectives. Include a list of materials needed. Include all directions. Include questions to be posed. Include solutions. Attach all black-line masters.

31. Where are we going? June 18, 2009: a complete module draft that you submit to Kathleen. June 26, 2009: a complete module, version 1 Fall 2009: Pilot Module in Your Classroom [notify Kathleen and Bethany of times and dates], Reflect, & Revise Module, version 2 Spring 2010: Share your module with another teacher, who teaches the module and provides you with an assessment [using a rubric]. Revise your module, complete the module overview and submit to Bethany, version 3.