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## Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop (2001) Center for Education (CFE)

### Citation Manager

. "Appendix C: Homework Problems." Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press, 2001.

 Page 169

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Knowing and Learning Mathematics for Teaching

## Appendix C: Homework Problems

The following “homework” problems were assigned at the end of the first evening and at the end of the next full day. Note that the problems are slightly different: The first is a task of teaching, the second a task of teacher preparation.

Day 1 Homework

A Task of Teaching: Preparing to Teach a Mathematics Problem

Several digits “8” are written, and some “+” signs are inserted to get the sum 1000. Figure out how it is done.

TASK: Prepare to teach this problem to a class. Do whatever you think you need to do to be ready to teach it to a specific class you have in mind.

Stand back and reflect: What mathematics did you use to do this task of preparing to teach? What sorts of mathematical understanding and sense did you draw on? How did you use what you did?

Day 2 Homework

A Task in Teacher Preparation: Comparing Two Versions of a Mathematics Problem

1. Several digits “8” are written, and some “+” signs are inserted to get the sum 1000. Figure out how it is done.

2. Write down as many 8's and + signs as you want in a row so that you write a statement that equals 1000. Find all the possible solutions to this problem.

TASK: A teacher took the original 8's problem and revised it for her class. How does problem B compare with the version in A?

Stand back and reflect: What opportunities for learning mathematics could be drawn from teachers' engagement with this task?

#### REFERENCE

Gelfand, I. M., & Shen, A ( 1993). Algebra. Boston, MA: Birkhäuser.

 Page 169
 Front Matter (R1-R16) Introduction (1-2) Workshop Overview: Knowing and Learning Mathematics for Teaching (3-7) Pre-Workshop Tasks (8-10) Teachers' Understanding of Fundamental Mathematics (11-22) Reconsidering the Mathematics That Teachers Need to Know (23-24) Investigating Teaching Practice: Setting the Stage (25-38) Investigating Teaching Practice: What Mathematical Knowledge, Skills, and Sensibilities Does It Take? (39-64) What Kinds of Mathematical Knowledge Matter in Teaching? (65-74) How Can Teachers Develop Such Mathematical Knowledge? (75-76) Investigating Alternative Approaches to Helping Teachers Learn Mathematics (77-104) Promising Approaches for Helping Prospective Elementary Teachers Learn Mathematics for Teaching (105-126) Concluding Remarks (127-128) Discussion Group Reports (129-130) Question #1 (131-136) Question #2 (137-143) Question #3 (144-148) Question #4 (149-154) Question #5 (155-162) Appendix A: Pre-Workshop Reading (163-165) Appendix B: Workshop Agenda (166-168) Appendix C: Homework Problems (169-169) Appendix D: Workshop Participant List (170-173) Appendix E: Transcript of Ball Videos (174-182) Appendix F: Explanation of the Unit on Weight (183-192) Appendix G: Excerpts from Investigations (193-200) Appendix H: Mathematics Case Methods Project (201-209) Appendix I: Biographical Information (210-217)

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Knowing and Learning Mathematics for Teaching Appendix C: Homework Problems The following “homework” problems were assigned at the end of the first evening and at the end of the next full day. Note that the problems are slightly different: The first is a task of teaching, the second a task of teacher preparation. Day 1 Homework A Task of Teaching: Preparing to Teach a Mathematics Problem Several digits “8” are written, and some “+” signs are inserted to get the sum 1000. Figure out how it is done. TASK: Prepare to teach this problem to a class. Do whatever you think you need to do to be ready to teach it to a specific class you have in mind. Stand back and reflect: What mathematics did you use to do this task of preparing to teach? What sorts of mathematical understanding and sense did you draw on? How did you use what you did? Day 2 Homework A Task in Teacher Preparation: Comparing Two Versions of a Mathematics Problem Several digits “8” are written, and some “+” signs are inserted to get the sum 1000. Figure out how it is done. Write down as many 8's and + signs as you want in a row so that you write a statement that equals 1000. Find all the possible solutions to this problem. TASK: A teacher took the original 8's problem and revised it for her class. How does problem B compare with the version in A? Stand back and reflect: What opportunities for learning mathematics could be drawn from teachers' engagement with this task? REFERENCE Gelfand, I. M., & Shen, A ( 1993). Algebra. Boston, MA: Birkhäuser.

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teaching stand