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

## Chapter: Appendix C: Homework Problems

« Previous: Appendix B: Workshop Agenda
Page 169
Suggested Citation:"Appendix C: Homework Problems." National Research Council. 2001. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10050.
×

## 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
Suggested Citation:"Appendix C: Homework Problems." National Research Council. 2001. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/10050.
×
Next: Appendix D: Workshop Participant List »
Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop Get This Book
×

There are many questions about the mathematical preparation teachers need. Recent recommendations from a variety of sources state that reforming teacher preparation in postsecondary institutions is central in providing quality mathematics education to all students. The Mathematics Teacher Preparation Content Workshop examined this problem by considering two central questions:

• What is the mathematical knowledge teachers need to know in order to teach well?
• How can teachers develop the mathematical knowledge they need to teach well?

The Workshop activities focused on using actual acts of teaching such as examining student work, designing tasks, or posing questions, as a medium for teacher learning. The Workshop proceedings, Knowing and Learning Mathematics for Teaching, is a collection of the papers presented, the activities, and plenary sessions that took place.

1. ×

## Welcome to OpenBook!

You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

Do you want to take a quick tour of the OpenBook's features?

No Thanks Take a Tour »
2. ×

« Back Next »
3. ×

...or use these buttons to go back to the previous chapter or skip to the next one.

« Back Next »
4. ×

Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

« Back Next »
5. ×

Switch between the Original Pages, where you can read the report as it appeared in print, and Text Pages for the web version, where you can highlight and search the text.

« Back Next »
6. ×

To search the entire text of this book, type in your search term here and press Enter.

« Back Next »
7. ×

Share a link to this book page on your preferred social network or via email.

« Back Next »
8. ×

View our suggested citation for this chapter.

« Back Next »
9. ×