Monday, August 10, 2009

Math problems of the week: 1900's algebra vs. Interactive Math Program

1. The last four problems of the Quadratic Equations chapter of New School Algebra (published in 1898), p. 292:

23. A boat's crew row 4 miles down a river and back again in 1 hour and 30 minutes. Their rate in still water is 2 miles an hour faster than twice the rate of the current. Find the rate of the crew and the rate of the current.

24. A number is formed by two digits. The units' digit is 2 more than the square of half the tens' digit, and if 18 is added to the number, the order of the digits will be reversed. Find the number.

25. A circular grass plot is surrounded by a path of a uniform width of 3 feet. The area of the path is 7/9 the area of the plot. Find the radius of the plot.

26. If a carriage wheel 11 feet round to 1/4 of a second less to revolve, the rate of the carriage would be five miles more per hour. At what rate is the carriage traveling?

2. The last homework assignment in the World of Functions chapter of Interactive Mathematics Program, Integrated High School Mathematics, Year 4 (published in 2000), p. 344-345:

Now that The World of Functions is completed, it is time to put together your portfolio for the unit. Compiling this portfolio has three parts.
*Writing a cover letter summarizing the unit
*Choosing papers to include from your work in this unit
*Discussing your personal mathematical growth in the unit.

Cover Letter for The World of Functions:

For your cover letter for The World of Functions, focus on these two key ideas.
*The distinguishing characteristics of each of the family of functions you worked with, considered in terms of real-world situations graphs, tables, and symbolic representations.
*Methods of combining functions or transforming functions to create new ones.

For each of the important aspects of the unit, choose an activity that illustrates that idea to include in your portfolio.

Selecting Papers from The World of Functions:
Your portfolio from The World of Functions should contain these items.

*Brake!, "Brake!" Revisited, and Better Breaking
Include a statement of how your understanding of the "braking" situation developed over the course of the unit.

*Linear Tables, Quadratic Tables, and Exponential Tables
Discuss how your understanding of the relationship between tables and algebraic representations grew through these three activities.

*Activities discussed in your cover letter

*Homework 29: Beginning Portfolio Selection
Include the activities from the unit that you selected in Homework 29: Beginning Portfolio Selection along with your written work about those activities

*A Problem of the Week
Select one of the three POWs you completed during this unit (One Mile at a Time, A Spin on Transitivity, or It's Off to College We Go).

Personal Growth
Your cover letter for The World of Functions describes how the unit develops. As part of your portfolio, write about your own personal development during this unit. You may want to specifically address this issue.

How do you feel you have developed during this unit in terms of your ability to explore problems and prove conjectures in mathematics?
You should include here any other thoughts you might like to share with a reader of your portfolio.

3. OILF's Extra Credit

Write a letter discussing our country's personal growth in algebra teaching and learning over the past 100 years.


Barry Garelick said...

Thank you for posting these examples. You may have already seen this, but if not, here are links to an article I wrote on traditional math. The beginning of the article features a quote from Sherry Fraser, one of the principals of IMP, which you may find interesting. I plan to do an update of this article.

Part 1

Part 2

Part 3

Katharine Beals said...

Thanks, Barry! Great article. I found the historical perspective quite interesting--esp the ascendancy of the NAEP over the Iowa tests. Would love to read more. Have you written anything on the political perspective--i.e., the branding of Reform Math critics as conservative/reactionary? (Another interest of mine).