Thursday, January 21, 2010

Math problems of the week: final high school math problems

1. The final problem in Interactive Mathematics Program: Integrated High School Mathematics, Year 4, p. 454:

It's the News

The central problem of this unit concerns election polls. Polls are used in many situations to get information about what people think and do. Such polls appear in newspapers regularly, although reports on the polls sometimes don't give as much information as they should.

Your first task in this activity is to find a newspaper or magazine article that reports on a poll.

Then summarize what the report says and discuss any shortcomings or weaknesses you see in the report. In particular, comment on any information that you think should have been included that would have helped you understand better what conclusions you could draw from the poll.

2. The final problem in Mallory's A Second Course in Algebra (first published in 1937), p. 477:

Find the area under the curve y = x2 - 8x + 12:
a. From x = 0 to x = 2; b. from x = 2 to x = 6.

3. Extra Credit:

A Second Course in Algebra entirely omits statistics (e.g., election polls); the Interactive Mathematics Program entirely omits calculus (e.g., area under the curve). Discuss the ideal ratio of statistics to calculus in high school mathematics.

Cheryl said...

Actually, both types of problems are being taught in our high schools today. (In fact, more calculus and college-level math, such as linear algebra, is being taught in high schools today than has been taught in the American public schools ever before.) It would be more fair to compare that final stats problem in IMP to the final problem given to a student from the 1930s who wasn't on the "calculus track". I'd be happy to be proven wrong, but I'd guess that the IMP problem better serves the population of students who does not continue with math courses than whatever used to be taught.

Katharine Beals said...

Unfortunately, though, students who only use the four year IMP aren't getting calculus. I'm concerned that readiness for high school calculus a la Dolciani is declining with the rise of Reform Math, and being replaced by what some mathematicians call "cookbook calculus" (and cookbook linear algebra?): calculus without the proofs and the deep understanding of limits, etc.

Anonymous said...

Wrt to the ideal ratio of statistics to calculus in high school math:

I wish ALL students (with rare exceptions - obviously the kids who can't add would be better off learning addition) would get what is considered a one semester college course in statistics (for non-STEM majors) in middle school (really, it's not too hard for middle school if you spread it out over a year instead of a semester). But, high school would be fine too. Calculus... more optional. As long as kids have a thorough preparation in algebra, trig, and geometry, they can take calculus in college and still be fine, even if they're majoring in engineering.

But ALL kids will be allowed to vote once they turn 18 and do other important stuff that requires an understanding of statistics, and studies have shown that even the majority of medical doctors have very little understanding of statistics (e.g. how the percentages of false positives and false negatives impact the meaning of diagnostic test outcomes).