Monday, July 27, 2009

Math problems of the week: 1930's Algebra vs. Interactive Math Project

From two of the most related problem sets on graphing:

1. From a problem set entitled "The End of a Function," from a subsection entitled "Going to the Limit," from a chapter entitled "The World of Functions," in Interactive Mathematics Program Integrated High School Mathematics, Year 4, p. 289

1. Look at examples of polynomials of different degrees. In each case, try to figure out what happens to the y-value as x increases in absolute value. (The result may depend on whether x is positive or negative.)

A graphing calculator can help you to some extent, but the graph that a calculator shows can only give you part of the picture. Thus, you should come up with algebraic or numerical explanations for your conclusions about the end behavior of your examples.

2. Next, look at functions from other families: exponential functions functions from the sine family, rational functions, and any other families you want to consider. Again, take notes on your results and any general conjectures that you make.

2. From the problem set entitled "Exercise 70A," from a subset entitled "The solution of Quadratic Equations by Means of Graphs," from a chapter entitled "Quadratic Equations; Radical Equation," in A Second Course in Algebra (first published in 1937), p. 253.

Solve the following equations graphically and find the values of x which determine maximum and minimum points on the curve.

1. x3 + 3x2 - 15 = 0
2. x3 - 7x2 + 16x -8 = 0
3. x3 - 12x -12 = 0
4. x3 + x2 - 1 = 0

3. Extra Credit

Compare the grades that the underachieving math buff is likely to receive on each assignment.

1 comment:

Beth said...

"Look at examples of polynomials of various degrees?" How vague is that?

Once you've got a school, with a class and a teacher and a grading system, it's just unreasonable to give these vague assignments. It's like saying, "go do something mathematical! Quiz at the end of the week!" I'd be totally confused if I were in this class.

It's like they've borrowed the form of progressive education (which I'm actually looking for) but taken it completely out of context. The result is just mush. It's an abdication of the teacher's job.