## Friday, December 9, 2011

### Math problems of the week: final algebra problems from the 1900s vs. the 21st century

I. The final problem in Wentworth's New School Algebra, published in 1898:

Find by a graph the number of real roots of:
x8 - 8 = 0
x3 - 5x2 + 8x + 14 = 0

II. The final problem in The University of Chicago Math Progject Algebra, published in 2002:

Use the table to plot the graph of the polynomial function
P(x) = 2x3 - x2- 6x

Why can you be sure that all the x-intercepts are listed in the table?

x__|__Value
-3_ |_-45__
-2_ |__-8__
-1.5 |__ 0_
-1_ |___3_
_-.5 |__2.5
_0_ |__0__
_.5_ |__-3_
_1_ |__-5_
_1.5|__-4.5
_2_ |__0_
_3_ |__27_

III. Extra Credit
Chicago Math students regularly use graphing calculators; 1900's math students didn't. So why do Chicago Math students get to rely on a table for their final algebra problem?

Mnemosyne's Notebook said...

As an algebra teacher, I can tell you that textbooks (and teachers) go with this approach because students cannot calculate the values of the polynomials even with calculators. Some of my fellow teachers say, "Oh, they'll always have calculators with them on their cell phones." My thinking is, "Oh, they'll always have their brains with them - so let's stuff that with some math." One of my state's GLOs is that students should be informed and ethical users of technology. Nothing about helping them have the ability to create any technology.

The assessments for our students allow the use of calculators - another excuse for the silicon crutches.

Mnemosyne's Notebook said...

And only a freak might consider the possibility that some nasty solar flairs could leave us with severely diminished electronics capabilities for several years. Why would we want to prepare for that? Somewhere, someone else will make calculators for our kids if that ever happens. Why prepare them for a world that might not be exponentially snazzier than today?

bky said...

A note about tables. I have a jr son who is taking what purports to be a high-school level algebra course (he can get 1 year of credit for alg I when he gets to high school). It is trivial junk. One thing that is weird is how often they are given a table of (x, y) values and have to figure out, over and over again, whether the points fall on a line or a hyperbola. In the meantime they don't do much of anything that I consider algebra. I think algebra is about manipulating formulas and doing calculations to solve problems. For them it's tables and graphs, tables and graphs, tables and graphs,....

Their curriculum is an unholy alliance of Connected Math and a giant book published by Holt. The Connected Math is full of what I call fake word problems. There will be wordiness establishing some (irrelevant) context and then they graph some "data" points that will fall on a line, or a y = kx curve for positive x. Bleh.

bky said...

I mean y = k/x curve. Over and over.