## Thursday, February 14, 2013

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

I. From the beginning of the "Special Rules" chapter (Chapter VI) of Wentworth's New School Algebra (published in 1898) [click to enlarge]:

II. The two problem sets within the entire Year 4 Interactive Mathematics Program that come closest to providing practice applying the Distribute Law to algebraic expressions [click to enlarge]:

(Oops, the first two of these can be simplified without applying the Distributive Law. The other two, by the way, among just a handle of problems throughout the entire book that require factoring)

(Oops, these problems, like the majority in the IMP book, don't involve any algebraic manipulation at all; just plugging in numbers.).

III. Extra Credit:

There are no problems in the Year 4 Interactive Mathematics Program that involve demonstration or application of "Special Rules" in polynomial multiplication--Square of Sums, Square of Differences, Product of Sum and Difference. Is application of these "Special Rules" a 21st Century Skill?

#### 1 comment:

Allan Folz said...

Can I say none of the above?

Obviously Interactive Math is a joke, reminds me of one about making a gin martini: waft the opened vermouth bottle over shaker, but I don't consider the late 19th century algebra book is an improvement.

Wentworth's isn't illustrating any underlying concepts. They are giving the student a long, very long, list of rules to be applied depending on the problem trying to be solved. It's like pre-Copernician astronomy. Who can remember all that crap. Who'd want to?

I humbly suggest for binomials you use FOIL -- Firsts, Outers, Inner's, Lasts. One thing to remember and it always works. Once they show facility with it, you can back up to show the underlying principle at work and then take a swing at applying the underlying principle on a trinomial or two, but only to show, yeah this is really hard, in fact, there's a better way (matrices & linear algebra) so let's move on.