Why Johnny will never be able to count

by Alexander Borisovich

(Review of Bob Hogan's and Char Forsten's "8-Step Model Drawing," ISBN: 9781884548956)

One should be either insane, or an American math educator, in order to propose solving 1-3-step word problems by memorizing an 8-step plan first. This is exactly what the authors of this book do (are?)

Recently "Primary Math," the elementary school math program from Singapore, became very popular. It is excellent indeed: concise, efficient, self-explanatory, child-friendly - and perhaps the only one in English that is also correct mathematically. One of its prominent features is pictorial explanation of mathematical ideas. Suppose you are stuck in the problem: "How many boys are in a class of 20, if there are 2 more girls than boys?" In "Primary Math," the idea will be explained by representing the numbers of girls and boys by two parallel horizontal segments, one 2 units longer than the other, so that you could see at once: "Aha! The number of boys is a half of what is left of 20 classmates when the 2 extra girls are subtracted!" By the way, this is how "natural" problem solvers think, beginning with Euclid (although the segments in the "Elements" are shown vertical).

In "8-Step Model Drawing," Bob Hogan and Char Forsten, apparently unaware of the ways problem solvers think but fascinated with their body language, attempt to improve the 23-century old practice (which they call "Singapore strategy"). To solve a problem, kids need to follow the authors' 8-step plan of drawing and labeling diagrams: Read the entire problem - decide who is involved - decide what is involved - draw unit bars of equal length (I really have no clue what they mean by this: The segments needed are neither unit nor equal!) - read each sentence one at a time - put the question mark in place - work computation to the side or underneath - answer the question in a complete sentence. A sample execution of the plan takes 4 (four!) pages, which include your (teacher's or parent's) script, but have little to do with mathematics at hand.

So, in case you are tempted, go buy the book, memorize the steps, recite the script, mimic the body language, and throw this art of problem solving at the kids - your students or children: Help them become as numerate as you are.