I thought this book would be light reading, and hopefully I would come across some interesting word problems and clever ways to approach them that I could use in my own classes. Indeed the book is full of a large variety of word problems, over hundred of them are solved in detail, and several of them are quite fun for someone who enjoys a little math with her warm drink of choice. Nonetheless, I confess that when I put the book down, it left an unpleasant aftertaste.
The book is well-organized, (mostly) well-written and doubtlessly intended for an audience that does not include me. So my reaction to it will certainly not be the reaction of the student who picks this book up with the hope to find shortcuts and simple algorithms to attack the diverse word problems that he has to face and solve using algebra. For the student who is looking for the shortcuts and the clear-cut simplistic explanations, the book might be just appropriate and it may even be helpful.
The few Amazon reviews so far have been quite positive, and are indeed truthful: the book is quite successful at providing a structure to the seemingly chaotic zoo of word problems, by classifying them into several categories depending on their main context. Thus a student who has difficulty with problems involving liquid solutions can immediately find where to go, while the students who only care about work problems (those problems that involve a task that can be done by different people at different rates) do not have to wade through much before they find their way to the relevant section. And the book is quite exhaustive; going over standard high school textbooks, I cannot easily come up with a word problem that will not fit into one of these categories.
However the idealist in me cringed a bit every time I turned the page to start a new chapter that addressed a new collection of problems. What troubled me is what the publisher of this book promotes as its main strength: All the problems are nicely classified into these well-defined packages. By dividing and conquering in this manner, the book helps the student to attack a problem by first identifying its type and then using the appropriate tools provided for that type. But in this way the book also allows the student to lose track of the whole, the underlying goal of word problems: to develop the student’s ability to extract the information that is given that can be represented best by a mathematical equation or two and actually come up with that representation. A student who reads the book from beginning to the end and who actually thinks along the way may in fact comprehend this beautiful and powerful fact, but my hunch is that that rare student would benefit from just about any other book containing a large collection of word problems. By creating this unnatural classification of the word problems it handles, the book does a disservice to the whole genre. Divide and conquer, sure, but don’t take out its soul along the way.
This is most likely not the author’s fault. In fact at each juncture you hear her voice, you get the sense that you are conversing with a caring, compassionate and competent teacher who is on your side, who wants you to succeed, who goes out of her way to simplify things for you as much as possible.
“Make things as simple as possible, but no simpler,” said Einstein; the author does not always follow him on that latter part. For instance in the part on percentages the reader is told explicitly that “You can’t change a fraction to a percent directly. First change a fraction into a decimal and then change the decimal into a percent” (p. 90). Thus the student loses the opportunity to see that problems may be attacked in multiple ways, that there are several different representations of the same ratio, and much more urgently that you can indeed convert certain fractions directly into a percent easily — especially if the denominator is a divisor of 100, this is in fact quite simple.
Dividing up word problems into neat little categories is counterproductive if the end goal is not only that the student pass an exam but also that he gain some understanding of the way numerical data can be embedded in written language and some experience working out the translation between the text and the mathematical representation. I say a lot more on this issue, tying word problems to the more general and urgent issue of quantitative literacy, in a paper of mine, so I will now step down from that soapbox.
All in all, the gist of this review is that the book was slightly disappointing. I think I will go and see if I can find the author’s other book, Math with Mom; I have a feeling I will like that one…
Karaali, Gizem. 2008. Word Problems: Reflections on Embedding Quantitative Literacy in a Calculus Course. Numeracy, 1 (2): Article 6. DOI: 10.5038/1936-4622.214.171.124 http://services.bepress.com/numeracy/vol1/iss2/art6
Gizem Karaali is assistant professor of mathematics at Pomona College.