A Man Left Albuquerque is not a book about word problems, at least not in the traditional sense. Instead of writing a book about the importance of word problems, how to write real-world word problems, or how to teach solution techniques, Susan Gerofsky has written a study of word problems that analyzes their structure as a linguistic genre. Her stated goal is to answer the question, “What are word problems?”
Gerofsky identifies several areas in which word problems are linguistically different from other established genres. For example, students learn that the story portion in a word problem is, in many cases, irrelevant, and is used merely to frame the problem. People, places and objects in a word problem could easily be changed to other people, places and objects without changing the underlying mathematical concept addressed in the problem. In fact, an entire word problem could be replaced by a single sentence of the form “If <these conditions> exist, find <this answer>”. Similarly changing other types of writing could have disastrous effects. Interviews and reports from other studies provide a connection to Gerofsky’s genre analysis when both instructors and students were asked to create a real-world word problem: people from both groups created word problems that were not substantially different in form from those in textbooks. Just like students studying literary genres in literature classes, these people were able to identify the “word problem form” and write a problem in that style.
Unfortunately for the author, it was the non-linguistic aspects of the book that I found most interesting. In fact, the more I read, the less attention I paid to the linguistic analysis and the more I concentrated on the responses of the interviewees and the discussion that followed.
Throughout the book, Gerofsky provides a nice history of the word problem, from antiquity to the present day, including both the intellectual and social aspects of problem solving found in other cultures. Prior to the existence of algebraic notation, mathematical problems, riddles and puzzles were posed in word problem format in order to set up a certain type of problem to be solved. In a similar manner, some of the instructors reported that they began with a mathematical computation in mind, and then looked for a real-world situation that could be used to clothe it. In spite of their efforts, the instructors expressed concern that the very nature of a word problem (having a well-defined problem, requiring only already-learned skills, and having only one correct answer) guarantees that it is not real-world at all. The necessity of completing the material that appears on the ubiquitous standardized tests further pressured the instructors to abandon the open-ended explorations that typify solving a true real-world problem.
The older students who were interviewed stated that they were able to jettison the trappings of the story and jump right to the problem. They did, however, report that the story might grab their attention in ways that a bare problem may not. Savvy students were able to see the underlying problem (for example, quadratic functions) and its connection to the story (trajectory of a model rocket) but, at the same time, understand that this was a calculation they were unlikely to perform in real life. Unfortunately, the students were not asked how they felt about the mathematically-based problems they faced in their science classes: it is possible that a similar trajectory problem in a physics class would be seen as relevant.
I was not surprised by anything I read in this book and found the technical material about genres difficult to read. The groups that were interviewed as part of the study were disturbingly small from a statistical point of view, but their responses were interesting nonetheless. I was, however, entertained by the history and the wealth of word problems from both new and old sources, and found myself with pencil in hand on more than one occasion. I also agreed with a stated conclusion that using pleasant or amusing imagery may be effective in capturing students’ attention: not every problem need to be of the real-world variety to be useful.
Recommending this book would be difficult as linguists may be put off by the mathematics and mathematicians by the linguistics. Parts of the book were interesting to read but it would not be useful to anyone looking for strategies to either write or teach solution techniques for word problems. While it truly is a book about word problems, it is not a book “about word problems” in any of the usual interpretations of that phrase.
Susan Slattery teaches at Villa Julie College in Stevenson, MD.