Improper use of physics-related context in high school mathematics problems: Implications for learning and teaching

School Science and Mathematics, Mar 2002 by Korsunsky, Boris

This article discusses potential pedagogical difficulties arising from using physics-related contexts in high-school mathematics problems. It is suggested that such problems should not require any external knowledge of physics by the students; meanwhile, the problems should not contradict the physics knowledge that the students may already have. Several examples of recently published textbook problems are presented along with the discussion of the context pitfalls. A simple technique (SCAN list) is proposed for evaluating the physics-related mathematics problems.

The Quest for the Real-life Problems

The quality of the word problems in secondary-- level mathematics textbooks is a common subject among educational researchers and teaching professionals. The tone of the discussion found in literature has often been rather critical:

Textbook story problems have a long history of criticism in the literature... Algebra story problems have earned a well-deserved reputation as a threat to student' achievement in secondary school mathematical courses... [They are] dull, predictable, and routine... (Silverman, Winograd, & Strohauer, 1992, p. 6)

Or as Mayer (1982) said, "[They are] simple story problems.. greeted with moans, fearful faces and incorrect answers..." ( p. 199).

Indeed, a brief look at the "traditional" textbooks, (for instance, Dolciani, Brown, & Cole, 1988; Fair & Bragg, 1990) instantly reveals how abstract most word problems were.

An "abstract" problem does not necessarily have to be a bad one, of course - the mathematicians could bury us in examples. However, research and teaching literature makes a strong case for including the "reallife" word problems as an integral component of the textbook content.

Notably, a proper definition of such problems is hard to come across, but a certain informal consensus appears to arise from the relevant literature. According to that consensus, a real-life problem has at least one of the following features: it is realistic (uses explicitly "real-world" settings); it is amusing to the student; it is relevant to the everyday life of the students. These features will be incorporated in the discussion througout this article. Such problems, it is argued, make the subject of mathematics not only more appealing and inspiring but also more "authentic" (see, for instance, Fairbairn, 1993; Kilman &Richards, 1992; Muth, 1986; Silverman et al., 1992).

It comes as no surprise, then, that the most recent reform movement in mathematics education produced, among other things, quite a few "real-life" mathematics curricula in the last few years - see, for instance, the list of"exemplary" and "promising" math programs on the US Department of Education web site (www.enc.org/ed/exemplary). Moved by the noble desire to improve the pedagogical effectiveness of the problems, the authors, inevitably, went into a largely uncharted territory.

The task of filling a textbook with a few hundred good problems is immense. However, using pedagogically unsound problems can do a lot of harm in the classroom and diminish the intended effect of using the real-life situations. It is important, therefore, to keep pointing out their shortcomings. One of them - the improper use of physics-related situations as the context of the problems - is the focus of this article.

Physics-related situations are, indeed, common in the real-life problems. Physics is, as many physicists say, "the description of the natural world by means of mathematics" - which makes it a context of choice for the problem writers. As an author of several articles on problem-solving and numerous physics problems written for both high-school and college use (Korsunsky, 1995a, 1995b, 1995c, 1997a, 1997b, 1999) who have focused on the use of the real-life context in problems (Korsunsky, 1997a), I was pleasantly surprised by the popularity of physics settings in the problems found in recently published textbooks. However, the number and seriousness of pedagogical "trouble spots" often accompanying such problems was disturbing. The goal of this article is to point out the most common ones and offer some remedies for both teachers and textbook authors.

The issue is not necessarily new. Traditional textbooks also used real-life context improperly (Pollak, 1978). However, the issue has come to bear much greater significance nowadays, as real-life problems have become more fashionable among the textbook writers.

Real-Life Mathematics Problems: A Missing Part in Educational Research

Research literature, while unequivocally favoring the real-life context in mathematics problems, points out several ways in which the context of a mathematics problem may, in fact, impede learning. The context-- related pitfalls that attracted most attention of researchers can be identified as follows:

* Genderbias(Chipman, 1988; Chipman, Marshall, & Scott, 1991; Marshall, 1984; Murphy & Ross, 1990);

* Culture- and language-related bias (Schwartz, 1988; Secada & De La Cruz, 1996; Short & Spanos, 1989);