Students’ use of standard algorithms for solving linear equations

This paper describes a study in which students ’ use of standard algorithms for solving linear equations were investigated. Of interest was whether students would discover a standard algorithm in this domain on their own, and whether the rate of discovery varied for two instructional interventions. 130 6th grade students participated in a week-long ‘math camp’ where they learned symbolic methods for solving equations. In a 2x2 design, some students were asked to re-solve previously completed problems using a different strategy, and other students were shown a brief demonstration of worked-out examples of solved equations. Results suggest the ‘solve it another way ’ intervention was successful in encouraging students to discover and use a variety of equation-solving strategies. However, viewing a demonstration of a standard algorithm did not increase the chances that students would use the demonstrated algorithm on the post-test. Doing mathematics frequently involves the use of algorithms. Knowledge of algorithms is an important component of our educational goals for US mathematics students at all levels (Morrow & Kenney, 1998; National Research Council, 2001). Our goals with respect to algorithms are for students to not only know how to use certain standard algorithmic methods but also to know why algorithms are effective and/or efficient (Dowker, 1997; Dowker, Flood, Griffiths, Harriss, & Hook, 1996), to understand why algorithms work (Morrow & Kenney, 1998; Skemp, 1978), and to be able to select from a variety of known algorithms, depending on which is most appropriate for a given problem (Star, 2001, 2002, 2004; Star, in press). This last capacity, which I refer to as procedural flexibility, is the focus of the present work. A common finding on national and international assessments is that too many US students lack procedural flexibility; too many students only know algorithms by rote and thus have difficulty when faced with novel o