The development of flexibility in equation solving

Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations.

“…Procedural knowledge is the ability to execute action sequences to solve problems, including the ability to adapt known procedures to novel problems (the latter ability is sometimes labeled transfer; Rittle- Johnson, Siegler, & Alibali, 2001). Procedural flexibility incorporates knowledge of multiple ways to solve problems and when to use them (Kilpatrick et al, 2001;Star, 2005Star, , 2007 and is an important component of mathematical competence (Beishuizen, van Putten, & van Mulken, 1997; Blö te, Van der Burg, & Klein, 2001;Dowker, 1992;Star & Seifert, 2006). Finally, conceptual knowledge is "an integrated and functional grasp of mathematical ideas" (Kilpatrick et al, 2001, p. 118).…”

The nature and development of experts’ strategy flexibility for solving equations

“…Existing research suggests that flexibility can be enhanced through appropriate instruction (Blöte, Van der Burg, & Klein, 2001;Rittle-Johnson & Star, 2007;Star & Seifert, 2006), but much more research is needed to fully understand the development of flexibility.…”

“…Similarly, Star and Seifert (2006) investigated the impact of an instructional intervention --having students solve the same problem in two different ways --on students' flexibility for solving algebraic equations. Specifically, students in an experimental group (n = 18) were asked to solve previously completed problems in new and different ways, while students in a control group (n = 18) solved a series of distinct problems.…”

“…We choose to navigate through this somewhat confusing terrain by drawing heavily upon the work of Star, defining flexibility as knowledge of multiple solutions as well as the ability and tendency to selectively choose the most appropriate ones for a given problem and a particular problem-solving goal (Star, 2005;Star & Rittle-Johnson, 2008;Star & Seifert, 2006). We assert that flexibility exists on a continuum; as students gain flexibility they might first show increased knowledge of multiple strategies, then particular preferences, and finally appropriate use of preferred strategies (Blöte et al, Experts' flexibility 6 2001).…”

It pays to compare: An experimental study on computational estimation

“…Procedural flexibility incorporates knowledge of multiple ways to solve problems and when to use them (National Research Council, 2001;Star, 2005Star, , 2007 and is an important component of mathematical competence (Beishuizen et al, 1997;Blöte, Van der Burg, & Klein, 2001;Dowker, 1992;Star & Rittle-Johnson, 2008;Star & Seifert, 2006). To disentangle knowledge from use, we included an independent measure of flexibility knowledge as well as coded for flexible use of strategies on the procedural knowledge assessment.…”