Understanding the Development of Flexibility in Struggling Algebra Students

Abstract

The ability to flexibly solve problems is considered an important outcome for school mathematics and is the focus of this paper. The paper describes the impact of a three-week summer course for students who struggle with algebra. During the course, students regularly compared and contrasted worked examples of algebra problems in order to promote flexible use of solution strategies. Assessments were designed to capture both knowledge and use of multiple strategies. The students were interviewed in order to understand their rationales for choosing particular strategies, as well as their attitudes toward instruction that emphasized multiple strategies. Findings suggest that students gained both knowledge of and appreciation for multiple strategies, but they did not always use alternate strategies. Familiarity, understandability, efficiency, and form of the problem were all considerations for strategy choice. Practical and theoretical implications are discussed.

Modeling Strategy Use in an Intelligent Tutoring System: Implications for Strategic Flexibility

“…The Rittle-Johnson and Star measure of strategic flexibility directs students to generate multiple solution paths; however, in a tutoring setting students are not prompted to choose multiple strategies. Studies of strategic flexibility have observed that when students are not asked to generate multiple strategies they will often use only one strategy to solve problems [4,6]. This makes it difficult to observe flexible strategy use indirectly.…”

“…Without instructing students to solve problems using multiple strategies, the likelihood of a student using a divergent strategy is low. Previous research on strategic flexibility has found that although students may be aware of many strategies, they often limit their choice to the most efficient one when problem solving [6]. Acknowledging these earlier findings, we identify two ways to improve research on strategic flexibility within ITSs.…”

“…Problem Types Work on strategic flexibility has found that while students may be aware of many strategies they will often learn to use the most efficient strategy for a specific problem [4,6]. To encourage the use of different strategies we used 6 variations of the linear equation.…”

“…Students who have high strategic flexibility are more likely to adapt their strategies, transferring their knowledge to solve new problems [8,4]. Conversely, students who lack strategic flexibility struggle to solve more difficult or unfamiliar problems that require the use of different strategies [6]. An active area of research concerns developing pedagogical methods to foster strategic flexibility and understanding the impact of strategic flexibility on problem solving.…”

“…Strategic flexibility refers to a student's knowledge of multiple strategies and their ability to choose the best of those strategies for a given problem [6,4]. Measures of strategic flexibility correlate with both the student's procedural and conceptual knowledge [1,7,4].…”