Exploring a Conceptual Model-Based Approach to Teaching Situated Word Problems

Abstract

The authors explored the effects of teaching conceptual model-based problem-solving instruction on students' ability to solve problems in various situations. Participants were 3 4th-and 5th-grade students with or at risk for mathematics disabilities. The authors used an adapted multiple-probe across-participants design to assess the functional relation between the intervention and the students' problem-solving performance. The results indicate that the intervention improved students' performance on researcherdesigned criterion tests and a norm-referenced standardized test (i.e., the problem-solving subtest of the KeyMath Revised Normative Update; A. J. Connolly, 1998). The authors discuss the results in the context of providing students with appropriate educational opportunities, including carefully designed instruction.

An exploratory study contrasting high- and low-achieving students' percent word problem solving

“…Within the mathematics education and special education research communities, there is growing evidence about the effectiveness of SBI in supporting students' learning of word problem solving, particularly in arithmetic (e.g., Fuchs et al, 2009;Fuchs, Seethaler, et al, 2008, Fuchs et al, 2010Fuson & Willis, 1989;Jitendra et al, 2007;Lewis, 1989;Willis & Fuson, 1988) and ratio/proportion word problem solving (e.g., Jitendra et al, 2009;Xin, 2008;Xin et al, 2005;Xin, Wiles, & Lin, 2008;Xin & Zhang, 2009). However, other studies have indicated…”

A Comparison of Two Mathematics Problem-Solving Strategies: Facilitate Algebra-Readiness

“…The results of preliminary studies that evaluated COMPS using single-subject design (Kazdin, 1982) indicate that there is a functional relationship between the intervention and students' improved performance on researcher-designed criterion tests that involve simple addition, subtraction, multiplication, and division problems (e.g., Xin, Wiles, & Lin, 2008) and on problems involving irrelevant information or multiple steps (e.g., Xin & Zhang, 2009). The results also show that students improved their prealgebra concept and skills after the COMPS instruction.…”

A preliminary discourse analysis of constructivist-oriented mathematics instruction for a student with learning disabilities

“…In addition, due to the large numbers involved in the problems, simply replying on mental mathematics or "guess and check" may not be helpful in solving the problems. Cronbach's alpha of the COMPS test was .86, and the alternate form reliability was .85 (Xin & Zhang, 2009). Each item was worth a total of one point; the percentage of problems solved correctly on each test was calculated as the total points earned divided by the total possible points.…”

“…To promote generalized problem solving skills, it is important that, following the concrete or semiconcrete modeling stage, students are provided with sufficient opportunities to directly apply abstract mathematical models (e.g., UR X # of Units D Product) for word problem representation. This requires systematic programming, which may involve strategically sampling a range of real-world contextualized problems, in order for students to conceptually understand each of the elements (e.g., unit rate) in the model equation (UR X # of Units D Product) and therefore reconstruct the mathematical model at the abstract level (Wagner, 2006;Xin & Zhang, 2009). Eventually, students should be able to use the model equation to solve not only problems with product as the unknown, but also problems with the factor as the unknown by directly applying the operation of division.…”