A working memory model applied to mathematical word problem solving

Abstract

The main objective of this study is (a) to explore the relationship among cognitive style (field dependence/independence), working memory, and mathematics anxiety and (b) to examine their effects on students' mathematics problem solving. A sample of 161 school girls (13-14 years old) were tested on (1) the Witkin's cognitive style (Group Embedded Figure Test) and (2) Digit Span Backwards Test, with two mathematics exams. Results obtained indicate that the effect of field dependency, working memory, and mathematics anxiety on students' mathematical word problem solving was significant. Moreover, the correlation among working memory capacity, cognitive style, and students' mathematics anxiety was significant. Overall, these findings could help to provide some practical implications for adapting problem solving skills and effective teaching/learning.Keywords Field-dependent/independent Á Working memory Á Word problem Á Mathematics anxiety Students find problem solving difficult. A problem is often defined as a goal that is not immediately attainable (Hambrick and Engle 2003). Successful problem solvers spend more time analyzing a problem and should consider a wide range of alternatives. They should be open minded, flexible, and make sense of the mathematics concepts they are learning (e.g., Fernandez et al. 1994). Students approach mathematical problem solving in fundamentally different ways, particularly problems requiring conceptual understanding and complicated strategies such as word problems.Students express great difficulties in handling a word or story problem (e.g.Nickson 2004). The order of information, the relation between known and unknown, and the transition from known to unknown all influence the understanding of a story problem on younger learners (Laborde 1990;Orton 1992). As Gagne (1983) suggested, in the process of mathematical word problem solving, the student should be able to translate the concrete to the abstract, and the abstract to the concrete. It seems that the mathematical word problem exam is a more distinctive and challenging task than the ordinary mathematics task (Alamolhodaei 2002).

The role of mathematical homework and prior knowledge on the relationship between students’ mathematical performance, cognitive style and working memory capacity

“…Many recent studies support the notion that working memory is related to arithmetic performance ( Fürst & Hitch, 2000;Heathcote, 1994;Kyoung-Min & So-Young , 2002;Logie, Gilhooly, & Wynn, 1994;Alamolhodaei, 2009), mathematics problem solving (Cary & Carlson, 2001;DeStefano & LeFevre, 2004;Klein & Bisanz, 2000;Seitz & Schumann-Hengsteler, 2000;Swanson, 2004;Swanson & Beebe-Frankenberger, 2004;Alamolhodaei, 2009), and even mathematics anxiety (Ashcraft & Kirk, 2001).For example, studies reported by Adams and Hitch (1998) suggested that mental arithmetic performance relies on the resources of working memory. It seems that a major source of mathematical misunderstanding and errors should be sought in memory transformation and subjective organization (Alamolhodaei, 2009). In addition, Ekbia and Alamolhodaei (2000) reported that schoolboys with higher WM capacity were more successful than those with lower WM in the mathematical problem solving, particularly word problems.…”

“…Solutions to such problems often require cognitive restructuring. Other researchers have also demonstrated the importance of field dependency in science education and mathematical problem solving, in particular word problems (Alamolhodaei, 2002(Alamolhodaei, , 2009Ekbia & Alamolhodaei, 2000;Johnstone & AI-Naeme, 1991;Witkin & Goodenough, 1981). In a more recent study, with the sample of 161 school girls (13-14 years old), Alamolhodaei (2009) also found that field independent students achieved higher results in both an ordinary mathematical exam and a word problem solving exam.…”

“…Moreover, school students with FI cognitive style achieved much better results than FD ones in mathematical problem solving, in particular word problems (Alamolhodaei, 2002). Therefore, recent studies showed a positive relationship between cognitive styles (FD/FI) and students' mathematical performance (Witkin and Goodenough 1981;Talbi 1990;Al-Naeme 1991, 1995;Alamolhodaei 1996;Ekbia and Alamolhodaei 2000;Alamolhodaei 2002;Alamolhodaei 2009). …”

“…For the measurement of the student's working memory capacity (WMC), DBT has been quoted as the normal test (Case 1974;Scardamalia 1977;Al-Naeme 1989, Niaz, 1988Talbi 1990;Johnstone et al 1993;Alamolhodaei, 2009;Raghubar et al, 2010). The sequence of numbers were presented by an expert and the students are asked to turn the numbers over in their mind then reproduce the sequence in the reverse order of presentation and write it down from left to right on their answer sheets.…”

“…The estimate of reliability of the GEFT is .82 (Witkin, Oltman, Raskin, & Karp, 1971). Students' cognitive styles were determined according to a criterion used by (Scardamalia 1977;Case 1974;Case and Globerson 1974;Johnstone et al 1993;Alamolhodaei 1996, Alamolhodaei 2002, 2009). …”