The problem model may be associated with an arithmetic strategy (e.g., counting up). How many marbles did Joe have in the beginning?” (see Kintsch & Greeno, 1985 Staub & Reusser, 1995), the problem model, which is influenced by education and problem-solving experience, includes three sets: marbles beginning (?), marbles won (3), marbles now (5), and the relations between those sets (? + 3 = 5). For example, in the change problem, “Joe won 3 marbles. Problem models are representations that contain only the elements essential for representing the mathematical structure of the problem ( Kintsch & Greeno, 1985). According to theories of WPS, as part of this translational process, problem solvers construct two types of mental representations: problem models and situation models ( Kintsch & Greeno, 1985 Nathan, Kintsch, & Young, 1992 Staub & Reusser, 1995).
#Word problem solver series
In addition, WPS requires a process of translating text to mathematical equations or a series of computations (i.e., using informal strategies, see Kieran, 1990, 1992 Koedinger & Nathan, 2004). Mathematical word problem solving (WPS) is complex because it requires students to read and understand written material that expresses numerical relations. This evidence suggests that although mathematical structure is fixed, different cognitive resources may act as limiting factors in WPS development when the WPS context is varied. Nonverbal reasoning predicted initial performance and growth for low-complexity WPS, but only growth for high-complexity WPS. Attentive behavior did not predict initial performance but did predict growth in low-complexity, whereas it predicted initial performance but not growth for high-complexity problems. Computational skills had an effect on initial performance in low- but not high-complexity problems and did not predict growth at either level of complexity. Language skills were related to initial performance at both levels of complexity and did not predict growth at either level.
At beginning of 3rd grade, 4 cohorts of students ( N = 261) were measured on computation, language, nonverbal reasoning skills, and attentive behavior and were assessed 4 times from beginning of 3rd through end of 5th grade on 2 measures of WPS at low and high levels of complexity. This study addressed predictors of the development of word problem solving (WPS) across the intermediate grades.