Problem Representation and Mathematical Problem Solving of Students of Varying Math Ability

Abstract

The purpose of this study was to examine differences in math problem solving among students with learning disabilities (LD, n = 25), low-achieving students (LA, n = 30), and average-achieving students (AA, n = 29). The primary interest was to analyze the processes students use to translate and integrate problem information while solving problems. Paraphrasing, visual representation, and problem-solving accuracy were measured in eighth grade students using a researcher-modified version of the Mathematical Processing Instrument. Results indicated that both students with LD and LA students struggled with processing but that students with LD were significantly weaker than their LA peers in paraphrasing relevant information. Paraphrasing and visual representation accuracy each accounted for a statistically significant amount of variance in problem-solving accuracy. Finally, the effect of visual representation of relevant information on problem-solving accuracy was dependent on ability; specifically, for students with LD, generating accurate visual representations was more strongly related to problem-solving accuracy than for AA students. Implications for instruction for students with and without LD are discussed.

The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children

“…In previous studies, a positive relationship between visual representation type and word problem solving performance has been established by calculating correlations between the total amount of (specific) visual representations produced and the total amount of correctly solved word problems (e.g., Blatto-Vallee, Kelly, Gaustad, Porter, & Fonzi, 2007;Guoliang, 2003;Hegarty & Kozhevnikov, 1999;Krawec, 2010Krawec, , 2012Van Garderen, 2006;Van Garderen & Montague, 2003). However, calculating the correlation between two sum scores is an example of a test-level approach entailing limitations to be considered in this study.…”

“…First, we have to consider that the established correlation between the total amount of (specific) visual representations and the total amount of correctly solved word problems might be explained by an underlying latent factor, such as a general measure of intelligence or cognitive ability (Boonen et al, 2013;Keith, Reynolds, Patel, & Ridley, 2008). Second, the relation might be explained by a mediating variable, for instance the capability of students to derive the correct mathematical operations from the visual representation and to determine the order in which these operations should be executed (i.e., the solution planning phase; see Mayer, 1985;Krawec, 2010). Finally, we have to acknowledge the possibility that a certain type of visual representation was made, but not used for answering the corresponding word problem.…”

Analysis Problem Solving in Mathematical Using Theory <i>Newman</i>

“…In this case, the following skills have been reported: the ability to understand a problem (Koedinger & Nathan, 2004), the capacity to apply appropriate resolution methods (Gerjets et al, 2004) and skills to build mental abstract models (Scheiter, Gerjets, & Schuh, 2010). Some scientists also mention the error of procces skills that cause domain errors related to performance in troubleshooting; for example, visual spatial domains, associated with the creation of inner representations through visual schemes (Krawec, 2010) and semantic-linguistic domains that allow individuals to connect different sections of text to achieve problem solutions (Van der Schoot, Bakker Arkema, Horsley, & Van Lieshout, 2009). On a separate issue, current research also reports the following difficulties regarding problem-solving word-solving skills skills (Ng & Lee, 2009): lack of understanding of the meaning of algebraic symbols; barriers to accurately transform data provided by natural language into mathematical equations; misinterpretation of the structure of semantic text and, consequently, a misunderstanding of the relationship between numbers and, finally, the difficulty of bringing semantic evidence from phrase to mathematical equations.…”

Efecto de la Representación Dinámica Integrada sobre la competencia matemática y la atención en niños con Trastorno por Déficit de Atención e Hiperactividad

“…En cuanto a la resolución de problemas, Krawec (2010) observó que, los estudiantes con DAM tienen dificultades para identificar la información relevante presente en el enunciado de un problema y que permite alcanzar la resolución final. Concluyó a su vez que, el alumnado con DAM muestra un déficit en la discriminación, que afecta a su capacidad para resolver los problemas adecuadamente.…”