Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training

Abstract

Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME), however, students primarily learn to apply the first of these skills (i.e., representational skills) in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded that reading comprehension skills should be given a (more) prominent role during word problem solving instruction in RME.

Exploring the relationship between metacognitive and collaborative talk during group mathematical problem-solving – what do we mean bycollaborativemetacognition?

“…The teacher explained to the students that the measurements were unrealistic, and it was clear from student discussions and laughter that they understood this. Furthermore, it was important for student motivation that the problems were realistic enough to engage them in learning but not so detailed or beyond their current understanding to make them think it was beyond their capabilities (Boonen, de Koning, Jolles, & van Der Schoot, 2016). On the basis of this rationale, the teacher decided that the introduction of new units could have been off-putting, and would have detracted from the mathematical essence of the problem.…”

Can “you” make a difference? Investigating whether perspective‐taking improves performance on inconsistent mathematical word problems

“…To ensure comparability across word problems, we applied the following rules: (a) the numerical values or answers contained no negative numbers or fractions, (b) a numerical value occurred only once in the same problem, (c) the numerical values used in consistent and inconsistent problems of each word problem type were matched for magnitude (Boonen et al, ; De Koning et al, ; van der Schoot et al, ). Additionally, as previous research indicates that the consistency effect most likely occurs if word problems have a sufficiently high difficulty level (e.g., Daroczy, Wolska, Meurers, & Nuerk, ; Hegarty, Mayer, & Green, ; van der Schoot et al, ; Verschaffel et al, ), (d) numerical values in each problem consisted of two‐digit numbers, and (e) the answer to each problem was between 28 and 80.…”

“…Moreover, (f) each compare word problem contained the relational keyword “less than” (i.e., marked word problem) as marked relational keywords are more difficult to transform to the required arithmetic operation (e.g. reversing “less than” to addition) than unmarked relational keywords (e.g., “more than”) and result in a larger consistency effect compared to word problems containing unmarked relational keywords (Boonen et al, ; Hegarty et al, ; Pape, ; van der Schoot et al, ).…”

“…In the present study, personalization was achieved using a different approach, that is, by encouraging an internal mental perspective by use of the pronoun “you.” Specifically, our goal was to investigate whether this way of personalizing word problems would provide an effective means to combat a robust and persistent phenomenon in mathematical word problem solving: the consistency effect. The consistency effect refers to the finding that more errors are made on mathematical word problems (i.e., arithmetic exercises presented as text instead of in the form of mathematical notation, Timmermans, Van Lieshout, & Verhoeven, ) when the relational keyword (e.g., more than) is inconsistent (e.g., subtraction) as compared with consistent (e.g., addition) with the required mathematical operation (Boonen, De Koning, Jolles, & van der Schoot, ; Hegarty, Mayer, & Monk, ; De Koning, Boonen, & van der Schoot, ; Lewis & Mayer, ; Pape, ; van der Schoot, Bakker‐Arkema, Horsley, & Van Lieshout, ; Verschaffel, De Corte, & Pauwels, ). What complicates performance on inconsistent word problems (Table , right panel) is that, typically, problem solvers superficially process the word problem text and hence most of the time do not fully or accurately represent the actual problem statement.…”

In a range of meaningful contexts: 25 years of struggle for meaning in mathematics teaching

“…One of the reasons for this lack of delivery is that the successful solving of a mathematical word problem requires both mathematical skills and reading comprehension skills (Boonen, de Koning, Jolles, & van der Schoot, 2016;Wijaya, van den Heuvel-Panhuizen, Doormana, & Robitzsch, 2014). Unlike "bare" mathematics problems in which the mathematics can be tackled directly, word problems require additional processing, including working out what mathematics is appropriate to use to solve the problem (Baranes, Perry, & Stigler, 1989).…”