Solving Arithmetic Word Problems

Abstract

This study was designed to determine a word problem difficulty classification in children with arithmetic learning disabilities (ALD; n = 104) in comparison with typically achieving students (n = 44). We tested variables such as (a) semantic structure (Change, Combine, Compare, and Equalize), (b) operation (subtraction and addition), and (c) position of the unknown quantity in the problem. Facet theory with multidimensional scaling techniques (MINISSA) was used to analyze the underlying dimensions in the responses of each group of participants. Our results indicate that although the word problem difficulty classifications for the 2 groups of children were different, the position of the unknown quantity had a greater influence on the level of difficulty of story problems than other variables. The noncanonical problems--specifically, those with the unknown term in the first place--although difficult for both groups of children, were the most difficult problems for children with ALD.

Simple pictorial mathematics problems for children: locating sources of cognitive load and how to reduce it

“…Therefore, our findings verify and extend the literature on the importance of the position of the unknown. Past research has demonstrated that bare or word problems with the unknown at the start are harder than corresponding problems with the unknown at the end (De Corte and Verschaffel 1981Verschaffel , 1987García et al 2006;Hiebert 1982). Our results show that the same occurs in pictorial problems.…”

“…+ 2 = 5), the problems with the unknown at the start are harder to solve than the ones with the unknown at the end (De Corte and Verschaffel 1981;Hiebert 1982). The same holds for word problems (De Corte and Verschaffel 1987;García et al 2006;Hiebert 1982). But it is unclear whether this result holds for pictorial problems too.…”

Does understanding relational terminology mediate effects of intervention on compare word problems?

“…Only for the subtype of compare problems with the unknown compared set was the mediation effect complete. For this subtype, which is easier than the unknown referent set subtype but harder than the unknown difference set subtype (e.g., Garcia et al, 2006; Morales et al, 1985; Riley & Greeno, 1988), the instructional focus on relational terminology appeared to provide adequate scaffolding, in and of itself, for promoting student success. Perhaps these problems of moderate difficulty, relative to the other two subtypes, were closer to the students’ zone of proximal development.…”

“…How many more animals does Rose have than Maury?). Compare problems are more difficult than combine or change problems for primary-grade students, even though the calculations required for all three problem types is similar (e.g., Briars & Larkin, 1984; Carpenter, & Moser, 1984; Cummins et al, 1988; De Corte, Verschaffel, & Verschueren, 1982; Garcia, Jimenez, & Hess, 2006; Morales et al, 1985; Powell et al, 2009; Riley & Greeno, 1988; Verschaffel, 1994). Compare problems are the most difficult problem type for two reasons.…”

“…The hypotheses in the present study were based on (a) previous SBI intervention research showing efficacy without the emphasis on relational terminology (Fuchs et al, 2008; Fuchs et al, 2009), (b) prior investigations of student performance on compare problems (e.g., Cummins et al, 1988; De Corte et al, 1985; Fuchs, Zumeta, et al, 2010; Garcia et al, 2006; Morales et al, 1985; Powell et al, 2009; Riley & Greeno, 1988; Verschaffel, 1994), and (c) earlier work suggesting a connection between understanding relational terminology and solving compare problems (e.g., Lewis & Mayer; 1987; Stern, 1993; Vershaffel, 1994; Vershaffel et al, 1992). First, we posited that students receiving WP intervention would significantly outperform those in CAL and control conditions on compare problems, who would perform comparably to each other.…”