Development of Operation-Specific Lexical Consistency Effect in Arithmetic Word Problem Solving

Keywords: Lexical consistency; word problem; arithmetic operation; arithmetic fluency; developmental trend

Word problems, referred to as arithmetic questions demonstrated in narratives, help students incorporate mathematical knowledge into their daily lives. Word problem solving is critical in mathematical learning as it requires integration of both numerical and linguistic information. In our previous study, we have demonstrated that adults showed an operation-specific lexical consistency effect in response fluency of word problem solving, suggesting that the processing of linguistic and numerical factors interact during word problem solution. Nonetheless, whether the processing varies at a young age is yet to be elucidated. Tackling the issue, we investigated age-related changes in word problem solving for school-age children and adolescents using the same experimental paradigm as in the previous study.

We examined a sample of 67 participants consisting of 30 children (15 male, 15 female, mean age = 9.76, SD = 1.22, ranged between 8.59 and 12.67) and 37 adolescents (18 male, 19 female, mean age = 14.64, SD = 1.97, ranged between 12.33 and 18.89). All the participants were administered with compare word problems which included relational statements, such as “Tom has 5 books. Jerry has 10 books more than Tom. How many books does Jerry have?” The problems varied in the type of operation needed to solve word problems (addition and subtraction) and the lexical consistency (consistent: the relational term is in line with the operation type, i.e., more-addition and less-subtraction; inconsistent: the relational term is in the opposite direction of the operation, i.e., more-subtraction and less-addition).

We found that children and adolescents displayed distinct operation and lexical consistency effects during word problem solutions. Among children, an interaction between consistency and operation was prominent only on task accuracy (F(1,29) = 13.3, p = .001) but not reaction time (F(1,29) = .621, p = .437). More specifically, a strong effect of consistency on children’s accuracy was detected for addition problems (F(1,29) = 37.5, p <.001, ηp2 = .564), but lessened for subtraction problems (F(1,29) = 17.9, p < .001, ηp2 = .381). In contrast, adolescents showed an adult-like profile. Specifically, no interaction was found in accuracy (F(1,36) = 3.17, p = .083), probably because of their accuracy reaching a ceiling; they instead demonstrated the consistency by operation interaction effect on reaction time (F(1,36) =7.58, p = .009) such that consistency effect was detected only for addition problems (F(1,36) = 9.82, p = .003) but not subtraction problems (F(1,36) = .468, p = .498).

These findings suggest that lexical consistency may affect numerical processing regarding response precision in the younger age. With the maturation of word problem skills, adolescents demonstrated an adult-like interaction effect between linguistic and numerical factors manifested in response fluency. In conclusion, by demonstrating a developmental shift from childhood to adolescence in word problem solution, we contribute to the current understanding of such critical practices in math and provide insights into how the corresponding skills develop with age.

Recommended citation: Chu, M.-Y., Ng, C.-T., & Chang, T.-T. (2022, Oct). Development of operation-specific lexical consistency effect in arithmetic word problem solving [Poster presentation]. Taiwanese Psychological Association (TPA) 61st Annual Meeting, Taipei City, Taiwan.
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