Do teachers need to inhibit heuristic Bias in mathematics problem-solving? Evidence from a negative-priming study

The influence of semantic alignment on the performance of addition and division operation: age-related differences

Semantic alignment refers to the cognitive tendency that people always seek for the matching of semantic relations between mathematical cognition and objects in specific situations. In developing individuals, language ability and mathematical ability are in the development stage, and the development of semantic consistency is more helpful to reveal the relationship between the two. From the perspective of semantic alignment, this study aims to explore the age-related difference in the effects of semantic relationship on arithmetic operations. Sixty-two children and 62 adults were recruited to perform an arithmetical verification task. The results showed that: (1) Compared with children, adults had shorter response times and higher accuracy in mathematical operations. (2) Both adults and children showed longer response times in division condition than that in addition condition. (3) Children are more affected by semantic alignment than adults in addition. (4) For addition operation, participants performed better under semantic consistent condition than under semantic inconsistent condition, but the opposite result was found for division operation. It indicated that semantic consistently promoted the addition operation and semantic inconsistently promoted the division operation. This suggests that teachers should pay attention to integrating mathematical conceptual knowledge and language context in future educational practice.

The role of working memory updating, inhibition, fluid intelligence, and reading comprehension in explaining differences between consistent and inconsistent arithmetic word-problem-solving performance

Children's performance in arithmetic word problems (AWPs) predicts their academic success and their future employment and earnings in adulthood. Understanding the nature and difficulties of interpreting and solving AWPs is important for theoretical, educational, and social reasons. We investigated the relation between primary school children's performance in different types of AWPs and their basic cognitive abilities (reading comprehension, fluid intelligence, inhibition, and updating processes). The study involved 182 fourth- and fifth-graders. Participants were administered an AWP-solving task and other tasks assessing fluid intelligence, reading comprehension, inhibition, and updating. The AWP-solving task included comparison problems incorporating either the adverb more than or the adverb less than, which demand consistent or inconsistent operations of addition or subtraction. The results showed that consistent problems were easier than inconsistent problems. Efficiency in solving inconsistent problems is related to inhibition and updating. Moreover, our results seem to indicate that the consistency effect is related to updating processes' efficiency. Path analyses showed that reading comprehension was the most important predictor of AWP-solving accuracy. Moreover, both executive functions-updating and inhibition-had a distinct and significant effect on AWP accuracy. Fluid intelligence had both direct and indirect effects, mediated by reading comprehension, on the overall measure of AWP performance. These domain-general factors are important factors in explaining children's performance in solving consistent and inconsistent AWPs.

Higher-order thinking word problem-solving errors made by low-performing pupils: Comparative case study across school types in Malaysia

The achievement gaps existed among the three types of Malaysian elementary schools with different instruction mediums. Thus, this study sought to compare the types of errors made by the low-performing students from different school types in solving word problems involving higher-order thinking skills by conducting a multiple case study. The study involved 18 low-performing students from a National Primary School (NPS), National-Type Chinese Primary School (NTCPS), and National-Type Tamil Primary School (NTTPS) in Malaysia. The students' errors in solving eight word problems were identified qualitatively through conducting four sessions of diagnostic interviews, followed by the Newman's Error Analysis. Then, a cross-case analysis was conducted. The findings indicated that the participants of the three school types made reading, comprehension, transformation, process skills and encoding errors. However, the NPS and NTTPS low-performing students made more process skills errors and encoding errors, as compared to the NTCPS low-performing students. The findings imply the need to enhance the procedural fluency of NPS and NTTPS low-performing students for reducing the achievement gaps among the school types.

Arithmetic Word Problems Revisited: Cognitive Processes and Academic Performance in Secondary School

Solving arithmetic word problems is a complex task that requires individuals to activate their working memory resources, as well as the correct performance of the underlying executive processes involved in order to inhibit semantic biases or superficial responses caused by the problem’s statement. This paper describes a study carried out with 135 students of Secondary Obligatory Education, each of whom solved 5 verbal arithmetic problems: 2 consistent problems, whose mathematical operation (add/subtract) and the verbal statement of the problem coincide, and 3 inconsistent problems, whose required operation is the inverse of the one suggested by the verbal term(s). Measures of reading comprehension, visual–spatial reasoning and deductive reasoning were also obtained. The results show the relationship between arithmetic problems and cognitive measures, as well as the ability of these problems to predict academic performance. Regression analyses confirmed that arithmetic word problems were the only measure with significant power of association with academic achievement in both History/Geography (β = 0.25) and Mathematics (β = 0.23).