The Relationship Between Accuracy of Numerical Magnitude Comparisons and Children's Arithmetic Ability: A Study in Iranian Primary School Children

The association between working memory and mathematical problem solving: A three-level meta-analysis

Although working memory (WM) is an important factor in mathematical problem solving (MPS), it remains unclear how well WM relates to MPS. Thus, we aimed to determine this relationship by using a meta-analysis. We searched electronic databases for studies published between 2000 and 2020 and established operational criteria. We conducted Egger’s regression tests and created funnel plots to test for publication bias. Finally, a three-level meta-analytic model analysis of data from 130 studies involving 43,938 participants and 1,355 effect sizes revealed a moderate relationship between WM and MPS (r = 0.280, 95% CI = [0.263, 0.314]). Moreover, moderator analyses showed that: (1) dressed-up word problems were more strongly tied to WM than to intra-mathematical problems; (2) the central executive function showed the strongest relation with MPS, whereas the phonological loop had the weakest; (3) gender ratio had significant moderating effects; and (4) some of the above-mentioned significant moderating effects were unique after controlling for other factors. Implications for research and practice were also discussed.

Numerical Magnitude Processing in Deaf Adolescents and Its Contribution to Arithmetical Ability

Although most deaf individuals could use sign language or sign/spoken language mix, hearing loss would still affect their language acquisition. Compensatory plasticity holds that the lack of auditory stimulation experienced by deaf individuals, such as congenital deafness, can be met by enhancements in visual cognition. And the studies of hearing individuals have showed that visual form perception is the cognitive mechanism that could explain the association between numerical magnitude processing and arithmetic computation. Therefore, we examined numerical magnitude processing and its contribution to arithmetical ability in deaf adolescents, and explored the differences between the congenital and acquired deafness. 112 deaf adolescents (58 congenital deafness) and 58 hearing adolescents performed a series of cognitive and mathematical tests, and it was found there was no significant differences between the congenital group and the hearing group, but congenital group outperformed acquired group in numerical magnitude processing (reaction time) and arithmetic computation. It was also found there was a close association between numerical magnitude processing and arithmetic computation in all deaf adolescents, and after controlling for the demographic variables (age, gender, onset of hearing loss) and general cognitive abilities (non-verbal IQ, processing speed, reading comprehension), numerical magnitude processing could predict arithmetic computation in all deaf adolescents but not in congenital group. The role of numerical magnitude processing (symbolic and non-symbolic) in deaf adolescents' mathematical performance should be paid attention in the training of arithmetical ability.

Materials count: Linear-spatial materials improve young children's addition strategies and accuracy, irregular arrays don't

Children who use advanced arithmetic strategies, such as count-on and decomposition, are more accurate when solving arithmetic problems and are more likely to later have higher levels of math achievement. The present study tested the hypothesis that instruction using linear-spatial representations would activate children's knowledge necessary for use of mental addition strategies and, thus, lead to greater accuracy on addition problems, than instruction using irregular representations of magnitude. As predicted, low-income kindergartners (n = 29) randomly assigned to practice sums up to 10 using materials that instantiated the linear-spatial features of a mental number line (i.e., discrete squares arranged in rows) demonstrated substantially more improvement in solving unpracticed addition problems than children who practiced with irregular materials (i.e., pictures of stars arranged in random arrays). This was particularly true for children with better initial numerical knowledge, which provided support for the idea that existing knowledge was activated. The use of count-on more than doubled from pretest to posttest among children in the linear-spatial condition and this mediated the difference in improvement between conditions. The importance of aligning instructional materials to relevant mental representations-consistent with the Cognitive Alignment Framework for instructional design-is discussed.