Characteristic behaviors of students with LD who have teacher-identified math weaknesses

Number Sense Makes All the Difference: Calculation Using Number Sense by Pupils With and Without Learning Difficulties in Math

The research examined the calculation methods used by pupils in Grades 3–6 when they were presented with problems that could be worked out efficiently and flexibly by applying number sense. The study was conducted with a convenience sample of 179 pupils between the ages 7 years and 10 months to 12 years and 10 months. in mainstream education in Israel, who attended schools belonging to different sectors and situated in different areas of the country with varied socioeconomic profiles. The test included addition, subtraction, multiplication, and division problems that pupils were asked to solve mentally, in writing and by identifying correctly and incorrectly solved problem. Some of the problems presented pupils with opportunities to apply number sense. As expected, the research findings showed significant differences in calculation accuracy between pupils with and without learning difficulties, especially in multiplication and division tasks. Still, the performance of pupils with difficulties in the accuracy variable was above average, and there was high variance within this group. We found significant differences between pupils with and without difficulties in the calculation-speed variable in all tasks and in all calculation modalities. One of the implications is that pupils, and especially those with difficulties, should be afforded enough time to work out problems, and should be presented with tasks that would enable them to use number sense in order to retrieve prior knowledge and apply it.

Identifying the nature of impairments in executive functioning and working memory of children with severe difficulties in arithmetic

An age-matched achievement-matched design was used to examine whether the executive functioning and working memory impairments exhibited by children with severe difficulties in arithmetic (SDA) are better viewed as developmental lags or as cognitive deficits. Three groups of children were included: 20 SDA children, 20 typically achieving children (CM) matched in chronological age with the SDA children, and 20 younger typically achieving children (AM) matched in achievement with the SDA group. While children with SDA did not exhibit impairments in color-word inhibition and verbal working memory, they did demonstrate impairments in shifting, quantity-digits inhibition, and visuospatial working memory. As children with SDA did not perform more poorly than their AM counterparts on any of these tasks, impairments in specific areas of executive functioning and working memory appear to reflect developmental lags rather than cognitive deficits.

Untangling the Contribution of the Subcomponents of Working Memory to Mathematical Proficiency as Measured by the National Tests: A Study among Swedish Third Graders

The aim with the present study was to examine the relationship between the subcomponents in working memory (WM) and mathematical performance, as measured by the National tests in a sample of 597 Swedish third-grade pupils. In line with compelling evidence of other studies, individual differences in WM capacity significantly predicted mathematical performance. Dividing the sample into four groups, based on their mathematical performance, revealed that mathematical ability can be conceptualized in terms of different WM profiles. Pupils categorized as High-math performers particularly differed from the other three groups in having a significant higher phonological ability. In contrast, pupils categorized as Low-math performers were particularly characterized by having a significant lower visuo-spatial ability. Findings suggest that it is important for educators to recognize and acknowledge individual differences in WM to support mathematical achievement at an individual level.

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

A synthesis of mathematical and cognitive performances of students with mathematics learning disabilities

The purpose of this study was to synthesize the findings from 23 articles that compared the mathematical and cognitive performances of students with mathematics learning disabilities (LD) to (a) students with LD in mathematics and reading, (b) age- or grade-matched students with no LD, and (c) mathematical-ability-matched younger students with no LD. Overall results revealed that students with mathematics LD exhibited higher word problem-solving abilities and no significant group differences on working memory, long-term memory, and metacognition measures compared to students with LD in mathematics and reading. Findings also revealed students with mathematics LD demonstrated significantly lower performance compared to age- or grade-matched students with no LD on both mathematical and cognitive measures. Comparison between students with mathematics LD and younger students with no LD revealed mixed outcomes on mathematical measures and generally no significant group differences on cognitive measures.

Metacognitive strategy use of eighth-grade students with and without learning disabilities during mathematical problem solving: a think-aloud analysis

The purpose of the study was to investigate the metacognitive abilities of students with LD as they engage in math problem solving and to determine processing differences between these students and their low- and average-achieving peers (n = 73). Students thought out loud as they solved three math problems of increasing difficulty. Protocols were coded and analyzed to determine frequency of cognitive verbalizations and productive and nonproductive metacognitive verbalizations. Results indicated different patterns of metacognitive activity for ability groups when type of metacognitive verbalization and problem difficulty were considered. Implications for instruction are discussed.