EPA2000: a multilingual, programmable computer assessment of off-line metacognition in children with mathematical-learning disabilities

Children's confidence on mathematical equivalence and fraction problems

Metacognition is how people think about their own thinking, and it includes children's confidence in their problem-solving solutions. We assessed children's metacognition in two areas of mathematics that are often plagued by misconceptions and often studied separately-mathematical equivalence (e.g., 3 + 4 = 5 +__) and fraction magnitude (e.g., 1/3 = 2/__). Specifically, we quantified children's metacognitive skills across these topics, examined whether these skills are topic-specific, and determined how these skills covary with domain-general executive functioning. A total of 80 elementary school children (Mage = 7.70 years, SD = 0.69) provided trial-by-trial performance data and confidence judgments on equivalence and fraction problems as well as assessments of executive function. Children's metacognitive skills were especially impaired when using incorrect strategies based on misconceptions, and we did not find robust evidence for cross-topic associations. We found modest associations between children's metacognitive skills and their working memory and inhibitory control. Findings have theoretical and practical implications for understanding which children struggle with these important mathematics concepts and why.

Children's confidence using incorrect strategies on mathematical equivalence problems

Children often struggle to solve mathematical equivalence problems correctly. The change-resistance theory offers an explanation for children's difficulties and suggests that some incorrect strategies represent the overgeneralization of children's narrow arithmetic experience. The current research considered children's metacognitive abilities to test a tacit assumption of the change-resistance theory by providing a novel empirical examination of children's strategy use and certainty ratings. Children were recruited from U.S. elementary school classrooms serving predominantly White students between the ages of 6 and 9. In Study 1 (n = 52) and Study 2 (n = 147), children were more certain that they were correct when they employed arithmetic-specific incorrect strategies relative to other incorrect strategies. These findings are consistent with the change-resistance theory and have implications for the development of children's metacognition.

The relationship between cognition and mathematics in children with attention-deficit/hyperactivity disorder: a systematic review

Cognitive processes play an imperative role in children's mathematics learning. Difficulties in cognitive functioning are a core feature of Attention Deficit Hyperactivity Disorder (ADHD) in children, who also tend to show lower levels of mathematics attainment than their typically developing peers. This review (registration number: CRD42020169708) sought to aggregate findings from studies assessing the relationship between cognition and mathematics in children with a clinical ADHD diagnosis aged 4-12 years. A total of 11,799 studies published between 1992 and August 2020 were screened for eligibility using various database (PsycINFO, PubMed, SCOPUS, EMBASE, ERIC, Web of Science, and additional sources), from which four studies met inclusion criteria. A narrative synthesis was conducted on the correlations between mathematics and cognitive domains, including an evaluation of the risk of bias within the studies. Across four studies meeting inclusion criteria, memory, inhibitory control, and processing speed were assessed. The results showed a positive association between cognition and mathematics performance in this population. The strength of associations across these studies varied as a function of the cognitive domain in question, means by which mathematics performance was assessed, as well as whether confounding factors such as age and IQ were controlled for. Collectively, this review demonstrates a lack of research in this area and points to various methodological considerations for identifying the association between cognition and mathematics performance in ADHD.

The Effect of Metacognitive Knowledge on Mathematics Performance in Self-Regulated Learning Framework-Multiple Mediation of Self-Efficacy and Motivation

Metacognition, self-efficacy, and motivation are important components of interaction in self-regulated learning (SRL). However, the psychological mechanism underlying the association among them in mathematical learning remained ambiguous. The present study investigated whether the relationship between metacognitive knowledge (MK) and mathematics performance can be mediated by self-efficacy and motivation. The sample comprised 569 students (245 male, Mage = 16.39, SD = 0.63) of Grade 10 in China. The MK in mathematics questionnaire, the self-efficacy questionnaire, the academic motivation scale, Raven advanced progressive matrix, and mathematics tests were used for data collection. Our results suggested that the mathematics performance could be predicted by MK, self-efficacy and intrinsic motivation. Moreover, the association between MK and mathematics performance was mediated by self-efficacy and intrinsic motivation, as revealed by a multiple mediation analysis. Additionally, there were sex differences in MK, self-efficacy and intrinsic motivation. The findings highlight the psychological mechanism in the mathematics of Chinese students and will help teachers to improve students’ mathematical learning in SRL framework more effectively. Implications for education and further studies are discussed.

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.

Cognitive skills in mathematical problem solving in Grade 3

BACKGROUND

Research on the relationship between cognitive skills and mathematical problem solving is usually conducted on adults or on participants with acquired deficits associated with brain injury (e.g.Cipolotti, 1995; Cohen, Dehaene, & Verstichel, 1994; McCloskey, 1992).

AIMS

In these studies we wanted to make a contribution to the field of children's mathematical problem solving. The first aim of this study was to investigate whether mathematical problem solving in children is merely determined by semantic elaboration, as hypothesized in some of the models of adult processing (semantic hypothesis). In addition, we aimed to investigate whether there is a continuum from very good to very poor mathematical problem solving among children with mathematical learning disabilities showing immature cognitive skills (maturational lag hypothesis).

SAMPLE

The participants were 376 third graders and 107 second graders.

METHOD

The internal structure of the data was analysed with a principal components analysis. In addition, two MANOVA were conducted to compare children with learning disabilities or problems with age-matched and performance-matched subjects.

RESULTS

Two components, a semantic and a non-semantic one, were needed to account for an adequate fit of the dataset. In addition, children with mathematical learning disabilities had less-developed cognitive skills compared with peers without learning disabilities, but they did not differ from younger children on seven of the nine cognitive skills.

CONCLUSIONS

This study highlighted that children's mathematical problem solving is not determined by one general component. The picture is more complex, since two mathematics components were found. In addition, although our findings point in the direction of the maturational lag hypothesis it may be important to assess the different cognitive skills and especially assess the number system knowledge, since it seems below average in children with mathematical learning disabilities, compared with the knowledge of younger children with comparable skills in mathematics.

Children with mathematics learning disabilities in Belgium

In Belgium, between 3% and 8% of the children in elementary schools have mathematics learning disabilities (MLD). Many of these children have less developed linguistic, procedural, and mental representation skills. Moreover, a majority of the children have been found to show inaccurate prediction and evaluation skills in Grade 3. MLD often become obvious in elementary school. Whereas some children are retained, others are referred to special education. During the last 10 years, the number of children in special education and the number of children with learning disabilities who are following a special guidance program in general education (inclusive education) have increased. Children in Belgium with MLD can get therapy for about 2 years. Nevertheless, many problems continue unresolved even in high school and adulthood.

Metacognition and mathematical problem solving in grade 3

This article presents an overview of two studies that examined the relationship between metacognition and mathematical problem solving in 165 children with average intelligence in Grade 3 in order to help teachers and therapists gain a better understanding of contributors to successful mathematical performance. Principal components analysis on metacognition revealed that three metacognitive components (global metacognition, off-line metacognition, and attribution to effort) explained 66% to 67% of the common variance. The findings from these studies support the use of the assessment of off-line metacognition (essentially prediction and evaluation) to differentiate between average and above-average mathematical problem solvers and between students with a severe or moderate specific mathematics learning disability.

VIDANN: a video annotation system

VIDANN is a computer program that allows participants to watch a video on a standard TV and to write their annotations (thought/feeling entries) on paper attached to a writing tablet. The system is designed as a Microsoft ActiveX module. It can be further adapted by the individual researcher through the use of a VBScript. All data, including the participant's handwriting, are stored in an XML database. An accompanying Wizard has been designed that enables researchers to generate VBScripts for standard configurations.