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

Metacognitive knowledge of attention in children with and without ADHD symptoms

Children with ADHD (Attention Deficit Hyperactivity Disorder) experience difficulty in managing attention in school, but it is not sufficiently clear what their attentional beliefs are. Drawing is a means of expression that is habitually used to access knowledge or ideas of children regarding their classroom experience. The aim of this study is to verify whether children with ADHD use pictorial indicators analogous to children without ADHD (N-ADHD). 92 primary school students participated in this study, half of whom diagnosed with ADHD. Children were asked to produce two specific thematic drawings on attention vs. inattention; their pictorial representations were analyzed using the Children's Awareness of Attention through Drawing (CAAD). The analysis showed principally that children with ADHD have a metacognitive awareness of attention similar to N-ADHD except for a delay in acquisition of the correct posture, for less maturation in the management of school materials and greater expression of negative feelings over time. Children with ADHD are aware of what is required in the school context but they are not able to pursue it. Behavioral intervention and structured learning are two targets of intervention that can help children with ADHD to adapt and to stay at school.

Inner Speech: Development, Cognitive Functions, Phenomenology, and Neurobiology

Inner speech-also known as covert speech or verbal thinking-has been implicated in theories of cognitive development, speech monitoring, executive function, and psychopathology. Despite a growing body of knowledge on its phenomenology, development, and function, approaches to the scientific study of inner speech have remained diffuse and largely unintegrated. This review examines prominent theoretical approaches to inner speech and methodological challenges in its study, before reviewing current evidence on inner speech in children and adults from both typical and atypical populations. We conclude by considering prospects for an integrated cognitive science of inner speech, and present a multicomponent model of the phenomenon informed by developmental, cognitive, and psycholinguistic considerations. Despite its variability among individuals and across the life span, inner speech appears to perform significant functions in human cognition, which in some cases reflect its developmental origins and its sharing of resources with other cognitive processes.

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.

Teaching mathematical word problem solving: the quality of evidence for strategy instruction priming the problem structure

This study examined the quality of the research base related to strategy instruction priming the underlying mathematical problem structure for students with learning disabilities and those at risk for mathematics difficulties. We evaluated the quality of methodological rigor of 18 group research studies using the criteria proposed by Gersten et al. and 10 single case design (SCD) research studies using criteria suggested by Horner et al. and the What Works Clearinghouse. Results indicated that 14 group design studies met the criteria for high-quality or acceptable research, whereas SCD studies did not meet the standards for an evidence-based practice. Based on these findings, strategy instruction priming the mathematics problem structure is considered an evidence-based practice using only group design methodological criteria. Implications for future research and for practice are discussed.

Knowing right from wrong in mental arithmetic judgments: calibration of confidence predicts the development of accuracy

Does knowing when mental arithmetic judgments are right--and when they are wrong--lead to more accurate judgments over time? We hypothesize that the successful detection of errors (and avoidance of false alarms) may contribute to the development of mental arithmetic performance. Insight into error detection abilities can be gained by examining the "calibration" of mental arithmetic judgments-that is, the alignment between confidence in judgments and the accuracy of those judgments. Calibration may be viewed as a measure of metacognitive monitoring ability. We conducted a developmental longitudinal investigation of the relationship between the calibration of children's mental arithmetic judgments and their performance on a mental arithmetic task. Annually between Grades 5 and 8, children completed a problem verification task in which they rapidly judged the accuracy of arithmetic expressions (e.g., 25 + 50 = 75) and rated their confidence in each judgment. Results showed that calibration was strongly related to concurrent mental arithmetic performance, that calibration continued to develop even as mental arithmetic accuracy approached ceiling, that poor calibration distinguished children with mathematics learning disability from both low and typically achieving children, and that better calibration in Grade 5 predicted larger gains in mental arithmetic accuracy between Grades 5 and 8. We propose that good calibration supports the implementation of cognitive control, leading to long-term improvement in mental arithmetic accuracy. Because mental arithmetic "fluency" is critical for higher-level mathematics competence, calibration of confidence in mental arithmetic judgments may represent a novel and important developmental predictor of future mathematics performance.

Problem representation and mathematical problem solving of students of varying math ability

The purpose of this study was to examine differences in math problem solving among students with learning disabilities (LD, n = 25), low-achieving students (LA, n = 30), and average-achieving students (AA, n = 29). The primary interest was to analyze the processes students use to translate and integrate problem information while solving problems. Paraphrasing, visual representation, and problem-solving accuracy were measured in eighth grade students using a researcher-modified version of the Mathematical Processing Instrument. Results indicated that both students with LD and LA students struggled with processing but that students with LD were significantly weaker than their LA peers in paraphrasing relevant information. Paraphrasing and visual representation accuracy each accounted for a statistically significant amount of variance in problem-solving accuracy. Finally, the effect of visual representation of relevant information on problem-solving accuracy was dependent on ability; specifically, for students with LD, generating accurate visual representations was more strongly related to problem-solving accuracy than for AA students. Implications for instruction for students with and without LD are discussed.