Subtypes of mathematical learning disability and their antecedents: A cognitive diagnostic approach

Using cognitive diagnostic modeling (CDM), this study identified subtypes of mathematics learning disability (MLD) based on children's numerical skills and examined the language and spatial precursors of these subtypes. Participants were 99 MLD children and 420 low achievers identified from 1839 Finnish children (966 boys) who were followed from preschool (age 6) to fourth grade (2007–2011). Five subtypes were identified: the arithmetic fluency deficit only subtype, the counting deficit subtype, the pervasive deficit subtype, the symbolic deficit subtype, and the counting and concept deficit subtype. Different subtypes depended on different constellations of language and spatial deficits. Findings highlight the effectiveness of CDM in identifying MLD subtypes and underscore the importance of understanding the specific deficits and antecedents of the subtypes.     

Scale and the evolutionarily based approximate number system: an exploratory study

ABSTRACT

Crosscutting concepts such as scale, proportion, and quantity are recognised by U.S. science standards as a potential vehicle for students to integrate their scientific and mathematical knowledge; yet, U.S. students and adults trail their international peers in scale and measurement estimation. Culturally based knowledge of scale such as measurement units may be built on evolutionarily-based systems of number such as the approximate number system (ANS), which processes approximate representations of numerical magnitude. ANS is related to mathematical achievement in pre-school and early elementary students, but there is little research on ANS among older students or in science-related areas such as scale. Here, we investigate the relationship between ANS precision in public school U.S. seventh graders and their accuracy estimating the length of standard units of measurement in SI and U.S. customary units. We also explored the relationship between ANS and science and mathematics achievement. Accuracy estimating the metre was positively and significantly related to ANS precision. Mathematics achievement, science achievement, and accuracy estimating other units were not significantly related to ANS. We thus suggest that ANS precision may be related to mathematics understanding beyond arithmetic, beyond the early school years, and to the crosscutting concepts of scale, proportion, and quantity.     

Visualising weekly learning outcomes (VWLO) and the intention to continue using a learning management system (CIU): the role of cognitive absorption and perceived learning self-regulation

Education and Information Technologies - This research, using goal setting theory, proposes a new educational intervention to improve the perceptions of a Learning management System (LMS) as an...     

Changes of interaction during the development of a mathematical learning environment

Two research questions are answered: how did teacher instructional skills develop during a whole school year? What is the influence of this development on the interactions between students during the co-operative learning moments? From the analysis, it appeared that the teachers’ instruction changed from direct instruction to a more process and group-oriented coaching style, and that students started to work collaboratively, using the graphic calculator in an exploratory and investigative manner. This more process and group-oriented coaching style may have supported the change in the interaction pattern during this school year. The analysis showed that students gradually developed a more exploratory way of collaborating, confirming improved collaborative learning. At the commencement of the school year, students were focused on each other and did not argue much, while at the end, they were discussing with one another.     

Metacognitive skills in Belgian third grade children (age 8 to 9) with and without mathematical learning disabilities

This paper presents a study on mathematical problem solving in third-grade pupils. The relationship between mathematics, metacognition and intelligence was investigated in children with (n = 191) and without mathematical learning disabilities (n = 268). A significant relationship was found between prediction, evaluation, intelligence, procedural and mathematical fact retrieval skills in children without mathematical learning disabilities. In the children with mathematical learning disabilities a relationship was found between metacognitive and procedural skills. No such relationship was found between intelligence and metacognition or between metacognition and mathematical fact retrieval skills. In addition it was investigated if children with mathematical learning disabilities had less adequate metacognitive skills than peers without learning problems. At group level significant differences were found between both groups. However on analyzing these results further, it was found that four out of five children with combined mathematical learning disabilities, half of the children with procedural disabilities and only 5% of the children with a retrieval deficiency had low metacognitive skills. Furthermore, metacognitive problems were found in one out of five children without learning disabilities. Moreover, a majority of the children with mathematical learning disabilities and inadequate metacognitive skills had problems with prediction and evaluation skills. Most third graders with low metacognitive skills only appeared to have problems predicting the level of difficulty of tasks. Inaccurate evaluations were found on a more regular basis in children with mathematical learning disabilities and inadequate metacognitive skills as opposed to the sample of children with inadequate metacognitive skills but without learning difficulties, where their occurrence was rather a one off. The implications of this study for diagnosis and treatment will be discussed later in this paper.     

Cognitive characteristics of children with mathematics learning disability (MLD) vary as a function of the cutoff criterion used to define MLD

Researchers of mathematics learning disability (MLD) commonly use cutoff scores to determine which participants have MLD. Some researchers apply more restrictive cutoffs than others (e.g., performance below the 10th vs. below the 35th percentile). Different cutoffs may lead to groups of children that differ in their profile of math and related skills, including reading, visual-spatial, and working memory skills. The present study assesses the characteristics of children with MLD based on varying MLD definitions of math performance either below the 10th percentile (n = 22) or between the 11th and 25th percentile (n = 42) on the Test of Early Math Ability, second edition (TEMA-2). Initial starting levels and growth rates for math and related skills were examined in these two MLD groups relative to a comparison group (n = 146) whose TEMA-2 performance exceeded the 25th percentile. Between kindergarten and third grade, differences emerged in the starting level and growth rate, suggesting qualitative differences among the three groups. Despite some similarities, qualitative group differences were also observed in the profiles of math-related skills across groups. These results highlight differences in student characteristics based on the definition of MLD and illustrate the value of examining skill areas associated with math performance in addition to math performance itself.     

Role of cognitive theory in the study of learning disability in mathematics

Gersten, Jordan, and Flojo (in this issue) provide the beginnings of an essential bridge between basic research on mathematical disabilities (MD) in young children and the application of this research for the early identification and remediation of these forms of learning disability. As they acknowledge, the field of MD is in the early stages of development, and thus recommendations regarding identification measures and remedial techniques must be considered preliminary. I discuss the importance of maintaining a tight link between theoretical and empirical research on children's developing numerical, arithmetical, and mathematical competencies and future research on learning disabilities in mathematics. This link will provide the foundation for transforming experimental procedures into assessment measures, understanding the cognitive strengths and weaknesses of children with these forms of learning disability, and developing remedial approaches based on the pattern of cognitive strengths and weaknesses for individual children.     

高等数学概念学习应注重规律

通过大量例子说明学习高等数学概念时应从概念引入、概念理解、概念应用、概念巩固诸方面注重规律.     

职业院校在组织学习过程中的障碍及其消除

办学环境的复杂变化使得组织学习成为职业院校办学过程中的重要环节．但职业院校在组织学习中并不是一帆风顺的。存在着各种各样的学习障碍。本文分析了职业院校组织学习的过程、每个阶段的学习障碍及障碍消除的策略。     

A rapid screening measure for the identification of visuospatial learning disability in schools

Verbal and nonverbal forms of developmental learning disabilities have been reported. Whereas there are several instruments for evaluating children for the presence of verbal learning disabilities at school, no screening tool is available to identify children who have nonverbal learning disabilities. This study aimed at devising and validating a short screening questionnaire that can be used by teachers in primary schools to identify those children who need to be referred for clinical services because they have a visuospatial learning disability (VSLD). An 18-item Shortened Visuospatial Questionnaire (SVS) was derived from an earlier, longer version. Its validation procedure was twofold and was achieved by (a) verifying that children who had been identified with the SVS questionnaire as having a VSLD actually showed visuospatial deficits on psychometric evaluation and by (b) rating with the SVS a clinically identified population of children with VSLD. The results of the validation procedure showed that the SVS is a quick, reliable, and valid instrument that may be helpful in identifying children with VSLD in primary school.     

20年来国内学习困难学生研究综述

学习困难问题是近20年来国内外心理学者研究的一个热点问题，如何提高这一类学生的学习能力具有重要意义。该文叙述了我国近年来有关学习困难研究的主要特点和主要研究领域，包括学习困难的界定和类型、学习困难的心理特点以及教育干预等方面的成果，在此基础上提出了未来研究要解决的问题。     

级数理论的知识体系和数学方法

主要针对高等数学中的级数理论,阐述它的知识体系与常用的数学方法.     

Interactive response system (IRS) for college students: individual versus cooperative learning

In this study, the researcher aimed to understand how students learned the targeted knowledge with an interactive response system (IRS) tool, and whether learners in two different learning modes: individual and group use of IRS, differed in their learning performance and knowledge retention after the IRS activity. These two kinds of IRS interaction were integrated into the course which included multiple choice questions for testing memorable knowledge and open-ended questions for enhancing organization and critical thinking ability via a methodology that involved 120 college students and included the analysis of tests, survey questionnaires and a course learning diary. Overall, the results were consistent with the consensus that students perceive the IRS as a positive addition to their classes, as its use increased course participation, fostered interaction, and promoted the general enjoyment of the class. The results revealed that the immediate learning performance of the learners who participated in the activity through group use of the IRS was better than that of the learners with individual IRS accounts; however, the individual IRS users seemed to have better learning retention of the learning contents, and showed significant improvement on the delayed tests. Furthermore, the study also confirmed that the IRS with collaborative work could promote the students’ academic and social-emotional performance because the collaborative learning allowed them to learn from peers’ opinions and to make judgments and co-examine the learning concepts again while finding the correct answer. This paper contributes data and analysis that highlight the pedagogical benefits of the implementation of an IRS, and supports the value of using the IRS for college education.