Mathematics education and students with learning disabilities: introduction to the special series

A Structural Equation Modeling of the Relationships Between Parenting Styles, Students' Personality Traits, and Students' Achievement Goal Orientation

Recently, researchers have shown an increased interest in achievement goal orientation correlates. What is not yet clear is the detailed relationships among students' goal orientation, students' personality traits, and parenting style. In so doing, this research responds to the need to analyze the importance of parenting styles (permissive, authoritative, and authoritarian) and students' traits (psychoticism, neuroticism, and extraversion) in explaining the achievement goal orientations (mastery approach, mastery avoidance, performance-approach, and performance-avoidance). In the exploratory correlational study, 586 Iranian students along with their parents were selected as the sample so as to evaluate the structure of the relationships between these variables. The results indicate that students' psychoticism and neuroticism predict students' goal orientations (positively: performance and mastery avoidance and negatively: mastery and performance approach) while extraversion did not. Only the authoritative style predicts mastery approach (positively) and psychoticism trait (negatively). Permissive and authoritarian styles do not directly or indirectly predict students' goal orientations.

Adaptive entropy theory polymerization method for path optimization in edge computing educational systems

In this paper, through the edge computing application path, the educational evaluation system was optimized using the adaptive entropy theory polymerization method which based on applying the path. By adding multiple constraints to filter out nodes and educational evaluation edges that do not meet the requirements, the improved algorithm is used to optimize the redundant paths to avoid loops and node detour problem. To improve the accuracy of education evaluation and evaluation, ensure the load balance in the domain, and solve the problems of single evaluation attribute and high overlap of education evaluation paths. This paper proposes a multi-attribute education evaluation model that refines the evaluation attributes of education evaluation and uses analytic hierarchy process perform weight distribution. The algorithm can improve the accuracy of the evaluation of the education evaluation system while ensuring the computational efficiency, and can ensure the load balance within the domain, and improve the network survival time.

Comparison of opportunities to respond and generation effect as potential causal mechanisms for incremental rehearsal with multiplication combinations

Incremental rehearsal (IR) is an intervention with demonstrated effectiveness in increasing retention of information, yet little is known about how specific intervention components contribute to the intervention's effectiveness. The purpose of this study was to further the theoretical understanding of the intervention by comparing the effects of opportunities to respond (OTR) and generation demand on retention of multiplication combinations. Using a between subject 2 × 2 factorial design, 103 4th and 5th grade students were taught seven multiplication combinations using one of four versions of IR that orthogonally varied OTR (high versus low) and generation demands (high versus low). A two-way ANOVA revealed main effects for OTR, generation demands, and an interaction of the two factors. The effect of generation demands was large (d=1.31), whereas the overall effect of OTR was moderate (d=0.66). Critically, the two factors interacted, with the largest learning gains observed when OTR and generation demands were both high. The results of this study suggest that generation demand is an important factor in the effectiveness of rehearsal interventions.

Comparison of a math fact rehearsal and a mnemonic strategy approach for improving math fact fluency

The current study used a randomized controlled trial to compare the effects of a practice-based intervention and a mnemonic strategy intervention on the retention and application of single-digit multiplication facts with 90 third- and fourth-grade students with math difficulties. Changes in retention and application were assessed separately using one-way ANCOVAs in which students' pretest scores were included as the covariate. Students in the practice-based intervention group had higher retention scores (expressed as the total number of digits correct per minute) relative to the control group. No statistically significant between-group differences were observed for application scores. Practical and theoretical implications for interventions targeting basic multiplication facts are discussed.

The effects of computer-assisted instruction on the mathematics performance and classroom behavior of children with ADHD

The present study examines the effects of computer-assisted instruction (CAI) on the mathematics performance and classroom behavior of three second-through fourth-grade students with ADHD. A controlled case study is used to evaluate the effects of the computer software on participants' mathematics performance and on-task behavior. Participants' mathematics achievement improve and their on-task behavior increase during the CAI sessions relative to independent seatwork conditions. In addition, students and teachers consider CAI to be an acceptable intervention for some students with ADHD who are having difficulty with mathematics. Implications of these results for practice and research are discussed.

Learning difficulties in numeracy in Australia

In this article, we provide an understanding of the term numeracy as it is used in Australia and a description of numeracy education in this country. In particular, we discuss the role of outcomes-based curriculum frameworks and outline the dominant teaching approaches. The focus is on students with learning difficulties and how they are identified and supported in schools. We create two vignettes based on real students with difficulties in numeracy, which highlight two of the most common problems. We report on the prevalence of learning difficulties in numeracy in Australia and describe some of the initiatives related to the assessment and enhancement of learning in numeracy that are being undertaken in various states in Australia. Finally, we identify some of the future challenges facing the Australian education system in this area. These challenges relate to teacher knowledge, mandated assessment, and the role of parents. We conclude the article by calling for the evaluation of current assessment and intervention initiatives as well as the development of a national program to support the goal of numeracy for all students.

Mathematics education in the United States: past to present

This article presents a historical review of mathematics education since the late 1950s in the United States. Three themes are used to organize the literature reviewed in the article: (a) broad sociopolitical forces, particularly highly publicized educational policy statements; (b) trends in mathematics research; and (c) theories of learning and instruction. At times, these themes coincide, as was the case in the 1990s. In other cases, such as the recent push for educational accountability, these themes conflict. Nonetheless, the themes go a long way to explain the serpentine nature of reform in the United States over the last 45 years. This article also attempts to account for developments in special education as well as general education research, something that does not appear in most historical presentations of mathematics education.

A Critical Analysis of Grade 3 Testing in Ontario

The recent re-introduction of province-wide group achievement testing in Ontario has placed new demands, challenges, and some stresses on students, parents, and teachers. As consultants, school psychologists are in a position to meet these challenges because of their advanced knowledge about standardized testing and their knowledge of what can be reasonably expected from students based on the students' cognitive development. This paper uses multiple perspectives to evaluate the Grade 3 Assessment, with the main focus on the degree to which the items reflect current curriculum guidelines. We also examine whether the demands placed on the children are consistent with what we know about the cognitive development of 8-9 year-old-children. Although the Grade 3 Assessment is based on the Ontario Curriculum (1997), many items exceed what should be expected from a typical Grade 3 student when children's cognition is considered. Given the political implications of province-wide testing, tests need to be impeccably constructed. This analysis is intended to provide school psychologists with a framework for disseminating information about the value and limitations of the Grade 3 Assessment.

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

Mathematics learning disabilities (LD) have gained increased attention over the last decade from both researchers and practitioners. A large percentage of students receiving learning disability services experience difficulties with mathematics, but little research has examined the specific mathematics behaviors of students with LD who have teacher-identified math weaknesses. This study examines the literature on mathematics LD and identifies specific behaviors from that body of research for the purpose of determining the extent to which those behaviors are observed in students with LD. Data are presented from observations of 391 special education professionals on 1724 students with LD, 870 of whom had identified math weaknesses and 854 of whom did not. Our results validate the existing literature and provide implications for teachers, researchers, and others interested in studying mathematics LD.

Arithmetic calculation, short-term memory, and language performance in children with specific language impairment: a 5-year follow-up

A 5-year follow-up of the arithmetic calculation abilities of low-income children with specific language impairment (SLI) is reported. The performance of fourth- and fifth-grade children with SLI was compared with that of typically developing low-income peers and with younger, typically developing low-income children. Short-term memory, language, and arithmetic calculation abilities were assessed. Compared to their age-matched peers, the SLI group exhibited low scores on a number recall task, a marked difficulty with mathematical calculation under timed conditions, and numerous errors when retrieving rote math facts such as 7 x 6 =. Although children with SLI made more written calculation errors than their age-matched peers, they did not differ in the type of errors made. However, strategies used to solve written calculation differed among the groups. Rather than use automatic math fact retrieval, children with SLI were more likely to use counting strategies to solve calculation problems. These findings offer further evidence that children with SLI have difficulty with rote memory. The findings also document the real-world consequences of slow, inefficient memory retrieval in children with SLI.