A life skills approach to mathematics instruction: preparing students with learning disabilities for the real-life math demands of adulthood

Maintenance in Mathematics for Individuals with Intellectual Disability: A Systematic Review of Literature

Despite the growing attention being paid to teaching mathematics for students with disabilities, the existing research tends to focus on mathematical skill acquisition, but not on skill maintenance. The researchers in this study reviewed all studies from 1975 to 2018 that involved teaching mathematics to individuals with intellectual disability. A total of 135 studies met inclusion criteria, but only 53 studies involved a maintenance phase (39.2%). Among the 53 studies, only 22 were included for the final analysis, after evaluating their methodological rigor. In those 22 studies, there was no consensus among researchers on the standards for conducting a maintenance phase (i.e., latency between intervention and maintenance phases, length of maintenance phase, number of maintenance sessions). Further, in the studies which included a maintenance phase, the most widely taught mathematical content was numbers and operations. All studies employed intervention packages which included more than one instructional method and/or materials and the most widely used instructional method was prompting while the most widely used instructional materials were visual supports and manipulatives. The results suggest that prompting is an evidence-based practice for individuals with intellectual disability in supporting maintenance, while explicit instruction, time delay, feedback, and instructional sequence (e.g., the virtual-representational-abstract instructional sequence) are potentially evidence-based practice for individuals with intellectual disability.

Comparing the effectiveness of two app-based number lines to teach price comparison to students with autism spectrum disorders

PURPOSE

A number line consisting of Arabic numerals is a commonly used instructional tool for teaching price comparison. However, typical number lines lack concrete visual cues, which may benefit students with autism spectrum disorders (ASD) who have not yet mastered the representation of Arabic numerals.

METHOD

This study investigated the effects of additional visual cues (i.e., dots) by comparing two types of app-based number line conditions: number lines with and without dots. A single-subject, alternating treatment design study was employed across five secondary students with ASD.

RESULTS

Both number line conditions were effective for four of the students in assisting them to select cheaper items and complete task analysis steps. The number line with dots was effective or slightly more effective in selecting smaller numbers for three of the students.

CONCLUSIONS

The findings of this study support the literature on the use of number lines as an effective tool to assist students in price comparison. The benefits of adding concrete visual cues and other teaching strategies (e.g., the holistic and decomposition models) were discussed. Implications for Rehabilitation This study investigated the effectiveness of concrete visual cues, such as dots, on a number line app for teaching students with ASD who had not yet developed the association of quantities with the numerals. We found that incorporation of a hybrid number comparison model - first holistic (for whole numbers) and then decomposition (for numbers after the decimal point) - is effective when teaching students how to compare prices with an uneven number of digits. This study provides an alternative for special education teachers to schedule practice, such as the use of simulated settings to achieve mastery, then transitioning to community-based settings to test skill generalization.

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.

[Symptoms diagnosis and treatment of dyscalulia]

Children with dyscalculia show deficits in basic numerical processing which cause difficulties in the acquisition of mathematical skills. This article provides an overview of current research findings regarding the symptoms, cause, and prognosis of dyscalculia, and it summarizes recent developments in the diagnosis, early intervention, and treatment thereof. Diagnosis has improved recently because newly developed tests focus not only on the math curriculum, but also on basic skills found to be impaired in dyscalculia. A controversial debate continues with regard to IQ achievement discrepancy. International studies have demonstrated the effectiveness of specialized interventions. This article summarizes the research findings from intervention studies, describes different treatment approaches, and discusses implications for clinical practice.

The Academic and Functional Academic Skills of Youth Who Are at Risk for Language Impairment in Residential Care

Purpose

Undiagnosed language impairment (LI) for youth in residential care is a concern as similar populations have shown elevated levels of language delays. Therefore, the purposes of this study were to identify the percentage of youth in residential care who are at risk for LI and to compare the demographic, academic achievement, and functional academic skills of youth with or without possible LI.

Method

Participants were 80 youth in residential care. Risk for LI was determined using the Clinical Evaluation of Language Fundamentals—4 Screening Test (E. Semel, E. H. Wiig, & W. A. Secord, 2004). Independent-samples t tests and chi-square analyses were conducted to assess the differences between groups. Measures used included the Woodcock-Johnson Test of Achievement (R. W. Woodcock, K. S. McGrew, & N. Mather, 2001) and the Kaufman Functional Academic Skills Test (A. S. Kaufman & N. L. Kaufman, 1994).

Results

More than half of the sample (54%) were identified as being at risk for LI. Statistically significant differences between youth with and without LI were found on academic variables. Specifically, youth who were at risk for LI presented academic achievement and functional academic scores in the low to low-average ranges.

Conclusion

Findings suggest that there is a need to screen youth entering residential programs for possible LI. Implications for treatment and program planning are discussed.

Solving arithmetic word problems: an analysis of classification as a function of difficulty in children with and without arithmetic LD

This study was designed to determine a word problem difficulty classification in children with arithmetic learning disabilities (ALD; n = 104) in comparison with typically achieving students (n = 44). We tested variables such as (a) semantic structure (Change, Combine, Compare, and Equalize), (b) operation (subtraction and addition), and (c) position of the unknown quantity in the problem. Facet theory with multidimensional scaling techniques (MINISSA) was used to analyze the underlying dimensions in the responses of each group of participants. Our results indicate that although the word problem difficulty classifications for the 2 groups of children were different, the position of the unknown quantity had a greater influence on the level of difficulty of story problems than other variables. The noncanonical problems--specifically, those with the unknown term in the first place--although difficult for both groups of children, were the most difficult problems for children with ALD.

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.