Comorbidity in Reading Comprehension and Word-Problem Solving Difficulties: Exploring Shared Risk Factors and Their Impact on Language Minority Learners

The purpose of this study was threefold: to examine unique and shared risk factors of comorbidity for reading comprehension and word-problem solving difficulties, to explore whether language minority (LM) learners are at increased risk of what we refer to as higher order comorbidity (reading comprehension and word-problem solving difficulties), and to examine the profiles of at-risk LM learners compared with at-risk non-LM learners. At-risk (LM n = 70; non-LM n = 89) and not-at-risk (LM n = 44; non-LM n = 114) students were evaluated on foundational academic (word reading, calculation), behavioral (behavioral attention), cognitive (working memory, processing speed, nonverbal reasoning), and language (vocabulary, listening comprehension) measures in English. Results indicated listening comprehension was the only shared risk factor for higher order comorbidity. Furthermore, LM learners were 3 times more likely to be identified as at-risk compared with non-LM learners. Finally, among at-risk learners, no differences were found on cognitive dimensions by language status, but LM learners had lower reading and listening comprehension skills than non-LM learners, with a relative advantage in behavioral attention. Results have implications for understanding higher order comorbidity and for developing methods to identify and intervene with higher order comorbidity among the growing population of LM learners.

Teaching Students With Mild Intellectual Disability to Solve Word Problems Using Schema-Based Instruction

This study, which used a multiple baseline across students’ design, examines the effectiveness of a modified schema-based instructional approach to improve the mathematical word problem-solving performance of three students with mild intellectual disability, two of them with autism spectrum disorder. Following the intervention, the three students improved their performance when solving addition and subtraction change word problems; however, their performance was inconsistent with change word problems. The effects of the instruction were generalized to two-step addition and subtraction word problems for the three participants. Moreover, the results were generalized to an untrained setting and were maintained 8 weeks after the instruction. The implications of these findings for teaching problem-solving skills to students with intellectual disability are discussed.

Exploring Visualisation as a Strategy for Improving Year 4 & 5 Student Achievement on Mathematics Word Problems

<p>Solving mathematics word problems is more difficult for many students than solving comparable number only problems. Given the wide use of word problems in class teaching and in assessments there is potential for students not to achieve to their full ability. This study aimed to investigate if students’ comprehension of mathematics word problems, their accuracy in choosing the correct operation, and the number of word problems solved correctly could be increased through using drawings and mental visualisation. This mixed method intervention study involved 10 Year 4 and 5 students in an inner city New Zealand school. Two separate interventions were used with different groups of five students identified as being at risk of low achievement in mathematics. Each group was involved in three intervention sessions to help with solving mathematics word problems. The first included instruction in creating drawings, and the second using mental visualisation. The study data included pre- and post-tests, verbal student reflections, and student drawings. Results showed that both groups made improvements during their interventions in the number of problems solved, the number of operations chosen correctly, and in their ability to identify and write the equation described in the word problems. Both groups also increased their achievement in number only problems. There were no significant differences between the results gained by students in the different interventions. The findings suggest that visualising word problems is an effective strategy for solving mathematics word problems and is an important step as a part of a mathematics word problem solving process. Implications for teachers include that creating representations is important for students’ understanding in mathematics and crucially, that creating both internal representations (visualisations) and external representations (drawings) can and needs to be taught for maximising achievement.</p>

Exploring Visualisation as a Strategy for Improving Year 4 & 5 Student Achievement on Mathematics Word Problems

<p>Solving mathematics word problems is more difficult for many students than solving comparable number only problems. Given the wide use of word problems in class teaching and in assessments there is potential for students not to achieve to their full ability. This study aimed to investigate if students’ comprehension of mathematics word problems, their accuracy in choosing the correct operation, and the number of word problems solved correctly could be increased through using drawings and mental visualisation. This mixed method intervention study involved 10 Year 4 and 5 students in an inner city New Zealand school. Two separate interventions were used with different groups of five students identified as being at risk of low achievement in mathematics. Each group was involved in three intervention sessions to help with solving mathematics word problems. The first included instruction in creating drawings, and the second using mental visualisation. The study data included pre- and post-tests, verbal student reflections, and student drawings. Results showed that both groups made improvements during their interventions in the number of problems solved, the number of operations chosen correctly, and in their ability to identify and write the equation described in the word problems. Both groups also increased their achievement in number only problems. There were no significant differences between the results gained by students in the different interventions. The findings suggest that visualising word problems is an effective strategy for solving mathematics word problems and is an important step as a part of a mathematics word problem solving process. Implications for teachers include that creating representations is important for students’ understanding in mathematics and crucially, that creating both internal representations (visualisations) and external representations (drawings) can and needs to be taught for maximising achievement.</p>

The Roles of Initial Mathematics, Reading, and Cognitive Skills in Subsequent Mathematics Performance: A Meta-Analytic Structural Equation Modeling Approach

In the present meta-analysis, we systematically investigated the relative contributions of students’ initial mathematics, reading, and cognitive skills on subsequent mathematics performance measured at least 3 months later. With one-stage meta-analytic structural equation modeling, we conducted analyses based on 580,437 students from 265 independent samples and 250 studies. Findings suggested fluency in both mathematics and reading, as well as working memory, yielded greater impacts on subsequent mathematics performance. Age emerged as a significant moderator in the model, such that the effects of comprehensive mathematics and working memory on subsequent mathematics increased with age, whereas attention and self-regulation’s impacts declined with age. Time lag between assessments also emerged as a significant moderator, such that the effects of word-problem solving and word recognition accuracy decreased as the time lag increased, whereas vocabulary, attention, and self-regulation’s effects increased as the time lag increased.

Analyzing Difficulties in Arithmetic Word Problem Solving: An Epistemological Case Study in Primary School

This paper focuses on difficulties that primary school students have in facing mathematical word problems. In particular, we are interested in exploring how they develop in the transition from grade 2 to grade 5. The research basis of the hypothesis is that some difficulties detected in grade 5 are already predictable in grade 2. Starting from the data collected in grade 5 by the National Standardized Assessment, we carry out a quantitative analysis looking for word problems in which students experience difficulties. Subsequently, we conduct a backward analysis of the grade 2 test of the same cohort of students in order to identify a set of word problems linked with those selected in grade 5 test. The analysis shows the presence of many common difficulties in the two grades. We design and carry out specific educational activities concerning word problem-solving in grade 2. These activities produce positive changes in the experimental class compared to the control class. This could suggest that a previous intervention in grade 2 could allow overcoming future difficulties in word problem text comprehension in grade 5.

Arithmetic Word-Problem Solving as Cognitive Marker of Progression in Pre-Manifest and Manifest Huntington’s Disease

Background: Arithmetic word-problem solving depends on the interaction of several cognitive processes that may be affected early in the disease in gene-mutation carriers for Huntington’s disease (HD). Objective: Our goal was to examine the pattern of performance of arithmetic tasks in premanifest and manifest HD, and to examine correlations between arithmetic task performance and other neuropsychological tasks. Methods: We collected data from a multicenter cohort of 165 HD gene-mutation carriers. The sample consisted of 31 premanifest participants: 16 far-from (>12 years estimated time to diagnosis; preHD-A) and 15 close-to (≤12 years estimated time to diagnosis; preHD-B), 134 symptomatic patients (early-mild HD), and 37 healthy controls (HC). We compared performance between groups and explored the associations between arithmetic word-problem solving and neuropsychological and clinical variables. Results: Total arithmetic word-problem solving scores were lower in preHD-B patients than in preHD-A (p < 0.05) patients and HC (p < 0.01). Early-mild HD patients had lower scores than preHD patients (p < 0.001) and HC (p < 0.001). Compared to HC, preHD and early-mild HD participants made more errors as trial complexity increased. Moreover, arithmetic word-problem solving scores were significantly associated with measures of global cognition (p < 0.001), frontal-executive functions (p < 0.001), attention (p < 0.001) and visual working memory (p < 0.001), mental rotation (p < 0.001), and confrontation naming (p < 0.05). Conclusion: Arithmetic word-problem solving is affected early in the course of HD and is related to deficient processes in frontal-executive and mentalizing-related processes.

Intensive Word Problem Solving for Students With Learning Disabilities in Mathematics

State exams frequently use word problems to measure mathematics performance making difficulties with word problem solving a barrier for many students with learning disabilities (LD) in mathematics. Based on meta-analytic data from students with LD, five empirically validated word-problem strategies are presented with components of model-based problem solving (MBPS) highlighted.