Remediating number combination and word problem deficits among students with mathematics difficulties: A randomized control trial.

The purposes of this study were to assess the efficacy of remedial tutoring for 3rd graders with mathematics difficulty, to investigate whether tutoring is differentially efficacious depending on students’ math difficulty status (mathematics difficulty alone vs. mathematics plus reading difficulty), to explore transfer from number combination (NC) remediation, and to examine the transportability of the tutoring protocols. At 2 sites, 133 students were stratified on mathematics difficulty status and site and then randomly assigned to 3 conditions: control (no tutoring), tutoring on automatic retrieval of NCs (i.e., Math Flash), or tutoring on word problems with attention to the foundational skills of NCs, procedural calculations, and algebra (i.e., Pirate Math). Tutoring occurred for 16 weeks, 3 sessions per week and 20–30 min per session. Math Flash enhanced fluency with NCs with transfer to procedural computation but without transfer to algebra or word problems. Pirate Math enhanced word problem skill as well as fluency with NCs, procedural computation, and algebra. Tutoring was not differentially efficacious as a function of students’ mathematics difficulty status. The tutoring protocols proved transportable across sites. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A comparison of single and multiple strategy instruction on third-grade students' mathematical problem solving.

The purposes of this study were to assess the differential effects of a single strategy (schema-based instruction; SBI) versus multiple strategies (general strategy instruction, GSI) in promoting mathematical problem solving and mathematics achievement as well as to examine the influence of word problem-solving instruction on the development of computational skills. Eighty-eight 3rd graders and their teachers were assigned randomly to conditions (SBI and GSI). Students were pre- and posttested on mathematical problem-solving and computation tests and were posttested on the Pennsylvania System of School Assessment Mathematics test, a criterion-referenced test that measures student attainment of academic standards. Results revealed SBI to be more effective than GSI in enhancing students' mathematical word problem-solving skills at posttest and maintenance. Further, results indicate that the SBI groups' performance exceeded that of the GSI group on the Pennsylvania System of School Assessment measure. On the computation test, both groups made gains over time. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

International gender × item difficulty interactions in mathematics and science achievement tests.

The author used data from the Third International Mathematics and Science Survey to examine whether Gender × Item Difficulty interactions like those in American mathematics exist in mathematics and science in 10 countries. For both mathematics and science, the author detected male advantages that were minimal on easy questions and increased as questions grew more difficult. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Relative efficacy of reciprocal and nonreciprocal peer tutoring for students at-risk for academic failure.

This study directly compared the academic gains of reciprocal peer tutoring, nonreciprocal peer tutoring, and a waiting-list control group. Participants included 59 elementary students from second-, third-, and fourth-grade classrooms who performed below average on curriculum-based measurement (CBM) math probes. Students involved in peer tutoring were trained to tutor basic math facts using a constant time delay procedure. Results indicated that the two types of peer tutoring produced comparable gains in basic math facts. Furthermore, both types of peer tutoring produced substantially larger academic gains than the waiting-list control group, demonstrating at-risk students can successfully tutor each other. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effects of small-group tutoring with and without validated classroom instruction on at-risk students' math problem solving: Are two tiers of prevention better than one?

This study assessed the effects of small-group tutoring with and without validated classroom instruction on at-risk students' math problem solving. Stratifying within schools, 119 3rd-grade classes were randomly assigned to conventional or validated problem-solving instruction (Hot Math, schema-broadening instruction). Students identified as at risk (n=243) were randomly assigned, within classroom conditions, to receive or not receive Hot Math tutoring. Students were tested on problem-solving and math applications measures before and after 16 weeks of intervention. Analyses of variance, which accounted for the nested structure of the data, revealed that the tutored students who received validated classroom instruction achieved better than the tutored students who received conventional classroom instruction (effect size=1.34). However, the advantage for tutoring over no tutoring was similar whether students received validated or conventional classroom instruction (effect sizes=1.18 and 1.13). Tutoring, not validated classroom instruction, reduced the prevalence of math difficulty. Implications for responsiveness-to-intervention prevention models and for enhancing math problem-solving instruction are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Student performance on and preferences for mathematics word problems: An investigation of the effects of explicit timing and interspersing procedures.

A within-subjects design was used to compare two instructional methods--explicit timing and interspersing--with 187 second-grade students. Students completed two mathematics word problem assignments under differing conditions. In the explicit timing condition, students were told they would be timed while working long mathematics word problems. In the interspersing condition, students were presented with brief mathematics problems between longer target mathematics word problems, but were not told they would be timed. Students then completed a preference survey. Results indicated that both assignments produced similar problem completion rates and the number of target problems and accuracy remained constant. Students reported that the explicit timing assignment required the most time and effort to complete and was the most difficult; however, there was no preference for homework choice. The significance of the current findings in relation to the explicit timing and interspersing literature, the continued need to compare two or more interventions directly, and the significance of student preference data are discussed. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

The relationship of style difficulty, practice, and ability to efficiency of reading and to retention.

Two groups of Ss, one of high and one of low mechanical ability, read a technical passage before an eye-movement camera. An "easy" style and a "hard" style passage were used, and Ss read the passage once or three times. Reading efficiency measures collected were words read per second and per fixation; retention measures were scores on modified recall and word recognition tests. The high ability group scored better on all measures than the low ability group; three readings yielded superior scores on the retention measures; and the "easy" style gave higher scores on the reading efficiency and modified recall measures. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Code-oriented instruction for kindergarten students at risk for reading difficulties: A randomized field trial with paraeducator implementers.

The purpose of this study was to evaluate the effectiveness of code-oriented supplemental instruction for kindergarten students at risk for reading difficulties. Paraeducators were trained to provide 18 weeks of explicit instruction in phonemic skills and the alphabetic code. Students identified by their teachers meeting study eligibility criteria were randomly assigned to 2 groups: individual supplemental instruction and control. Students were pretested in December, midtested, and posttested in May-June of kindergarten. At posttest, treatment students significantly outperformed controls on measures of reading accuracy, reading efficiency, oral reading fluency, and developmental spelling. Treatment students had significantly higher linear growth rates in phonemic awareness and alphabetic knowledge during the kindergarten treatment. At a 1-year follow-up, significant group differences remained in reading accuracy and efficiency. Ethical challenges of longitudinal intervention research are discussed. Findings have policy implications for making supplemental instruction in critical early reading skills available. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems.

The purpose of this study was to examine the cognitive correlates of 3rd-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Third graders (N = 312) were measured on language, nonverbal problem solving, concept formation, processing speed, long-term memory, working memory, phonological decoding, and sight word efficiency as well as on arithmetic, algorithmic computation, and arithmetic word problems. Teacher ratings of inattentive behavior also were collected. Path analysis indicated that arithmetic was linked to algorithmic computation and to arithmetic word problems and that inattentive behavior independently predicted all 3 aspects of mathematics performance. Other independent predictors of arithmetic were phonological decoding and processing speed. Other independent predictors of arithmetic word problems were nonverbal problem solving, concept formation, sight word efficiency, and language. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Mathematics attitudes and mathematics outcomes of U.S. and Belarusian middle school students.

Two multivariate studies examined the applicability of the theory of planned behavior in gauging students' attitudes toward mathematics, as well as the predictive power of mathematics attitudes in explaining students' grades in mathematics. Middle-school students from the United States (N = 382) and Belarus (N = 339) participated. Confirmatory factor analysis supported the viability of the theory for both samples. The analyses revealed that between 25% and 32% of the variance in mathematics grades could be explained by the theory of planned behavior components. In fact, 17% of the variation in test grades could be explained by the theory of planned behavior over and above the effects of mathematics ability test scores. Mean score differences between countries were small (ds = .15 to .27), with Belarusian students scoring more highly on attitudes and control but less highly on subjective norms and intentions. The article concludes with discussion of potential interventions and the need to expand results to different age groups and achievement domains, as well as the need for longitudinal and cross-cultural research. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Teaching reading to poor readers in the intermediate grades: A comparison of text difficulty.

The authors compared the influence of text difficulty--reading-level matched or grade-level matched--on the growth of poor readers' reading ability over 18 weeks of 1-to-1 tutoring. Forty-six 3rd-5th graders, including 25 with disabilities, were assigned randomly to 1 of 2 tutoring approaches or a control condition. Significant differences favored tutored children. Between approaches, the only significant difference was oral reading fluency, which favored students who read material at their reading level. Students who began with lower fluency made stronger gains in text matched to reading level; students with higher fluency profited from both treatments. When the 3 groups were combined, fluency was the strongest contributor to reading comprehension outcomes. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities?

The purpose of this study was to examine the interplay between basic numerical cognition and domain-general abilities (such as working memory) in explaining school mathematics learning. First graders (N = 280; mean age = 5.77 years) were assessed on 2 types of basic numerical cognition, 8 domain-general abilities, procedural calculations, and word problems in fall and then reassessed on procedural calculations and word problems in spring. Development was indexed by latent change scores, and the interplay between numerical and domain-general abilities was analyzed by multiple regression. Results suggest that the development of different types of formal school mathematics depends on different constellations of numerical versus general cognitive abilities. When controlling for 8 domain-general abilities, both aspects of basic numerical cognition were uniquely predictive of procedural calculations and word problems development. Yet, for procedural calculations development, the additional amount of variance explained by the set of domain-general abilities was not significant, and only counting span was uniquely predictive. By contrast, for word problems development, the set of domain-general abilities did provide additional explanatory value, accounting for about the same amount of variance as the basic numerical cognition variables. Language, attentive behavior, nonverbal problem solving, and listening span were uniquely predictive. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The effect of word frequency, word predictability, and font difficulty on the eye movements of young and older readers.

Young adult and older readers' eye movements were recorded as they read sentences containing target words that varied in frequency or predictability. In addition, half of the sentences were printed in a font that was easy to read (Times New Roman) and the other half were printed in a font that was more difficult to read (Old English). Word frequency, word predictability, and font difficulty effects were apparent in the eye movement data of both groups of readers. In the fixation time data, the pattern of results was the same, but the older readers had larger frequency and predictability effects than the younger readers. The older readers skipped words more often than the younger readers (as indicated by their skipping rate on selected target words), but they made more regressions back to the target words and more regressions overall. The E-Z Reader model was used as a platform to evaluate the results, and simulations using the model suggest that lexical processing is slowed in older readers and that, possibly as a result of this, they adopt a more risky reading strategy. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Task engagement and mathematics performance in children with attention-deficit hyperactivity disorder: Effects of supplemental computer instruction.

Examined the effects of using software with a game format (as a supplement to teacher instruction) to improve math performance of 3 male 4th- to 6th-grade students with attention-deficit hyperactivity disorder. Following baseline (observation under normal classroom conditions), the math software was introduced sequentially using a multiple baseline design across participants. Observational data were collected during the baseline and experimental conditions along with a set of curriculum-based math probes, which were used throughout the study. The hypothesis that math software with a game format would improve the academic performance and increase attention of all participants was partially supported. Implications for practice and further research are discussed. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Contribution of spelling instruction to the spelling, writing, and reading of poor spellers.

The contribution of supplemental spelling instruction to spelling, writing, and reading was examined. Second-grade children experiencing difficulties learning to spell participated in 48 20-min sessions designed to improve their spelling skills. In comparison with peers in a contact control condition receiving mathematics instruction, students in the spelling condition made greater improvements on norm-referenced spelling measures, a writing-fluency test, and a reading word-attack measure following instruction. Six months later, students in the spelling treatment maintained their advantage in spelling but not on the writing-fluency and reading word-attack measures. However, spelling instruction had a positive effect at maintenance on the reading word-recognition skills of children who scored lowest on this measure at pretest. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Functional disruption of the brain mechanism for reading: Effects of comorbidity and task difficulty among children with developmental learning problems.

Objective: The study investigated the relative degree and timing of cortical activation associated with phonological decoding in poor readers. Method: Regional brain activity was assessed during performance of a pseudoword reading task and a less demanding, letter-sound naming task by three groups of students: children who experienced reading difficulties without attention problems (N = 50, RD) and nonreading impaired (NI) readers either with (N = 20) or without attention-deficit/hyperactivity disorder (ADHD; N = 50). Recordings were obtained with a whole-head neuromagnetometer, and activation profiles were computed through a minimum norm algorithm. Results: Children with RD showed decreased amplitude of neurophysiological activity in the superior temporal gyrus, bilaterally, and in the left supramarginal and angular gyri during late stages of decoding, compared to typical readers. These effects were restricted to the more demanding pseudoword reading task. No differences were found in degree of activity between NI and ADHD students. Regression analyses provided further support for the crucial role of left hemisphere temporoparietal cortices and the fusiform gyrus for basic reading skills. Conclusions: Results were in agreement with fMRI findings and replicate previous MEG findings with a larger sample, a higher density neuromagnetometer, an overt pseudoword reading task, and a distributed current source-modeling method. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

The nature of teachers' pedagogical content beliefs matters for students' achievement gains: Quasi-experimental evidence from elementary mathematics.

In a longitudinal study of 496 students in 27 self-contained German elementary school classrooms, performance in mathematical word problems and arithmetic tasks was measured at the end of Grades 2 and 3. A questionnaire was used to assess the degree to which teachers' pedagogical content beliefs in elementary mathematics reflect a cognitive constructivist orientation, rather than an associationist or direct-transmission view of learning and teaching. Our findings show that a cognitive constructivist orientation was associated with larger achievement gains in mathematical word problems. Moreover, teachers with a direct transmission view were not more successful than teachers with a cognitive constructivist orientation in fostering students' computational proficiency. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A meta-analysis of writing instruction for adolescent students.

There is considerable concern that the majority of adolescents do not develop the competence in writing they need to be successful in school, the workplace, or their personal lives. A common explanation for why youngsters do not write well is that schools do not do a good job of teaching this complex skill. In an effort to identify effective instructional practices for teaching writing to adolescents, the authors conducted a meta-analysis of the writing intervention literature (Grades 4-12), focusing their efforts on experimental and quasi-experimental studies. They located 123 documents that yielded 154 effect sizes for quality of writing. The authors calculated an average weighted effect size (presented in parentheses) for the following 11 interventions: strategy instruction (0.82), summarization (0.82), peer assistance (0.75), setting product goals (0.70), word processing (0.55), sentence combining (0.50), inquiry (0.32), prewriting activities (0.32), process writing approach (0.32), study of models (0.25), grammar instruction (- 0.32). (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Enhancing assignment perceptions in students with mathematics learning disabilities by including more work: An extension of interspersal research.

Active student responding is often required to remedy computation skill deficits in students with learning disabilities. However, these students may find computation assignments unrewarding and frustrating, and be less likely to choose to engage in assigned computation tasks. In the current study, middle school students with learning disabilities worked on control assignments containing 15 four-digit minus four-digit target computation problems and interspersal assignments containing 15 similar problems and five additional one-digit minus one-digit problems. Results showed that interspersing the brief problems did not reduce target problem accuracy levels or opportunities to respond to target problems. Students did complete more total problems (i.e., target and single-digit problems) on the interspersal assignment. Even though the interspersal assignment contained more work, significantly more students rated it as requiring less effort to complete and selected it for homework. Discussion focuses on applied implications, causal mechanisms, and future research related to the interspersal procedure and the discrete task completion hypothesis. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

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

Current mathematics instruction does not address the day-to-day needs of many students with learning disabilities. Although the vast majority of students with learning disabilities are not college bound, much of mathematics instruction provides college preparation. Too often, classes in mathematics ignore the skills needed in home and community and on the job. The present article examines the ways in which general mathematics instruction, focused on daily living skills, can easily be integrated into the classrooms of students with learning disabilities.