Carol L. Hamlett

The Prevention, Identification, and Cognitive Determinants of Math Difficulty.

This study examined the efficacy of preventive 1st-grade tutoring in mathematics, estimated the prevalence and severity of mathematics disability, and explored pretreatment cognitive characteristics associated with mathematics development. Participants were 564 first graders, 127 of whom were designated at risk (AR) for mathematics difficulty and randomly assigned to tutoring or control conditions. Before treatment, all participants were assessed on cognitive and academic measures. Tutoring occurred 3 times weekly for 16 weeks; treatment fidelity was documented; and math outcomes were assessed. Tutoring efficacy was supported on computation and concepts/applications, but not on fact fluency. Tutoring decreased the prevalence of math disability, with prevalence and severity varying as a function of identification method and math domain. Attention accounted for unique variance in predicting each aspect of end-of-year math performance. Other predictors, depending on the aspect of math performance, were nonverbal problem solving, working memory, and phonological processing.

Explicitly Teaching for Transfer: Effects on Third-Grade Students' Mathematical Problem Solving.

The purpose of this study was to assess the effects of explicitly teaching for transfer by (a) broadening the categories by which students group problems requiring the same solution methods and (b) prompting students to search novel problems for these broad categories. This transfer treatment was combined with instruction on solution methods. The effectiveness of a combined treatment (transfer-plus-solution instruction) was contrasted to solution instruction alone and to teacher-designed instruction. Twenty-four 3rd-grade teachers, with 375 students, were assigned randomly to conditions. Treatments were conducted for 16 weeks. Improvement on immediate- and near-transfer measures supported the utility of solution instruction. Improvement on near- and far-transfer measures revealed the added contribution of explicitly teaching for transfer. (PsycINFO Database Record (c) 2016 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.

Problem Solving and Computational Skill: Are They Shared or Distinct Aspects of Mathematical Cognition?.

The purpose of this study was to explore patterns of difficulty in 2 domains of mathematical cognition: computation and problem solving. Third graders (n = 924; 47.3% male) were representatively sampled from 89 classrooms; assessed on computation and problem solving; classified as having difficulty with computation, problem solving, both domains, or neither domain; and measured on 9 cognitive dimensions. Difficulty occurred across domains with the same prevalence as difficulty with a single domain; specific difficulty was distributed similarly across domains. Multivariate profile analysis on cognitive dimensions and chi-square tests on demographics showed that specific computational difficulty was associated with strength in language and weaknesses in attentive behavior and processing speed; problem-solving difficulty was associated with deficient language as well as race and poverty. Implications for understanding mathematics competence and for the identification and treatment of mathematics difficulties are discussed.

Effects of Expert System Consultation within Curriculum-Based Measurement, Using a Reading Maze Task

This study assessed the effects of expert system instructional consultation within curriculum-based measurement (CBM). Thirty-three special educators and 63 students with mild to moderate disabilities were assigned randomly to three groups: CBM with expert system instructional consultation (CBM-ES). CBM with no consultation (CBM-NES), and control (i.e., no CBM). CBM teachers implemented a CBM system for 17 weeks. Analyses indicated that students in both CBM groups achieved better than the control group on several key reading outcome measures, assessing fluency and comprehension. However, the CBM-ES teachers planned more diverse instructional programs than did the CBM-NES teachers, and their students achieved better than the CBM-NES and control students on an outcome measure requiring written recalls.

Mathematics Screening and Progress Monitoring at First Grade: Implications for Responsiveness to Intervention:

The predictive utility of screening measures for forecasting math disability (MD) at the end of 2nd grade and the predictive and discriminant validity of math progress-monitoring tools were assessed. Participants were 225 students who entered the study in 1st grade and completed data collection at the end of 2nd grade. Screening measures were Number Identification/Counting, Fact Retrieval, Curriculum-Based Measurement (CBM) Computation, and CBM Concepts/Applications. For Number Identification/Counting and CBM Computation, 27 weekly assessments were also collected. MD was defined as below the 10th percentile at the end of 2nd grade on calculations and word problems. Logistic regression showed that the 4-variable screening model produced good and similar fits in accounting for MD—calculation and MD—word problems. Classification accuracy was driven primarily by CBM Concepts/Applications and CBM Computation; CBM Concepts/Applications was the better of these predictors. CBM Computation, but not Number Identification/Counting, demonstrated validity for progress monitoring.

Effects of Preventative Tutoring on the Mathematical Problem Solving of Third-Grade Students with Math and Reading Difficulties:

This study assessed the effects of preventative tutoring on the math problem solving of third-grade students with math and reading difficulties. Students (n = 35) were assigned randomly to continue in their general education math program or to receive secondary preventative tutoring 3 times per week, 30 min per session, for 12 weeks. Schema-broadening tutoring taught students to (a) focus on the mathematical structure of 3 problem types; (b) recognize problems as belonging to those 3 problem-type schemas; (c) solve the 3 word-problem types; and (d) transfer solution methods to problems that include irrelevant information, 2-digit operands, missing information in the first or second positions in the algebraic equation, or relevant information in charts, graphs, and pictures. Also, students were taught to perform the calculation and algebraic skills foundational for problem solving. Analyses of variance revealed statistically significant effects on a wide range of word problems, with large effect sizes. Findings support the efficacy of the tutoring protocol for preventing word-problem deficits among third-grade students with math and reading deficits.

Classwide Curriculum-Based Measurement: Helping General Educators Meet the Challenge of Student Diversity

This study examined the effectiveness of innovative curriculum-based measurement (CBM) classwide decision-making structures within general education mathematics instruction, with and without recommendations for how to incorporate CBM feedback into instructional planning. Forty general educators, each of whom had at least one student with an identified learning disability for math instruction, were randomly assigned to three groups: CBM with classwide reports that summarized information and provided instructional recommendations, CBM with reports but without recommendations, and contrast (no CBM). Results indicated that only the CBM teachers who received instructional recommendations designed better instructional programs and effected greater achievement for their students.

Effects of Alternative Goal Structures within Curriculum-Based Measurement

This study assessed the effects of alternative goal structures within curriculum-based measurement (CBM) in the area of math. Subjects were 30 special education teachers, assigned randomly to a dynamic goal CBM, static goal CBM, or control group for 15 weeks. Each teacher selected two mildly or moderately handicapped pupils for participation. Analyses of variance conducted on fidelity of treatment measures indicated that dynamic goal teachers increased goals more frequently and, by the studys completion, employed more ambitious goals. Multivariate analyses of covariance indicated that students in the dynamic goal group had better content mastery than did control students, whereas students in the static goal group did not. Content coverage for the three groups was comparable. Implications for special education goal-setting practice are discussed.

Monitoring Reading Growth Using Student Recalls: Effects of Two Teacher Feedback Systems

AbstractThe purpose of this study was to compare two types of teacher feedback, using an ongoing measurement system that involved students’ performance on a reading recall task. Twenty-two teachers were assigned randomly to two treatment groups. In the performance indicator feedback group, teachers received graphs that displayed students’ total number of content words retold over time; in the performance indicator with qualitative feedback group, teachers received graphs along with a structured analysis of the story components students included in their recalls. Teachers used the monitoring systems for 15 weeks, with 41 students with reading problems. Multivariate analyses of covariance indicated that teachers in the performance indicator with qualitative feedback group wrote more specific instructional plans and effected better growth with their pupils. Achievement differences were larger as the outcome measures related more directly to the recall task embedded within the ongoing measurement system. Impl...