Search

Summary As standardized measures of cognitive abilities and academic achievement continue to evolve, so do the relations between the constructs represented in these measures. A large, nationally representative sample of school-aged children and youth between 6 and 19 years of age (N = 4,194) was used to systematically evaluate the relations between cognitive abilities and components of academic achievement in mathematics. The cognitive abilities of interest were those identified from the Cattell–Horn–Carroll model of intelligence. Specific areas of mathematics achievement included math calculation skills and math problem solving. Results suggest that fluid reasoning (Gf), comprehension-knowledge (Gc), and processing speed (Gs) have the strongest and most consistent relations with mathematics achievement throughout the school years. Copyright © 2017 John Wiley & Sons, Ltd.

Laboratory research has shown that when subjects are given a choice between fixed-ratio and bi-valued mixed-ratio schedules of reinforcement, preference typically emerges for the mixed-ratio schedule even with a larger ratio requirement. The current study sought to replicate and extend these findings to children's math problem completion. Using an ABCBC reversal design, four fourth-grade students were given the choice of completing addition problems reinforced on either a fixed-ratio 5 schedule or one of three mixed-ratio schedules; an equivalent mixed-ratio (1, 9) schedule, a mixed-ratio (1, 11) schedule with a 20% larger ratio requirement, and an equally lean mixed-ratio (5, 7) schedule without the small fixed-ratio 1 component. This was followed by a reversal back to the preceding phase in which preference for the mixed-ratio schedule had been observed, and a final reversal back to the mixed-ratio (5, 7) phase. Findings were consistent with previous research in that all children preferred the mixed-ratio (1, 9) schedule over the equivalent fixed-ratio 5 schedule. Preference persisted for the leaner mixed-ratio (1, 11) schedule for three of the four children. Indifference or preference for the fixed-ratio 5 alternative was observed in phases containing the mixed-ratio (5, 7) schedule. These results extend previous research on risky choice to children's math problem completion and highlight the importance of a small ratio component in the emergence of preference for bi-valued mixed-ratio schedules. Implications of these results for arranging reinforcement to increase children's academic responding are discussed.

Generalized conditioned reinforcers (GCRs) in the form of tokens are commonly used in behavioral treatment. However, it is possible for non-tangible consequences to also function as GCRs. For example, a vocal stimulus (e.g., good job) associated with completion of a work task, access to preferred actives, and peer interaction could function as a GCR. The purpose of this study was to examine the effects of pairing a vocal stimulus with multiple edible reinforcers on the Frequency math problem completion. The results suggest that a vocal statement paired with an array of four back-up reinforcer functioned as a GCR for completing math problems for two typically developing children identified as having minor deficits in math skills. Copyright © 2015 John Wiley & Sons, Ltd.

Development of early math skill depends on a prerequisite level of cognitive development. Identification of specific cognitive skills that are important for math development may not only inform instructional approaches but also inform assessment approaches to identifying children with specific learning problems in math. This study investigated the specific cognitive correlates of math problem solving across early grade levels (1–4) while controlling for basic calculation skills. As expected, basic calculation skill was a significant predictor of math problem solving across the entire sample. However, the addition of cognitive measures almost doubled the variance explained (R2 = .61). Additionally, only select cognitive variables contributed to the prediction of math problem solving, and these variables change in importance as children develop higher-level math skills. Results are discussed within a developmental model, which emphasizes the increasing importance of abstract code representations required in higher levels of math performance.

The purpose of this article is to offer teacher training and professional development recommendations in mathematics based on the findings of a federally funded 3-year intervention study that improved the problem solving of middle school students with a focus on students with learning disabilities. Over the 3-year project, 29 seventh and eighth grade teachers implemented a problem-solving intervention based on cognitive strategy instruction. Though the intervention was successful in improving students’ problem-solving performance, several issues related to teaching effectiveness and teacher training came to light. The article will: (1) describe the intervention and its implementation, (2) present the findings of the study, and (3) discuss the issues of effectiveness and possible solutions via teacher education and professional development.

The purpose of these studies was to extend the use of stimulus preference assessments to children in foster care. In Study 1, subjects completed a computerized 4-point Likert-type questionnaire designed to assess preference for a wide range of stimuli and activities. Next, items identified as highly preferred (HP) and less preferred (LP) on the questionnaire were tested using a computerized paired-stimulus preference assessment. Results showed complete correspondence between the results of the computerized preference assessments for 11 of 17 subjects. Studies 2 and 3 evaluated whether the stimuli identified as HP in Study 1 would function as reinforcers. Overall, subjects allocated their engagement to HP items, and those HP items could be used as reinforcers for math problem completion. Collectively, these studies demonstrated that computerized preference assessments may be a feasible method of identifying preferences in the foster care system. Implications for their use in foster care are discussed.

Solving word problems is a common area of struggle for students with learning disabilities (LD). In order for instruction to be effective, we first need to have a clear understanding of the specific errors exhibited by students with LD during problem solving. Error analysis has proven to be an effective tool in other areas of math but has had little application to errors in word problems. Using an error analysis approach, this study aimed to investigate in depth the various types and frequency of errors made by students with LD and their AA peers during math problem solving. The resulting similarities and differences between the two groups of students are discussed with insight into underlying cognitive processes, and implications for future research.

The purpose of this qualitative study was: (a) to explore the cognitive and metacognitive processes of mathematics problem-solving discourse of 10-year-old students in Russia, Spain, Hungary, and the United States; and (b) to explore the patterns of social interactions during small group work. Data were analyzed using a cognitive/metacognitive framework adopted from Artzt and Armour-Thomas. The analysis of think-aloud transcripts, students' reflective journals, and field observation notes revealed similar patterns of cognitive/metacognitive processes of the problem-solving discourse at the four research sites and distinct patterns of social interactions. Implications of how children used metacognition to impact learning during mathematics problem solving are discussed.

Fjellstedt and Sulzer-Azaroff (1973) used differential reinforcement of short latencies to decrease a child's latency to comply with instructions. We replicated this contingency with a young man diagnosed with Asperger syndrome across two tasks (question answering and math problem solving). We added a differential reinforcement contingency to teach the participant to discriminate between math problems that could be answered rapidly and those that required more time for accurate performance.

Recently the American Physiology Society (APS) has been working to increase learning and making science fun for elementary school students. Physiology Understanding Week (PhUn) is the APS initiative to use interactive experiments to engage school-age children with science and physiology. In this project we used a Biopac MP40 system to measure brain activity of fourth grade students at Dixie Bee Elementary School. The activity was divided in 5 different sessions, one per room, in two different days, reaching 116 elementary school students. Each room was divided in small 4-student groups with the following general activity set-up: 1) brief presentation about brain physiology using a brain model, 2) measuring brain activity during 3 different conditions, 3) analyzing collected data, and 4) discussing obtained results. Three electrodes were placed behind the student's ear, 2 students per group. Brain activity was collected during 4 different activities: 1) resting with eyes closed, 2) doing a math problem, 3)...

This article, to be published in three parts, shows why interoperability of sensor fusion systems is a math problem, and how to solve it. Part I (Track Management) explains the minimum that sensor fusion systems must communicate to each other in order to interoperate. Part 11 (System Architecture) demonstrates that there are significant constraints on the architecture of interoperable sensor fusion systems. Part III (Seeking Solutions) discusses optimal solutions to the constrained architecture problem, along with the relationship of interoperability to other sensor fusion engineering problems. It concludes by outlining the steps necessary to make existing sensor fusion systems interoperate.

We examined a combined approach of manipulating reinforcer dimensions and delay fading to promote the development of self-control with 3 students diagnosed with attention deficit hyperactivity disorder. First, we administered a brief computer-based assessment to determine the relative influence of reinforcer rate (R), reinforcer quality (Q), reinforcer immediacy (I), and effort (E) on the students' choices between concurrently presented math problems. During each session, one of these dimensions was placed in direct competition with another dimension (e.g., RvI involving math problem alternatives associated with high-rate delayed reinforcement vs. low-rate immediate reinforcement), with all possible pairs of dimensions presented across the six assessment conditions (RvQ, RvI, RvE, QvI, QvE, IvE). The assessment revealed that the choices of all 3 students were most influenced by immediacy of reinforcement, reflecting impulsivity. We then implemented a self-control training procedure in which reinforcer immediacy competed with another influential dimension (RvI or Qvl), and the delay associated with the higher rate or quality reinforcer alternative was progressively increased. The students allocated the majority of their time to the math problem alternatives yielding more frequent (high-rate) or preferred (high-quality) reinforcement despite delays of up to 24 hr. Subsequent readministration of portions of the assessment showed that self-control transferred across untrained dimensions of reinforcement.

In order to clarify the concurrent validity of the Peabody Individual Achievement Test (PIAT) and the Metropolitan Achievement Test (MAT), product-moment correlations were computed for all subscores and total scores for 26 normal-range public school third-grade girls and boys. The reading comprehension subtests correlated.81, spelling.88, and PIAT Mathematics with MAT Total Math.64. Correlations were computed for the Otis-Lennon Mental Ability Test and the PIAT General Information subtest as.77, and the Otis-Lennon and the PIAT Total Test scores as.79. Concurrent validity of the PIAT with both tests is tentatively considered adequate except in the area of mathematics, in which the PIAT, relative to the MAT, appears to be reflecting ability to handle math concepts (.68) more accurately than math computation (.41) or math problem solving (.56). Correlations with IQ partialed out suggest the PIAT Total Test, and PIAT and MAT reading and spelling measures, are relatively uninfluenced by IQ variations, whereas with IQ held constant, the weak positive correlations between the PIAT and MAT math subtests became essentially random relationships.