The focus of this study was connections among 3 aspects of mathematical cognition at 2nd grade: calculations, word problems, and prealgebraic knowledge. We extended the literature, which is dominated ...by correlational work, by examining whether intervention conducted on calculations or word problems contributes to improved performance in the other domain and whether intervention in either or both domains contributes to prealgebraic knowledge. Participants were 1,102 children in 127 second-grade classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation intervention, word-problem intervention, and business-as-usual control. Intervention, which lasted 17 weeks, was designed to provide research-based linkages between arithmetic calculations or arithmetic word problems (depending on condition) and prealgebraic knowledge. Multilevel modeling suggested calculation intervention improved calculation but not word-problem outcomes; word-problem intervention enhanced word-problem but not calculation outcomes; and word-problem intervention provided a stronger route than calculation intervention to prealgebraic knowledge.
This classroom experiment investigates the effects of adding representational pictures to multiple-choice and constructed-response test items to understand the role of the response format for the ...multimedia effect in testing. Participants were 575 fifth- and sixth-graders who answered 28 science test items-seven items in each of four experimental conditions in a balanced 2 × 2 within-subject design, with the factors being multimedia (text-only vs. text-picture) and response format (multiple-choice vs. constructed-response). Consistent with multimedia and generative learning theory, there was a multimedia effect for testing in which students were more successful in solving the items, gave higher metacognitive ratings of expected success, and gave higher satisfaction ratings for test items that contained text and corresponding pictures than text alone both for multiple-choice and constructed-response items. Consistent with problem solving theory, there was a response format effect in which students were more successful and gave higher metacognitive and satisfaction ratings for multiple-choice items than constructed-response items. Furthermore, pictures were slightly more beneficial for improving students' performance on constructed-response items as compared with multiple-choice items. Thus, the addition of pictures and multiple-choice response options to word problems can be employed to adapt item difficulty by design and support instructional control.
Educational Impact and Implications Statement
What can be done to adjust the difficulty of science test items such as found on standardized assessments and classroom tests? Two adjustments that caused better accuracy on science test items for 575 fifth- and sixth graders were: (a) to present text and corresponding visualizations rather than text alone (multimedia effect in testing); and (b) to use multiple-choice format (i.e., students choose out of given responses) rather than constructed-response format (i.e., students write a response). Adding visualizations to text improved performance on both multiple-choice and constructed-response items, although it was slightly more beneficial for constructed-response items.
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.
This paper proposes a novel nature-inspired meta-heuristic optimizer, called Reptile Search Algorithm (RSA), motivated by the hunting behaviour of Crocodiles. Two main steps of Crocodile behaviour ...are implemented, such as encircling, which is performed by high walking or belly walking, and hunting, which is performed by hunting coordination or hunting cooperation. The mentioned search methods of the proposed RSA are unique compared to other existing algorithms. The performance of the proposed RSA is evaluated using twenty-three classical test functions, thirty CEC2017 test functions, ten CEC2019 test functions, and seven real-world engineering problems. The obtained results of the proposed RSA are compared to various existing optimization algorithms in the literature. The results of the tested three benchmark functions revealed that the proposed RSA achieved better results than the other competitive optimization algorithms. The results of the Friedman ranking test proved that the RSA is a significantly superior method than other comparative methods. Finally, the results of the examined engineering problems showed that the RSA obtained better results compared to other various methods. Source codes of RSA are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/101385-reptile-search-algorithm-rsa-a-nature-inspired-optimizer
•Developed a novel optimization algorithm inspired by hunting behaviour of Reptiles (RSA).•Tested RSA against classical, CEC2017, CEC2019 test functions and engineering problems.•Compared the RSA to other well-known optimization algorithms.•Demonstrated effectiveness and superiority of the proposed RSA.
The purpose of this study was to examine child-level pathways in development of prealgebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and ...fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of Grade 2; calculation accuracy and calculation fluency at end of Grade 2; and prealgebraic knowledge and word-problem solving at end of Grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than prealgebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students' foundational mathematics skills or cognitive processes.
Since 1975, researchers have conducted interventions to improve the word-problem performance of elementary school students facing mathematics difficulties. The current study reports a meta-analysis ...of 52 studies that examined the effect of these interventions. We estimated multivariate, random-effects models (REM) with robust variance estimation (RVE) with and without outliers. Results showed a large, positive, and significant mean weighted effect size (g = 1.01 for the model with outliers; g = 0.81 for the model without outliers). Findings of meta-regression analyses showed several moderators, such as sample composition, group size, intervention dosage, group assignment approach, interventionist, year of publication, and dependent measure type, significantly explained heterogeneity in effects across studies. A sensitivity analysis showed these results were generally robust to outliers. We offer possible explanations for the findings and discuss study limitations. Finally, we propose recommendations for future research and classroom practice.
Although algebra is a prerequisite for higher mathematics, few studies have examined the mathematical and cognitive capabilities that contribute to the development of algebra word problems solving ...skills. We examined changes in these relations from second to ninth grades. Using a cross-sequential design that spanned 4 years, children from 3 cohorts (Mage = 7.85, 10.05, and 12.32) were administered annual tests of algebra word problems, mathematical skills (mathematical relational tasks, arithmetic word problems), and cognitive capabilities (working memory, updating, inhibitory, task switching, and performance intelligence). The cross-sectional findings showed that ability to solve mathematical relational problems was associated strongly with performance in algebra word problems. Working memory and updating explained variance in the relational, but not the algebra problems. Using an autoregressive cross-lagged model with structured residuals to analyze the longitudinal data, we found relational and arithmetic performance predicted independently algebra performance from one year to the next. The strength of these relations was consistent across grades. These findings point to the importance of developing skills in relational problems as one of the tools for improving algebra performance.
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.
The focus of this article is the well documented association between low working memory capacity and difficulty with mathematical word-problem solving. We begin by describing a model that specifies ...how various cognitive resources, including working memory, contribute to individual differences in word-problem solving and by then summarizing findings on the relation between working memory and word-problem solving. This sets the context for the article’s main purpose and major section: to describe the findings of research studies that take one of two approaches for addressing the needs of students with low working memory within word-problem solving intervention. One approach focuses on
compensating
for working memory limitations; the other on
building
working memory capacity. We then suggest the need for research on integrating the two approaches by embedding working memory training within explicit word-problem solving intervention.
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