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This study is a qualitative descriptive research with the aim of describing students' mathematical problem solving with Field Dependent (FD) and Field Independent (FI) cognitive styles. The subjects of this study consisted of 2 grade VIII junior high school students with Field Dependent (FD) and Field Independent (FI) cognitive styles. The selection of both subjects also considers equal mathematical ability, equal gender, communicative, and willing. The data is analyzed based on the polya problem-solving stages, namely understanding the problem, planning the solution, implementing the solution plan, and rechecking. The results of the study showed that the mathematical problem solving of the two students in solving the problem was relatively the same. At the stage of understanding the problem, both students are able to write down what is known and what is asked in the question, but FD tends to write the same thing about what is in the problem while FI uses his own language. At the stage of planning the settlement of FD fans, FIs are equally able to make strategies or steps to solve the problem. At the stage of implementing the settlement plan, FD and FI are both able to carry out the strategy that has been prepared previously. FI is confident that the answer obtained is correct. However, it is different from FD where he is not sure or doubtful about the answer because in the process of solving the problem there are errors caused by lack of thoroughness. At the stage of re-checking, the FI confidently said that he had re-examined carefully and was confident in the answers obtained. In contrast to FD who said he had double-checked but was not sure whether the answer obtained was correct or not.

This study is a descriptive qualitative research with the aim of describing the critical thinking process of Junior High School students in solving mathematical problems in terms of reflective and impulsive cognitive style. The subjects of this study consisted of 2 students of grade VIII junior high school with reflective cognitive style and impulsive cognitive style. The selection of both subjects also considers equivalent mathematical ability, same sex, communicative, and willing. Data collection technique is done by providing MFFT (Matching Familiar Figured Test), mathematical problem solving tasks, and interviews. Data were analyzed based on critical thinking indicators contained in FRISCO (Focus, Reason, Inference, Situation, Clarity, Overview). The results showed that the critical thinking process of both students in solving the problem is relatively the same. At the stage of understanding the second problem, students already meet the FRISCO indicator. At the stage of making a plan, reflective students already meet the FRISCO indicator, but impulsive students do not do an overview. At the stage of implementing the plan impulsive students do not pass the overview. At the last stage, namely re-examining, impulsive students do not do situation and clarity. In addition between reflective and impulsive students have different ways or solutions in solving math problems. Students with reflective cognitive style in answering a given problem can understand something as a whole, analyze it much better, and do the planning and follow the plan, so that students with reflective cognitive style can do the process of thinking critically when facing a given problem.

The objective of this research aims to develop mathematical learning activities through active learning management. The sample group used in this research consists of 23 students in grade 4. The research tools used include 15 lesson plans, a multiple-choice test with 20 items to measure learning performance, a multiple-choice test with 20 items to measure problem-solving abilities in mathematics, and a questionnaire to measure student satisfaction towards active learning management for mathematics subjects, consisting of 20 items. The statistical analysis used to analyze the data includes percentage, mean, standard deviation, and hypothesis testing. The research findings revealed that the active learning activities had an efficiency of 86.86/80.45. Students had learning score after the implementation is significantly higher than before, with statistical significance at the .05 level. The problem-solving abilities of students was higher than the criterion of 80%. Furthermore, students had level of satisfaction towards active learning management at the highest level. [ABSTRACT FROM AUTHOR]

Children with autism spectrum disorders (ASDs) often display atypical learning styles; however, little is known regarding learning-related brain plasticity and its relation to clinical phenotypic features. Here, we investigate cognitive learning and neural plasticity using functional brain imaging and a novel numerical problem-solving training protocol. Children with ASD showed comparable learning relative to typically developing children but were less likely to shift from rule-based to memory-based strategy. While learning gains in typically developing children were associated with greater plasticity of neural representations in the medial temporal lobe and intraparietal sulcus, learning in children with ASD was associated with more stable neural representations. Crucially, the relation between learning and plasticity of neural representations was moderated by insistence on sameness, a core phenotypic feature of ASD. Our study uncovers atypical cognitive and neural mechanisms underlying learning in children with ASD, and informs pedagogical strategies for nurturing cognitive abilities in childhood autism.

Good teaching materials have an impact on the quality of mathematics learning and can help students become more engaged in their learning and develop their problem-solving skills. It is necessary to develop LKPD utilizing a discovery learning paradigm helped by QR codes in order to boost problem-solving abilities. This study uses a reliable and useful discovery learning paradigm with the use of a QR code to identify the characteristics of LKPD. The Plomp model, which has three steps total—the preparatory stage, the development stage, and the assessment—is used in this particular sort of study, which is called development research. For class VIII of junior high school, LKPD employs a discovery learning methodology with the use of a QR code. The tools employed are validation sheets, observation sheets, questionnaires, interviews, and final exams. The findings demonstrated the validity, applicability, and efficacy of the LKPD for class VIII junior high school students using the discovery learning approach. LKPD practicality was 87%, while LKPD validity was 89%. The average student score on tests measuring their ability to solve mathematical problems was 92%, which indicates the success of the program.

Although prior research has highlighted the significance of representations for mathematical learning, there is still a lack of research on how students use multimodal external representations (MERs) to solve mathematical tasks in digital game-based learning (DGBL) environments. This exploratory study was to examine the salient patterns problem solvers demonstrated using MERs when they engaged in a single-player, three-dimensional architecture game that requires the acquisition and application of math knowledge and thinking in game-based context problem solving. We recorded and systematically coded the behaviors of using MERs demonstrated by 20 university students during 1.5 hours of gameplay. We conducted both cluster and sequential analyses with a total of 2654 encoded behaviors. The study indicated that the maneuverable visual-spatial representation was most frequently used in the selected architecture game. All of the participants performed a high level of representational transformations, including both treatment and conversion transformations. However, compared to the students in the second cluster who were mostly non-game players, students in the first cluster (composed of mainly experienced video game players) displayed a higher frequency of interacting with various MERs and a more cautious and optimized reflective problem-solving process. [ABSTRACT FROM AUTHOR]

This study's purpose was to investigate effects of 3 intervention approaches for building working memory (WM) and improving word-problem solving (WPS). Children with mathematics difficulties (n = 240; 7.51 years [SD =.33]) were randomized to 4 conditions: a control group, general WM training with contiguous math practice, WPS intervention without WM training, and WPS intervention with domain-specific WM training. WM, WPS, and arithmetic were assessed before and 1–3 weeks after intervention; delayed WPS and arithmetic posttesting occurred 4–6 weeks later. Multilevel modeling of main effects and mediation effects were employed. Compared to control, general WM training with contiguous math practice and WPS intervention without WM training increased WM and WPS. The 3rd training condition, WPS intervention with domain-specific WM training, which minimized WM training time, improved WPS but without effects on WM. Both WPS intervention conditions outperformed general WM training on WPS. Conclusions are as follows. (a) General WM training with contiguous math practice improves WM and WPS. (b) WM training is not a substitute for WPS intervention when the goal is to strengthen WPS. (c) WPS intervention without WM training improves WM but is not a substitute for WM training when the goal is to strengthen WM. (d) For WM effects to accrue, WM training needs to occur with sufficient intensity. (e) WM plays a causal role in WPS, but not in arithmetic. Implications are drawn for research and practice, including assessing instructional supports in future research to build cognitive-academic bidirectionality. Educational Impact and Implications Statement: This study provides the basis for the following conclusions about interventions to improve working memory and word-problem solving for second graders with mathematics difficulties. First, general working memory training with math practice (without word-problem solving intervention) improves working memory as well as word-problem solving. Yet, working memory training is not a substitute for word-problem solving intervention when the goal is to strengthen word-problem solving, because WPS outcome is stronger with WPS intervention. Conversely, word-problem solving intervention (without working memory training) improves working memory. Yet, word-problem solving intervention is not a substitute for working memory training when the goal is to strengthen working memory, because WM outcome is stronger with general WM training. [ABSTRACT FROM AUTHOR]

Narrative as a game design feature constantly yields mixed results for learning in the literature. The purpose of this exploratory mixed-methods case study was to examine design heuristics and implications governing the role of narratives in a digital game-based learning (DGBL) environment for math problem solving. We collected data via observation, semi-structured interviewing, and video recording with twenty-seven college students with diverse demographic backgrounds. Video logging resulted in 2276 behavioral events for quantitative analysis. The study indicated: (1) 11 narrative-governed actions for game-based math problem solving; (2) the positive correlations between narrative usage and successful game-based math problem solving; and (3) the gender effects: girls are supported by game narratives designed with intrinsic integration (i.e., object-oriented narrative) for math problem solving more than boys. The study findings highlighted the critical role of game narratives in a sandbox DGBL environment for math problem solving as well as gender-inclusive design of narratives. A set of data-driven design heuristics and implications for the game narrative in DGBL were delineated and suggested. [ABSTRACT FROM AUTHOR]

Previous research on sex differences in mathematical achievement shows mixed findings, which have been argued to depend on types of math tests used and the type of solution strategies (i.e., verbal versus visual‐spatial) these tests evoke. The current study evaluated sex differences in (a) performance (development) on two types of math tests in primary schools and (b) the predictive value of verbal and visual‐spatial working memory on math achievement. Children (N = 3175) from grades 2 through five participated. Visual‐spatial and verbal working memory were assessed using online computerized tasks. Math performance was assessed five times during two school years using a speeded arithmetic test (math fluency) and a word problem test (math problem solving). Results from Multilevel Multigroup Latent Growth Modeling, showed that sex differences in level and growth of math performance were mixed and very small. Sex differences in the predictive value of verbal and visual‐spatial working memory for math performance suggested that boys seemed to rely more on verbal strategies than girls. Explanations focus on cognitive and emotional factors and how these may interact to possibly amplify sex differences as children grow older. [ABSTRACT FROM AUTHOR]

The study aimed to examine the possibility of teaching primary school students a learner-generated drawing strategy, among other constructivist learning strategies. The teacher-guided program “Learning with Understanding” began by discussing the broader topics of the learning process, followed by teaching specific strategies, and ended with an overview of all strategies and reflective discussions. During 18 program lessons, primary school teachers taught, practiced, and raised metacognitive awareness of three learning strategies—elaboration of new information with familiar material and daily practice, organization of material into categories and elaboration, and organization of information through drawing. This study examined composing drawings for math word problems before and after the program. The sample consisted of second- and fourth-grade students from eight Estonian schools. The intervention group included 110 students from second grade and 80 students from fourth grade. The control group consisted of 121 second-grade students, and 82 fourth-grade students. Before and after the intervention, students had to solve two math word problems and compose a drawing, if needed. The results showed that before the intervention, neither the control group nor the intervention group students drew almost any drawings. However, after the intervention, both the control group and the intervention group students started to draw more drawings. Also, the intervention group students composed both more drawings and more schematic drawings. The effect of the intervention was visible at both grade levels. Comparing the correctness of answers with the drawing type showed that the fourth grade obtained significantly more correct answers when no drawings were made, while in the second grade, students had fewer correct answers when they had not compiled a drawing. Thus, we showed that even very young students could learn to compose schematic drawings; however, drawings alone may not be of help to solve the problem.

Tujuan penelitian ini adalah untuk mengetahui bagaimana kesulitan belajar dalam memecahkan masalah yang ditinjau dari minat dan apa saja faktor penyebab peserta didik mengalami kesulitan dalam memecahkan masalah tersebut ditinjau dari minat belajar. Penelitian menggunakan metode deskriptif dengan pendekatan kualitatif. Subjek dipilih secara purposive sampling yaitu membuka 6 orang, 2 orang minat belajar tinggi, 2 orang minat belajar sedang dan 2 orang minat belajar. Instrumen yang digunakan adalah angket minat belajar, soal tes pemecahan masalah dan wawancara.Angket minat belajar dianalisis berdasarkan pengelompokan minat belajar, tes pemecahan masalah berdasarkan indikator kesulitan dalam memecahkan masalah dan analisis secara kualitatif menurut Milles dan Huberman. Hasil penelitian menunjukkan bahwa peserta didik dengan minat belajar, peserta didik mengalami kesulitan dalam menyusun rencana, peserta didik dengan minat belajar sedang mengalami kesulitan dalam menyelesaikan rencana, serta peserta didik mengalami kesulitan dalam menyusun rencana, menyelesaikan rencana, dan menyelesaikan menyelesaikan kembali.

Efforts to increase moderate-to-vigorous physical activity (MVPA) in school-age children are associated with improved health, cognitive, and academic outcomes. However, questions remain about whether similar benefits are observed in early childhood. We hypothesized that motor competence, not MVPA, would be related to improved cognitive and academic skill development in early childhood. For this study, 283 children were recruited from 13 community-based preschools (55% female; M = 4.2 years old, SD =.6; 41% non-Hispanic White, 37% non-Hispanic Black; 10% Hispanic, 10% mixed race, 2% Asian, 1% American Indian). Children's physical activity, motor competence, executive function (EF), and math problem-solving skills were measured using the same protocol in three assessments in a single academic year (i.e., fall, winter, spring). Although motor competence was strongly correlated with contemporaneous measures of EF and math problem-solving skills (rs =.51–.63), MVPA was weakly correlated with EF and math problem-solving skills (rs =.03–.18). Mixed linear models demonstrated that improvements in children's motor competence were related to improvements in their EF and math problem-solving skills (ps <.001), their improvements in MVPA were not statistically significant related to any of the outcomes. These within-child associations provide a stronger basis of inference by controlling for all time-invariant confounders. The results of this study suggest that efforts to improve motor competence skills in young children may improve EF and math problem-solving skills, though experimental studies are required to rigorously test this idea. [ABSTRACT FROM AUTHOR]

Focusing on students with mild disabilities, this study aimed to examine the effect of STAR problem solving strategy on their a) solving change problems involving one-step addition and subtraction, b) maintaining their acquisition of solving change problems involving one-step addition and subtraction after 1, 3, and 5 weeks, c) generalizing their performance in solving problems to the classroom environment. Three students with mild mental disabilities participated in the study. A multiple probe across participants design was used in the study. The number of problems that students solved correctly was determined by scoring the data. The data are shown graphically and analysed visually. Findings emphasized the effectiveness of STAR strategy for students with mild mental disabilities when solving change problems that involve a one-step addition and subtraction, indicating that those who acquired this strategy could demonstrate the same problem solving performance 1, 3, and 5 weeks after the intervention. Also, students were observed to generalize their strategy performance to the classroom environment. The findings of the research were discussed within the framework of the relevant literature and theoretical views, and suggestions were made for teachers in terms of interventions and for researchers considering further studies. [ABSTRACT FROM AUTHOR]

The purpose of this study was to examine the effects of cognitive strategies and metacognitive functions of students with learning disabilities (LD), students with lowachieving (LA), and students with average-achieving (AA) over their math problem-solving performance. The study sample consisted of 150 students with 50 students from each group. Study data were collected through Think-Aloud Protocols, Metacognitive Experiences Questionnaire, Math Problem Solving Assessment-Short Form, and 10 math problems. Study findings revealed that the significant predictors of math problem-solving performance were metacognitive strategies and experiences regarding students with LD, metacognitive strategies and knowledge considering students with LA, and metacognitive strategies in students with AA. A statistically significant relationship was found between problem-solving performance of students with LD and their metacognitive strategies and metacognitive experiences. Problem-solving performance and metacognitive strategies of students with LA were found to be close to a high level, and their metacognitive knowledge had a moderate relationship. It was also observed to be moderately related to problem-solving performance and metacognitive strategies in students with AA. The findings were discussed within the relevant literature scope, and suggestions were made for teachers in terms of implementation and researchers for further studies. [ABSTRACT FROM AUTHOR]

This mixed-method study aims to explore the feasibility of using the game-based, multimodal representation of mathematical problems to support middle school students' practice and performance of math problem representation and solving. A three-dimensional architectural simulation game, called E-Rebuild, was developed to engage students in architecture-themed math problem solving and learning. Based on the data collected from 56 middle graders, the study findings suggested that interacting with game-based multimodal math problems helped students develop a systematic perspective and an analytical demeanor in coordinating external problem representations distributed across game objects and actions. Game-based problem solving promoted participants' mathematical test performance as well as mental rotation task performance. [ABSTRACT FROM AUTHOR]

The present study examined the extent to which college students’ academic mindsets predicted their persistence when solving challenging math problems. The study included an experimental manipulation, in which participants initially received either an easy or a difficult arithmetic task. Following the manipulation, all participants solved two target math problems: one that was solvable but very hard and another that was unsolvable. Time spent attempting to solve each problem served as a measure of persistence. Results showed the predicted pattern for the solvable target problem, but not for the unsolvable problem. That is, for the solvable problem, the more of a fixed mindset participants had, the less persistent they were after completing a relatively difficult arithmetic task than after completing an easy task. The results suggest that, for certain types of math problems, students’ persistence may vary as a function of academic mindset and previous experiences of math success or failure.

Children with autism spectrum disorders (ASDs) often display atypical learning styles; however, little is known regarding learning-related brain plasticity and its relation to clinical phenotypic features. Here, we investigate cognitive learning and neural plasticity using functional brain imaging and a novel numerical problem-solving training protocol. Children with ASD showed comparable learning relative to typically developing children but were less likely to shift from rule-based to memory-based strategy. While learning gains in typically developing children were associated with greater plasticity of neural representations in the medial temporal lobe and intraparietal sulcus, learning in children with ASD was associated with more stable neural representations. Crucially, the relation between learning and plasticity of neural representations was moderated by insistence on sameness, a core phenotypic feature of ASD. Our study uncovers atypical cognitive and neural mechanisms underlying learning in children with ASD, and informs pedagogical strategies for nurturing cognitive abilities in childhood autism., Competing Interests: JL, HC, DA, JK, LC, MR, VM No competing interests declared, (© 2023, Liu, Chang et al.)

Individual differences in children's math performance have been associated with math anxiety, attention problems, working memory (WM), and reading skills, but the mechanisms by which these factors jointly contribute to children's math achievement are unknown. Here, we use structural equation modeling to characterize the relation between these factors and their influence on non-verbal Numerical Operations (NO) and verbal Math Reasoning (MR) in 330 children (M=8.34years). Our findings indicate that WM plays a central role in both non-verbal NO and verbal MR, whereas math anxiety and reading comprehension have unique and more pronounced influences on MR, compared to NO. Our study elucidates how affective and cognitive factors distinctly influence non-verbal and verbal mathematical problem solving. [ABSTRACT FROM AUTHOR]

How does processing differ during purely symbolic problem solving versus when mathematical operations can be mentally associated with meaningful (here, visuospatial) referents? Learners were trained on novel math operations (↓, ↑), that were defined strictly symbolically or in terms of a visuospatial interpretation (operands mapped to dimensions of shaded areas, answer = total area). During testing (scanner session), no visuospatial representations were displayed. However, we expected visuospatially-trained learners to form mental visuospatial representations for problems, and exhibit distinct activations. Since some solution intervals were long (~10 s) and visuospatial representations might only be instantiated in some stages during solving, group differences were difficult to detect when treating the solving interval as a whole. However, an HSMM-MVPA process (Anderson and Fincham, 2014a) to parse fMRI data identified four distinct problem-solving stages in each group, dubbed: 1) encode; 2) plan; 3) compute; and 4) respond. We assessed stage-specific differences across groups. During encoding, several regions implicated in general semantic processing and/or mental imagery were more active in visuospatially-trained learners, including: bilateral supramarginal, precuneus, cuneus, parahippocampus, and left middle temporal regions. Four of these regions again emerged in the computation stage: precuneus, right supramarginal/angular, left supramarginal/inferior parietal, and left parahippocampal gyrus. Thus, mental visuospatial representations may not just inform initial problem interpretation (followed by symbolic computation), but may scaffold on-going computation. In the second stage, higher activations were found among symbolically-trained solvers in frontal regions (R. medial and inferior and L. superior) and the right angular and middle temporal gyrus. Activations in contrasting regions may shed light on solvers’ degree of use of symbolic versus mental visuospatial strategies, even in absence of behavioral differences. [ABSTRACT FROM AUTHOR]

Surprisingly little is known about whether relationships between cognitive and emotional states remain stable or change over time, or how different patterns of stability and/or change in the relationships affect problem solving abilities. Nevertheless, cross-sectional studies show that anxiety/worry may reduce working memory resources, and the ability to minimize the effects anxiety/worry is higher in individuals with greater WM capacity. To investigate the patterns of stability and/or change in cognition-emotion relations over time and their implications for problem solving, 126 14-year-olds’ algebraic WM and worry levels were assessed twice in a single day before completing an algebraic math problem solving test. We used latent transition analysis to identify stability/change in cognition-emotion relations, which yielded a six subgroup solution. Subgroups varied in WM capacity, worry, and stability/change relationships. Among the subgroups, we identified a high WM/low worry subgroup that remained stable over time and a high WM/high worry, and a moderate WM/low worry subgroup that changed to low WM subgroups over time. Patterns of stability/change in subgroup membership predicted algebraic test results. The stable high WM/low worry subgroup performed best and the low WM capacity-high worry unstable across time subgroup performed worst. The findings highlight the importance of assessing variations in cognition-emotion relationships over time (rather than assessing cognition or emotion states alone) to account for differences in problem solving abilities.

This study examined 1) experiences of six discrete emotions ‒ joy, pride, contentment, worry, shame, hopelessness ‒ after solving a math problem of students aged 10–12 years, and 2) the contribution of self-concept, metacognitive experiences (feeling of difficulty and feeling of success) and performance on emotions experienced after the task, controlling for gender and emotions experienced before the task. Results indicated a decrease in joy and contentment after problem solving. Performance did not contribute to emotions apart from hopelessness. The influence of performance on hopelessness was mediatized by metacognitive experiences. Self-concept contributed to joy, pride and shame but its influence became non-significant when we controlled for metacognitive experiences. Feeling of success mediatized the effect of self-concept on joy, pride and shame. Metacognitive experiences were also found to be important predictors of all emotions except worry. The need for new paradigms to study emotions in education is discussed. [ABSTRACT FROM AUTHOR]

Surprisingly little is known about whether relationships between cognitive and emotional states remain stable or change over time, or how different patterns of stability and/or change in the relationships affect problem solving abilities. Nevertheless, cross-sectional studies show that anxiety/worry may reduce working memory (WM) resources, and the ability to minimize the effects anxiety/worry is higher in individuals with greater WM capacity. To investigate the patterns of stability and/or change in cognition-emotion relations over time and their implications for problem solving, 126 14-year-olds' algebraic WM and worry levels were assessed twice in a single day before completing an algebraic math problem solving test. We used latent transition analysis to identify stability/change in cognition-emotion relations, which yielded a six subgroup solution. Subgroups varied in WM capacity, worry, and stability/change relationships. Among the subgroups, we identified a high WM/low worry subgroup that remained stable over time and a high WM/high worry, and a moderate WM/low worry subgroup that changed to low WM subgroups over time. Patterns of stability/change in subgroup membership predicted algebraic test results. The stable high WM/low worry subgroup performed best and the low WM capacity-high worry "unstable across time" subgroup performed worst. The findings highlight the importance of assessing variations in cognition-emotion relationships over time (rather than assessing cognition or emotion states alone) to account for differences in problem solving abilities. [ABSTRACT FROM AUTHOR]

This study compared mathematical outcomes in children with predominantly moderate to severe traumatic brain injury (TBI; n = 50) or orthopedic injury (OI; n=47) at 2 and 24 months post-injury. Working memory and its contribution to math outcomes at 24 months post-injury was also examined. Participants were administered an experimental cognitive addition task and standardized measures of calculation, math fluency, and applied problems; as well as experimental measures of verbal and visual-spatial working memory. Although children with TBI did not have deficits in foundational math fact retrieval, they performed more poorly than OIs on standardized measures of math. In the TBI group, performance on standardized measures was predicted by age at injury, socioeconomic status, and the duration of impaired consciousness. Children with TBI showed impairments on verbal, but not visual working memory relative to children with OI. Verbal working memory mediated group differences on math calculations and applied problems at 24 months post-injury. Children with TBI have difficulties in mathematics, but do not have deficits in math fact retrieval, a signature deficit of math disabilities. Results are discussed with reference to models of mathematical cognition and disability and the role of working memory in math learning and performance for children with TBI. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this theoretically-based study was to examine the effects of yellow-highlighting ‘relevant’ words and units within math word problems. Initial differences were documented between 10 girls at-risk for ADHD and 10 comparisons on the performance of group and individual assessments of math computations and word problems, as had previously been reported for boys. To address these deficits (faster speed and lower accuracy) for the at-risk group, these fourth-grade girls were randomly assigned word problems under two experimental conditions (highlight vs. nohighlight) within a counterbalanced condition- and form-order design. Intervention gains were (a) slower rate of performance, (b) decreased off-task behavior, and (c) improved problem solving performance, differentially for girls at-risk for ADHD when their materials were first presented with highlighting – the effects of which carried over to a non-highlight condition. The theoretical, practical, and future research implications of this study are addressed. [Copyright &y& Elsevier]

The purpose of the study was to investigate the metacognitive abilities of students with LD as they engage in math problem solving and to determine processing differences between these students and their low- and average-achieving peers (n = 73). Students thought out loud as they solved three math problems of increasing difficulty. Protocols were coded and analyzed to determine frequency of cognitive verbalizations and productive and nonproductive metacognitive verbalizations. Results indicated different patterns of metacognitive activity for ability groups when type of metacognitive verbalization and problem difficulty were considered. Implications for instruction are discussed. [ABSTRACT FROM PUBLISHER]

This study investigated the effects of cognitive strategy instruction on the mathematical problem solving of three adolescents with spina bifida. Conditions of the multiple-baseline across-individuals design included baseline, two levels of treatment, posttesting, and maintenance. Treatment 1 focused on one-step math problems, and Treatment 2 focused on two-step problems. All students substantially improved as measured by performance on criterion tests of math problem solving. Discussion centers on the need for intervention studies with students with spina bifida that specifically address their unique characteristics and the adaptations and accommodations that benefit these students. [ABSTRACT FROM PUBLISHER]

Whether because individuals are made aware of negative stereotypes about how they should perform or are in a high-stakes testing situation, a stressful environment can adversely affect the success people have in solving math problems. I review work examining how unwanted failure in math occurs and individual differences in those most likely to fail. This work suggests that a high-stress situation creates worries about the situation and its consequences that compete for the working memory (WM) normally available for performance. Consequently, the performance of individuals who rely most heavily on WM for successful execution (i.e., higher-WM individuals) is most likely to decline when the pressure is on. [ABSTRACT FROM AUTHOR]

This study evaluated the effectiveness of fine motor physical activity with tactile stimulation during two conditions of math problem solving, visual and auditory. Eight 4th and 5th grade students with attention problems participated. Using an alternating treatments design, students solved as many math story problems as they could, presented on worksheets or verbally during two conditions, with and without tactile stimulation during 20 min. Motor behavior, recorded from videotape, and number of correctly completed word problems were measured. Results suggest that fine motor manipulation of a tactile stimulation object reduced excessive motor movement and increased task completion of students with attention problems. [ABSTRACT FROM AUTHOR]

Two experiments demonstrate how, individual differences in working memory (WM) impact the strategies used to solve complex math problems and how consequential testing situations alter strategy use. In Experiment 1, individuals performed multistep math problems under low- or high-pressure conditions and reported their problem-solving strategies. Under low-pressure conditions, the higher individuals' WM, the more likely they were to use computationally demanding algorithms (vs. simpler shortcuts) to solve the problems, and the more accurate their math performance. Under high-pressure conditions, higher WM individuals used simpler (and less efficacious) problem-solving strategies, and their performance accuracy suffered. Experiment 2 turned the tables by using a math task for which a simpler strategy was optimal (produced accurate performance in few problem steps). Now, under low-pressure conditions, the lower individuals' WM, the better their performance (the more likely they relied on a simple, but accurate, problem strategy). And, under pressure, higher WM individuals performed optimally by using the simpler strategies lower WM individuals employed. WM availability influences how individuals approach math problems, with the nature of the task performed and the performance environment dictating skill success or failure. [ABSTRACT FROM AUTHOR]

The study was conducted to determine whether the language of math word problems would affect how Filipino-English bilingual problem solvers would model the structure of these word problems. Modeling the problem structure was studied using the problem-completion paradigm, which involves presenting problems without the question. The paradigm assumes that problem solvers can infer the appropriate question of a word problem if they correctly grasp its problem structure. Arithmetic word problems in Filipino and English were given to bilingual students, some of whom had Filipino as a first language and others who had English as a first language. The problem-completion data and solution data showed similar results. The language of the problem had no effect on problem-structure modeling. The results were discussed in relation to a more circumscribed view about the role of language in word problem solving among bilinguals. In particular, the results of the present study showed that linguistic factors do not affect the more mathematically abstract components of word problem solving, although they may affect the other components such as those related to reading comprehension and understanding. [ABSTRACT FROM AUTHOR]

Researchers have suggested that among bilinguals, solving word problems in mathematics is influenced by linguistic factors (K. Durkin & B. Shire, 1991; L. Verschaffel, B. Greer, & E. De Corte, 2000). Others have suggested that students exhibit a strong tendency to exclude real-world constraints in solving mathematics word problems (L. Verschaffel, E. De Corte, & S. Lasure, 1994). In the present study, the authors explored the effects of stating word problems in either Filipino or English on how Filipino-English bilingual students solved word problems in which the solution required the application of real-world knowledge. The authors asked bilingual students to solve word problems in either their first or second language. For some of the word problems, real-life constraints prevented straightforward application of mathematical procedures. The authors analyzed the students' solutions to determine whether the language of the word problems affected the tendency to apply real-life constraints in the solution. Results showed that the bilingual students (a) rarely considered real-life constraints in their solutions, (b) were more successful in understanding and solving word problems that were stated in their first language, and (c) were more likely to experience failure in finding a solution to problems stated in their second language. The results are discussed in terms of the relationship between linguistic and mathematical problem-solving processes among bilinguals. [ABSTRACT FROM AUTHOR]