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The current study aimed to investigate children’s difficulties in word problem solving through assessing their ability to mathematize, or to identify the semantic role of the unknown from word problems. Fifth graders (n = 213) were given an advanced word problem reasoning task in which they had to match word problems with schematic diagrams that depict different processes (multiplication versus division) and the unknown being in different semantic roles (e.g., unit size, number of units, or total in an equal group problem). They were also tested on their mathematical problem solving as well as some potential confounding variables (i.e., intelligence and working memory) and mediators. The ability to identify the semantic role of the unknown was shown to be longitudinally predictive of children’s mathematical problem solving performance even after controlling for the effects of covariates and autoregressor. Such a relation was partially mediated by children’s ability to convert word problems into the correct number sentences/equations. The findings not only highlight the importance of unknown identification in mathematical problem solving process, but also provide a practical tool to assess such an ability. 相似文献
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数学问题解决中的模式识别的研究视角,可以分为基于数学解题认知过程与解题策略角度、基于"归类"的视角、基于数学问题解决中模式识别与其他因素的关系的视角等,具体研究领域涉及几何解题中的视觉模式识别、几何问题解决中的模式识别、解代数应用题的认知模式、数学建模中的模式识别等.由于在知觉领域与问题解决领域"模式识别"的表述存在一定的混乱性,将基于数学问题解决的模式识别界定为:当主体接触到数学问题后,与自己认知结构中的某数学问题图式相匹配的思维与认知过程.并进一步通过其与"归类"的区别与联系、与"化归"的区别与联系使"基于数学问题解决的模式识别"的概念得以澄清.在范围上,把问题解决中的模式识别界定为一种思维过程的阶段或者思维策略,认为它是解题的重要组成部分,但并不是解题的全部.对于未来的展望,期望系统的理论研究、期望对学生问题解决中模式识别的认知过程与机理的实质性的研究以及对学生问题解决中模式识别的教学实验研究. 相似文献
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This study aimed to investigate the interplay between mathematical word problem skills and reading comprehension. The participants were 225 children aged 9–10 (Grade 4). The children’s text comprehension and mathematical word problem‐solving performance was tested. Technical reading skills were investigated in order to categorise participants as good or poor readers. The results showed that performance on maths word problems was strongly related to performance in reading comprehension. Fluent technical reading abilities increased the aforementioned skills. However, even after controlling for the level of technical reading involved, performance in maths word problems was still related to reading comprehension, suggesting that both of these skills require overall reasoning abilities. There were no gender differences in maths word problem‐solving performance, but the girls were better in technical reading and in reading comprehension. Parental levels of education positively predicted children’s maths word problem‐solving performance and reading comprehension skills. 相似文献
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Gisèle Lemoyne Jacinthe Giroux Diane Biron 《European Journal of Psychology of Education - EJPE》1990,5(3):273-291
This study analyses children development of semantic, linguistic, procedural and schematic knowledge in the context of writing arithmetic word problems. 139 children aged between 8 and 12 years old were presented with a task which consisted in writing arithmetic word problems, according to some contraints: words, questions or measures to include in their problems; type of problems to write. Results show the relevance of actual theoritical models of problem solving (Mayer, 1983; Kintsch & Greeno, 1985). Schematic knowledge seem indeed more important than other knowledge in the process of writing arithmetic word problems; semantic knowledge are also used to choose relevant numbers or measures; the roles of linguistic and procedural knowledge seem less evident. Finally, some hypotheses related with the development of mental models of arithmetic word problems are formulated. 相似文献
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《Early education and development》2013,24(2):155-168
The purpose of the present study was threefold: (a) to examine the extent to which kindergarten children acquire metacognitive knowledge related to mathematics; (b) to investigate the relationships between children's metacognitive knowledge and general ability; and (c) to examine the relative roles of general ability and metacognition in facilitating word problem solutions. Participants were 32 kindergarten children. Results showed that preschoolers acquired a substantial metacognitive knowledge about mathematical word problems. That knowledge was highly correlated with mathematics performance, even after general ability was controlled. The study further shows that metacognition explained more of the variance in mathematics performance than general ability. The theoretical and practical implications of the study are discussed. 相似文献
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Zemira R. Mevarech 《Early education and development》1995,6(2):155-168
The purpose of the present study was threefold: (a) to examine the extent to which kindergarten children acquire metacognitive knowledge related to mathematics; (b) to investigate the relationships between children's metacognitive knowledge and general ability; and (c) to examine the relative roles of general ability and metacognition in facilitating word problem solutions. Participants were 32 kindergarten children. Results showed that preschoolers acquired a substantial metacognitive knowledge about mathematical word problems. That knowledge was highly correlated with mathematics performance, even after general ability was controlled. The study further shows that metacognition explained more of the variance in mathematics performance than general ability. The theoretical and practical implications of the study are discussed. 相似文献
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Sarah R. Powell 《Learning disabilities research & practice》2011,26(2):94-108
Solving word problems is a difficult task for students at‐risk for or with learning disabilities (LD). One instructional approach that has emerged as a valid method for helping students at‐risk for or with LD to become more proficient at word‐problem solving is using schemas. A schema is a framework for solving a problem. With a schema, students are taught to recognize problems as falling within word‐problem types and to apply a problem solution method that matches that problem type. This review highlights two schema approaches for second‐ and third‐grade students at‐risk for or with LD: schema‐based instruction and schema‐broadening instruction. A total of 12 schema studies were reviewed and synthesized. Both types of schema approaches enhanced the word‐problem skill of students at‐risk for or with LD. Based on the review, suggestions are provided for incorporating word‐problem instruction using schemas. 相似文献
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This study analysed the effectiveness of presenting mathematical problems as ‘authentic’, which simulated the main aspects of situations in which students are usually involved. To do so, four independent variables were considered: level of mathematical difficulty (easy or difficult); rewording: standard problems (similar to those presented in textbooks), authentic and containing irrelevant situational information; mathematical ability (measured by means of the BADyG test); and reading comprehension level (measured with the comprehension task from the PROLEC-R test). The dependent measure was the success rate of a sample of 156 primary education children (grades four, five and six) in solving each kind of word problem. The results showed that the authentic versions of difficult problems were solved more successfully than other versions by students with high levels of mathematical aptitude and reading comprehension. That means that authentic wording is useful when children are able to understand the added information and have the mathematical knowledge necessary to interpret it. 相似文献
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The aim of this study was to analyse the role of verbal and visuo-spatial working memory (WM) and language skills (vocabulary, listening comprehension) in predicting preschool and kindergarten-aged children’s ability to solve mathematical word problems presented orally. The participants were 116 Finnish-speaking children aged 4–7?years. The results showed that verbal WM (VWM) did not have a direct effect on word problems in young children but was indirectly related to word problems through vocabulary and listening comprehension. These results suggest that in young children, VWM resources support language skills which, furthermore, contribute to variation in solving orally presented word problems. The results also showed that visuo-spatial WM had a direct effect on performance in word problems, suggesting that it plays an important role in word problem solving among this age group. 相似文献
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Compared with standard arithmetic word problems demanding only the direct use of number operations and computations, realistic problems are harder to solve because children need to incorporate “real‐world” knowledge into their solutions. Using the realistic word problem testing materials developed by Verschaffel, De Corte, and Lasure [Learning and Instruction, 4(4), 273–294, 1994], two studies were designed to investigate (a) Chinese elementary school children’s ability to solve realistic word problems and (b) the different effects of two instructional interventions (warning vs. process‐oriented) on their performance. The results indicated that, contrasting to the standard problem solving, the participating children demonstrated a strong tendency to exclude real‐word knowledge and realistic considerations from their solution processes when solving the realistic problems. Process‐oriented instruction, calling for a deep‐level processing, was more likely than warning instruction to promote the activation of realistic considerations, but it was not effective at helping children arrive at realistic or correct answers. Finally, the results and their implications for mathematical teaching are discussed. 相似文献
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Janet Warfield 《Early Childhood Education Journal》2001,28(3):161-167
A kindergarten teacher's practice was investigated in order to understand her knowledge of her children's mathematical thinking, the ways in which she acquired that knowledge, and the uses she made of that knowledge in making instructional decisions. The focus of the investigation was the teacher's knowledge of her children's thinking about numbers, including counting and addition, subtraction, multiplication, and division. The teacher had attended Cognitively Guided Instruction workshops at which she had the opportunity to learn about research on children's mathematical thinking. She gathered information on her own children's thinking by posing word problems, listening to children as the described their strategies for solving the problems, and talking to other adults about her children. She used that information to select problems to pose in subsequent lessons. 相似文献
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Dominic Voyer 《International Journal of Science and Mathematics Education》2011,9(5):1073-1092
Many factors influence a student’s performance in word (or textbook) problem solving in class. Among them is the comprehension
process the pupils construct during their attempt to solve the problem. The comprehension process may include some less formal
representations, based on pupils’ real-world knowledge, which support the construction of a ‘situation model’. In this study,
we examine some factors related to the pupil or to the word problem itself, which may influence the comprehension process,
and we assess the effects of the situation model on pupils’ problem solving performance. The sample is composed of 750 pupils
of grade 6 elementary school. They were selected from 35 classes in 17 Francophone schools located in the province of Quebec,
Canada. For this study, 3 arithmetic problems were developed. Each problem was written in 4 different versions, to allow the
manipulation of the type of information included in the problem statement. Each pupil was asked to solve 3 problems of the
same version and to complete a task that allowed us to evaluate the construction of a situation model. Our results show that
pupils with weaker arithmetic skills construct different representations, based on the information presented in the problem.
Also, pupils who give greater importance to situational information in a problem have greater success in solving the problem.
The situation model influences pupils’ problem solving performance, but this influence depends on the type of information
included in the problem statement, as well as on the arithmetic skills of each individual pupil. 相似文献
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在高职英语教学实践过程中,具有一定词汇量和相当语法知识,并具有一定语言能力的高职学生,常常在无单词、语法障碍,并熟悉文章结构、类型的情况下,仍然对文章感到迷惑不解,这一问题属于语言心理学家研究的内容图式问题。内容图式问题的根源在于学生缺乏与文章相关的背景知识和超语言知识来激活学生已有的内容图式。扩展学生的内容图式,或者是建立新的内容图式,可以有效地帮助学生理解所阅读的文章。 相似文献
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Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties? 总被引：1，自引：0，他引：1
The aim of this study was to compare Japanese and Belgian elementary school pupils' (lack of) activation of real-world knowledge during understanding and solving arithmetic word problems in a school context. The word problem test used in a study by Verschaffel, De Corte, and Lasure (1994) was collectively administered to 91 Japanese fifth graders. Besides standard problems which can be modeled in a straightforward way by one or two basic arithmetic operations with the given numbers, this test contained a series of problematic items which cannot be modeled and solved in such a way, at least if one seriously takes into account the realities of the context evoked by the problem statement. The results of the study revealed that Japanese pupils, similarly to Belgian children, have a strong tendency to neglect commonsense knowledge and realistic considerations during their solution of word problems. Moreover, a comparison of Japanese pupils with and without extra hints aimed at improving the disposition towards more realistic mathematical problem solving revealed that these extra hints had only a small effect. 相似文献
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We investigated the longitudinal relations between cognitive skills, specifically language-related skills, and word-problem solving in 340 children (6.10–9.02 years). We used structural equation modeling to examine whether word-problem solving, computation skill, working memory, nonverbal reasoning, oral language, and word reading fluency measured at second grade were associated with performance on measures of word-problem solving in fourth grade. Results indicated that prior word-problem solving, computation skill, nonverbal reasoning, and oral language were significantly associated with children’s later word-problem solving. Multi-group modeling suggested that these relations were not significantly different for boys versus girls. Implications of these findings are discussed. 相似文献
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Limin Chen Wim Van Dooren Qi Chen Lieven Verschaffel 《International Journal of Science and Mathematics Education》2011,9(4):919-948
In the present study, which is a part of a research project about realistic word problem solving and problem posing in Chinese
elementary schools, a problem solving and a problem posing test were administered to 128 pre-service and in-service elementary
school teachers from Tianjin City in China, wherein the teachers were asked to solve 3 contextually challenging division-with-remainder
(DWR) word problems and pose word problems according to 3 symbolic expressions. Afterwards, they were also given 2 questionnaires
wherein they had to evaluate 3 different pupil reactions to, respectively, 1 problem solving item and 1 problem posing item
about DWR. First, our results revealed that teachers behaved quite ‘realistically’ not only when solving and posing DWR problems
themselves but also when evaluating elementary school pupils’ DWR problem solving and problem posing performance. Second,
we found a correspondence between teachers’ own performance on the tests and their evaluations of pupils’ reactions. Third,
the present study provides some further insight into the role of one of the instructional factors that is generally considered
responsible for the strong and worldwide tendency among elementary school children to neglect real-world knowledge and realistic
considerations in their endeavours to solve and pose mathematical word problems, namely the teachers’ conceptions and beliefs
about this topic. 相似文献
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The current study aimed at identifying the difficulties experienced by children with mathematics learning disability (MLD) in the problem representation phase of arithmetic word problem solving using a novel problem types identification task. An MLD group (n = 66) and a typically achieving control group (n = 139) were recruited for an assessment on problem type identification as well as some domain-general and mathematics-related cognitive abilities. Results from ANCOVA showed that the MLD group scored significantly lower than the typically achieving control group on this assessment, after controlling for the effect of cognitive correlates, reading achievement and arithmetic performance. Furthermore, this assessment significantly predicted MLD membership even after taking children's arithmetic competency into account. The current study confirmed the difficulties in problem representation of arithmetic word problems experienced by students with MLD and provided evidence for the need to introduce schema instructions in mathematics classes. 相似文献
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Carlos O. Calderón-Tena 《Educational Psychology in Practice》2016,32(2):107-121
This study investigated the role of broad cognitive processes in the development of mathematics skills among children and adolescents. Four hundred and forty-seven students (age mean [M] = 10.23 years, 73% boys and 27% girls) from an elementary school district in the US southwest participated. Structural equation modelling tests indicated that calculation complexity was predicted by long-term retrieval and working memory; calculation fluency was predicted by perceptual processing speed, phonetic coding, and visual processing; problem solving was predicted by fluid reasoning, crystallised knowledge, working memory, and perceptual processing speed. Younger students’ problem solving skills were more strongly associated with fluid reasoning skills, relative to older students. Conversely, older students’ problem solving skills were more strongly associated with crystallised knowledge skills, relative to younger students. Findings are consistent with the theoretical suggestion that broad cognitive processes play specific roles in the development of mathematical skills among children and adolescents. Implications for educational psychologists are discussed. 相似文献