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1.
The study investigates the relationship between memory updating and arithmetic word problem solving. Two groups of 35 fourth graders with high and low memory-updating abilities were selected from a sample of 89 children on the basis of an updating task used by Palladino et al. [Memory & Cognition 29 (2002) 344]. The two groups were required to solve a set of arithmetic word problems and to recall relevant information from another set of problems. Several span tasks, a computation test, and the PMA verbal subtest were also administered. The group with a high memory-updating ability performed better in problem solving, recalling text problems, and in the computation test. The two groups did not differ in the PMA verbal subtest or in the digit and word spans. Results were interpreted as supporting the importance of updating ability in problem solving and of the substantial independence between memory updating and problem solving on one hand and verbal intelligence on the other.  相似文献   

2.
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   

3.
McNeil NM 《Child development》2008,79(5):1524-1537
Do typical arithmetic problems hinder learning of mathematical equivalence? Second and third graders (7–9 years old; N= 80) received lessons on mathematical equivalence either with or without typical arithmetic problems (e.g., 15 + 13 = 28 vs. 28 = 28, respectively). Children then solved math equivalence problems (e.g., 3 + 9 + 5 = 6 + __), switched lesson conditions, and solved math equivalence problems again. Correct solutions were less common following instruction with typical arithmetic problems. In a supplemental experiment, fifth graders (10–11 years old; N= 19) gave fewer correct solutions after a brief intervention on mathematical equivalence that included typical arithmetic problems. Results suggest that learning is hindered when lessons activate inappropriate existing knowledge.  相似文献   

4.
The focus of this paper is on sense-making and the use of real-world knowledge in mathematical modeling in schools. Arguments are put forward that classroom word problem solving is more—and also less—than the analysis of subject-matter structures. Students easily “solve” stereotyped, even unsolvable, problems without any regard to the constraints of factual reality. Mathematics learning in schools is inseparable not only from the materials employed, but from the macro- and microcultural web of practices within the social context of schooling. It represents, beyond the insightful activity of ideal problem solving, a type of socio-cognitive skill.The two experiments reported replicate and extend a study by Verschaffel, De Corte, and Lasure (1994). In the first experiment, a list of standard problems that could be solved by straightforward use of arithmetic operations, and a parallel list of problems which were problematic with respect to realistic mathematical modeling, were administered to fourth and fifth graders. In the second experiment, a similar list of problematic problems was presented to seventh graders under three socio-contextual conditions varying in the degree to which the pupils were told or signaled that the problems were more difficult to solve than it seemed at first or that they even could be unsolvable. The result of both studies was that most pupils “solved” a significant part of the unsolvable problems without evincing “realistic reactions”. This overall finding is discussed with respect to three issues:
  • 1. 
    (i) the quality of word problems employed in mathematics education,
  • 2. 
    (ii) the culture of teaching and learning, and
  • 3. 
    (iii) the more general issue of social rationality in school mathematics problem solving.
  相似文献   

5.
The present study aims to investigate the effects of a design experiment developed for third-grade students in the field of mathematics word problems. The main focus of the program was developing students?? knowledge about word problem solving strategies with an emphasis on the role of visual representations in mathematical modeling. The experiment involved five experimental and six control classes (N?=?106 and 138, respectively) of third-grade students. The experiment comprised 20 lessons with 73 word problems, providing a systematic overview of the basic word problem types. Teachers of the experimental classes received a booklet containing lesson plans and overhead transparencies with different types of visual representations attached to the word problems. Students themselves were invited to make drawings for each task, and group work and teacher-led discussion shaped their beliefs about the role of visual representations in word problem solving. The effect sizes of the experiment were calculated from the results of two tests: an arithmetic skill and a word problem test, and the unbiased estimates for Cohen??s d proved to be 0.20 and 0.62. There were significant changes also in experimental group students?? beliefs about mathematics. The experiment pointed to the possibility, feasibility, and importance of learning about visual representations in mathematical word problem solving as early as in grade?3 (around age 9?C10).  相似文献   

6.
Fractions are an important but notoriously difficult domain in mathematics education. Situating fraction arithmetic problems in a realistic setting might help students overcome their difficulties by making fraction arithmetic less abstract. The current study therefore investigated to what extent students (106 sixth graders, 187 seventh graders, and 192 eighth graders) perform better on fraction arithmetic problems presented as word problems compared to these problems presented symbolically. Results showed that in multiplication of a fraction with a whole number and in all types of fraction division, word problems were easier than their symbolic counterparts. However, in addition, subtraction, and multiplication of two fractions, symbolic problems were easier. There were no performance differences by students’ grade, but higher conceptual fraction knowledge was associated with higher fraction arithmetic performance. Taken together this study showed that situating fraction arithmetic in a realistic setting may support or hinder performance, dependent on the problem demands.  相似文献   

7.
When solving word problems, many children encounter difficulties in making sense of the information and integrate it into a meaningful schema. This is the fundamental phase on which subsequent problem solution depends. To better understand the processing underlying this fundamental phase, this study examined the roles of schema construction and knowledge of mathematical vocabularies in word problem solving. The participants were 139 Chinese third graders studying in Hong Kong. Path analysis showed that there were two kinds of pathways to word problem solving: language-related and number-related. In particular, reading fluency was related to word problem solving in two mediated language-related pathways: one via schema construction, the other via knowledge of mathematical vocabularies. In the number-related pathway, arithmetic concept was related to word problem solving via knowledge of mathematical vocabularies. These findings highlight the specific roles of schema construction and mathematical vocabulary in word problem solving, thereby providing useful implications of how best to support children in understanding and integrating the information from the problem.  相似文献   

8.
The study presented here will examine the connection between teaching and development, focusing in particular on how children solve “missing addend” story problems. Vygotsky’s theory of development will serve as the framework. Ordinarily, when second graders are forced to solve a problem of this type by choosing an arithmetic operation (+ or ?), half of them fail. The most frequent error is choosing addition. The subjects in the experiment presented here were second graders who had always been given the opportunity to use objects or drawings to “act out” (model) the actions expressed in the problem statament. They had never been in the above “forced-choice” situation. Moreover, they had been taught to use a “forward strategy” to solve subtraction problems like 42–36 (to get from 36 to 40, it takes 4; and then to get to 42, it takes 2 more) and a “backward strategy” for subtraction problems like 42–6. When given the following missing-addend problem: “Pierre has 63 pieces of candy and paul has 4. Paul wants to have the same number of pieces as Pierre. How many pieces of candy must Paul buy?” none of these children performed an addition, approximately half did a subtraction, and the others succeeded by using a breakdown strategy or a drawing. The overall success rate was 92%. The results obtained suggest a way of operationalizing the notion of “zone of proximal development” for problem solving of this type.  相似文献   

9.
In this study, we investigated fifth graders’ (n = 52) fall literacy, academic language, and motivation and how these skills predicted fall and spring comprehension monitoring on an eye movement task. Comprehension monitoring was defined as the identification and repair of misunderstandings when reading text. In the eye movement task, children read two sentences; the second included either a plausible or implausible word in the context of the first sentence. Stronger readers had shorter reading times overall suggesting faster processing of text. Generally fifth graders reacted to the implausible word (i.e., longer gaze duration on the implausible vs. the plausible word, which reflects lexical access). Students with stronger academic language, compared to those with weaker academic language, generally spent more time rereading the implausible target compared to the plausible target. This difference increased from fall to spring. Results support the centrality of academic language for meaning integration, setting standards of coherence, and utilizing comprehension repair strategies.  相似文献   

10.
Abstract

The present study examined phonological processing skills (phonological memory, phonological awareness, and rapid automatised naming, RAN) in relation to early Chinese reading and early Chinese mathematics for young children. Early Chinese reading was assessed with single character reading and multi-character word reading, and early mathematics was assessed with procedural arithmetic and arithmetic story problems. Among 86 Chinese kindergarteners, phonological processing skills explained 20% of the variance in character reading and 28% of the variance in word reading; they accounted for 8% of the variance in arithmetic and 11% of the variance in story problem performance. Specifically, findings further highlight the general importance of phonological awareness in early Chinese single character reading, word reading, simple arithmetic and story problems, and the specific role of RAN in single character reading and simple arithmetic.
  • Highlights

  • Phonological awareness and rapid automatised naming explained unique variance in Chinese single character reading and procedural arithmetic.

  • Only phonological awareness significantly accounted for unique variance in Chinese word reading and arithmetic story problems.

  • The associations of phonological awareness with procedural arithmetic and arithmetic story problem were maintained even beyond other variables.

  相似文献   

11.
This study examined the associations of phonological processing skills with reading and arithmetic ability in Chinese kindergartners (Mage = 5.56 years), third graders (Mage = 9.72 years), and fifth graders (Mage = 11.75 years) (N = 413) of Han descent. The results showed that phonological awareness and rapid automatized naming (RAN) showed stronger relations than phonological memory with reading and arithmetic across grades. Furthermore, the associations of phonological awareness and RAN with reading were much stronger in kindergartners than in primary school children, whereas their relationships with arithmetic remained stable across grades. Among phonological skills, phonological awareness has a unique influence on arithmetic that is independent of Chinese character reading in third-graders and kindergartners. In contrast, RAN uniquely explained the variation in arithmetic skills in fifth graders when reading was statistically controlled for. These findings have important implications for understanding the co-development of reading and arithmetic across grades and raise the possibility of training in phonological awareness and/or RAN to help children at risk for learning disabilities.  相似文献   

12.
While previous studies mainly focused on children’s additive and multiplicative reasoning abilities, we studied third to sixth graders’ preference for additive or multiplicative relations. This was investigated by means of schematic problems that were open to both types of relations, namely arrow schemes containing three given numbers and a fourth missing one. In study 1, children had to fill out the missing number, while in study 2, children had to indicate all possibly correct answers among a set of given alternatives. Both studies explicitly showed the existence of a preference for additive relations in some children, while others preferred multiplicative relations. Mainly younger children preferred additive relations, whereas mainly children in upper primary education preferred multiplicative relations. Number ratios also impacted children’s preference, especially in fifth grade. Moreover, the results of study 2 provided evidence for the strength of children’s preference and showed that calculation skills do not coincide with preference, and hence, that preference and calculation skills are two distinct child characteristics. The results of both studies using these open problems resembled previous research results using classical multiplicative or additive word problems. This supports the hypothesis that children’s preferred type of relations may be at play in solving classical word problems as well—besides their abilities—and may hence be an additional factor explaining the mistakes that children make in those word problems. This research line thus seems promising for further research as well as educational practice.  相似文献   

13.
The present study used multiple calibration indices to capture the complex picture of fifth graders' calibration of feeling of confidence in mathematics. Specifically, the effects of gender, type of mathematical problem, instruction method, and time of measurement (before and after problem solving) on calibration skills were investigated. Fourteen classes (N = 389 fifth graders) were randomly selected from two school mathematics programs, namely the gradual program design and the realistic program design. Students completed two different types of mathematical problems (a set of computation problems and a set of application problems) and reported their feeling of confidence (that they would find the right solution) when first reading the problem statement and again after they had produced the solution of each of the problems. Students' calibration skills were measured using three indices of calibration. Effects on the calibration of feeling of confidence due to gender, instruction method, type of mathematical problem, and time of measurement were found and are discussed.  相似文献   

14.
Abstract

With a sample of 7,752 fourth- to seventh-grade students in 25 schools which were randomized at the school level to condition, this article reports experimental impacts of an enhanced version of Word Generation on student outcomes at the end of Year 1 and of Year 2. Word Generation employs analysis, synthesis, critique, and problem-solving activities to build students’ academic language, perspective taking, and ultimately their reading comprehension. Results indicate that the program improves the proximate outcome of academic vocabulary included in the curriculum after the first and second year of implementation for all students (Y1 effect size (ES)?=?.22, Y2?=?.28 for fourth and fifth graders; Y1 ES?=?.13, Y2?=?.16 for sixth and seventh graders). For those in the fourth and fifth grades, their perspective positioning skills also improved at the end of the first year (ES?=?.14), and their academic language skills (ES?=?.06), perspective articulation and positioning skills (ES?=?.12, .19), and reading comprehension (ES?=?.15) improved at the end of the second year. Among sixth and seventh graders, there were improvements in perspective positioning skills (ES?=?.19) and reading comprehension (ES?=?.10) at the end of Year 2. Effects after both Years 1 and 2 were stronger in high-exposure classrooms.  相似文献   

15.
The goal of the present study was to test three competing hypotheses about the nature of comprehension problems of students who are poor in reading comprehension. Participants in the study were first, second, and third graders, totaling nine cohorts and over 425,000 participants in all. The pattern of results was consistent across all cohorts: Less than 1 percent of first‐ through third‐grade students who scored as poor in reading comprehension were adequate in both decoding and vocabulary. Although poor reading comprehension certainly qualifies as a major problem rather than a myth, the term specific reading comprehension disability is a misnomer: Individuals with problems in reading comprehension that are not attributable to poor word recognition have comprehension problems that are general to language comprehension rather than specific to reading. Implications for assessment and intervention are discussed.  相似文献   

16.
For students’ success in treating word problems, language obstacles have been identified. Interventions are required for students to overcome them, likewise professional development and curriculum support for teachers. But how much support do teachers need? In a controlled trial evaluation study, two interventions for n = 275 fifth graders are compared: The language-responsive intervention (LRI) uses the variation principle and strategic scaffolding fostering comprehension strategies and language awareness. The information-problems-only intervention (IPI) uses the same set of word problems, but teachers were only informed about typical obstacles. For the evaluation study, the ANOVA shows that in both interventions, students have significantly more learning gains than in the no-treatment group, and substantially more in the LRI than in IPI. Students with different language backgrounds profit comparably from LRI, but in different subscales. In conclusion, identifying obstacles is not enough for implementing effective teaching, it should be enhanced by curriculum support.  相似文献   

17.
Abstract

This study investigated the effects of instruction in environmental education on the attitudes of elementary school children toward the environment. One class of third graders was provided with two hours of environmental education instruction. A comparable class of third graders served as a control group. Both classes were pre- and posttested using an author-designed environmental attitude questionnaire. Analyses of these data showed that 1) the experimental group had significantly improved attitudes on a pre-post basis and 2) this same group had significantly more positive attitudes toward the environment when compared with the control group. When tested again as fifth graders, the experimental group remained significantly more positive toward the environment than the fifth grade control group.  相似文献   

18.
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   

19.
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   

20.
Solving arithmetic word problems such as “Mary has 25 marbles. She has 5 more marbles than John. How many marbles does John have?”, in which the relational term (more than) interferes with the arithmetic operation (subtraction), relies in part on the ability to inhibit an overlearned ‘add if more or subtract if less’ heuristic in children, adolescents and adults. Here, we used a negative priming (NP) paradigm to investigate whether experts in mathematics need to inhibit this heuristic when solving this type of arithmetic word problem. We found NP effects in experts in mathematics, but with a smaller amplitude than those in non-experts (N = 40). We replicate these results in a second experiment (N = 62) in which we matched experts and non-experts on general intelligence and inhibitory control ability. This suggests that experts also need to inhibit the ‘add if more or subtract if less’ heuristic to solve such problems but were more efficient at inhibiting the heuristic than non-experts.  相似文献   

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