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1.
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
2.
Recent research has documented that many pupils show a strong tendency to exclude real-world knowledge from their solutions of school arithmetic word problems. In the present study, a test consisting of 14 word problems—half of which were problematic from a realistic point of view—was administered to a large group of students from three different teacher training institutes in Flanders. For each word problem, the student-teachers were first asked to solve the problem themselves, and afterwards to evaluate four different answers given by pupils. The results revealed a strong tendency among student-teachers to exclude real-world knowledge from their own spontaneous solutions of school word problems as well as from their appreciations of the pupils' answers. 相似文献
3.
陈妍 《安阳师范学院学报》2010,(3):126-130
为了探讨小学生在解答数学应用题时考虑问题真实情境的实际状况,本研究采用问卷法对城乡两所小学的198名五、六年级学生进行了数学应用题解题测验。研究结果表明：（1）被试在解答数学应用题时能够考虑到问题真实情境的人数比例约为38.3%,做出常规回答的人数比例为54.5%,后者显著高于前者（χ^2=5.564,p〈.05）。（2）六年级学生在解决问题的过程中比五年级学生能更多考虑到问题的真实情境（χ^2=4.616,p〈.05）。（3）改变问题的设置形式后,原来按常规回答的学生中,约有25%在解答变换模式的同一道题目中考虑到了问题的真实情境。（4）不同题目,学生的反应存在一定差异,但总体来说学生对不同类型的题目（无关条件题目,条件不充分题目）的回答情况还是存在一致性的。 相似文献
4.
Wim Van Dooren Lieven Verschaffel Patrick Onghena 《Journal of Mathematics Teacher Education》2003,6(1):27-52
In this study we investigate the arithmetic andalgebra word problem-solving skills andstrategies of future primary and secondaryschool teachers in Flanders (Belgium).Moreover, we describe the evolution of theseskills and strategies from the beginning to theend of their teacher education. The resultsshow that future secondary school mathematicsteachers preferred the use of algebra, evenwhen an arithmetic solution was morestraightforward. The solutions of futureprimary school teachers were more diverse: onesubgroup tended to apply exclusively arithmeticmethods (which led to failures on the mostdifficult word problems), whereas anothersubgroup was more adaptive in its strategychoices. Finally, student teachers evolved intheir problem-solving skills during theirteacher education, but not in their strategypreferences. The research findings indicatethat, in the education of pre-service primaryand secondary school teachers, there is a needfor an explicit treatment of pupils' transitionfrom arithmetical to algebraic thinking. 相似文献
5.
数学应用意识是指运用所获得的数学知识去解决同类或类似的问题的过程 ,特别是根据不同问题情境的要求和制约灵活使用已有知识的能力 ,并通过在不同的情境中对原有知识的使用达到对原有知识重组和再学习的目的。学生在解决数学应用题时 ,数学应用意识普遍淡薄。造成学生缺乏数学应用意识的主要原因在于学校的数学课堂情境与真实生活数学情境存在着根本差异。研究表明通过创设类似真实的数字情境能够促进学生数学应用意识的发展。 相似文献
6.
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
7.
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
8.
This study investigated the effect of initial instruction on the processes children use to solve addition and subtraction word problems. Prior to instruction and following a two-month introductory unit on addition and subtraction, 43 first-grade children were individually tested on verbal problems representing different addition and subtraction situations. Prior to instruction, the children's solution processes directly modeled the action or relationships described in the problem. Following instruction, they generally used a separating strategy for all subtraction problems. Although they could solve the problems, few children could coordinate their solutions with the arithmetic sentence they wrote to represent the problem. 相似文献
9.
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
10.
The mastery of word problems is seen as an important test of mathematical ability. When solving such problems, students supposedly go beyond rote learning and mechanical exercises to apply their knowledge to realistic problem situations in which mathematical reasoning becomes an important instrument for making concrete judgements. Research shows that performance on word problems is often surprisingly poor. Non-realistic, and even logically inconsistent, answers to word problems are often accepted by students, and there are many signs that students seldom make so-called realistic considerations when applying their mathematical knowledge to real world events. The study reported is a follow-up of the work by Verschaffel, De Corte, and Lasure (1994) in which the difficulties students have in making realistic considerations were clearly illustrated. In the present study, students (10–12 years of age) worked in groups, and the tasks given (estimating distances) were introduced as part of a general discussion of how to calculate distances to school. Results show that the participants were clearly able to entertain different assumptions regarding how to measure distances, and they make distinctions between alternative options when discussing, for instance, the distance between two villages as indicated on a road sign on the one hand, and when talking about the shortest possible distance on the other. It is argued that the problem of what constitutes a realistic consideration when solving word problems is far from simple but has to be understood in context. 相似文献
11.
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
12.
Word problems play a crucial role in mathematics education. However, the authenticity of word problems is quite controversial.
In terms of the necessity of realistic considerations to be taken into account in the solution process, word problems have
been classified into two categories: standard word problems (S-items) and problematic word problems (P-items). S-items refer
to those problems involving the straightforward application of one or more arithmetical operations with the given numbers,
whereas P-items call for the use of real-world knowledge and real-life experience in the problem-solving process. This study
aims to explore how Chinese upper elementary school mathematics teachers think of the place and value of P-items in the elementary
mathematics curriculum. 相似文献
13.
Every word problem has a solution-The social rationality of mathematical modeling in schools 总被引：1，自引：0，他引：1
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.
14.
Ceneida Fernández Salvador Llinares Wim Van Dooren Dirk De Bock Lieven Verschaffel 《European Journal of Psychology of Education - EJPE》2012,27(3):421-438
This study investigates the development of proportional and additive methods along primary and secondary school. In particular, it simultaneously investigates the use of additive methods in proportional word problems and the use of proportional methods in additive word problems. We have also studied the role played by integer and non-integer relationships between the given numbers and the nature of quantities (discrete or continuous) in the development of these phenomena. A test consisting of additive and proportional missing-value word problems was solved by 755 primary and secondary school students (from fourth to tenth grade). The findings indicate that the use of additive methods in proportional situations increased during primary school and decreased during secondary school, whereas the use of proportional methods in additive situations increased along primary and secondary school. Moreover, the presence or absence of integer ratios strongly affects this behavior, but the nature of quantities only has a small influence on the use of proportional methods. 相似文献
15.
16.
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
17.
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
18.
George L.C. Hills 《Instructional Science》1981,10(1):67-93
A father is now 20 years older than his son. In 8 years, the father's age will be 5 years more than twice the son's age. Find their present age.Word problems, such as this one, are a perennial source of difficulty for students of school mathematics. Unfortunately, very little is known about why they are problematic, mainly because so little is known about how students understand such problems or the strategies they use in their efforts to solve them. Traditional research into word problems has shed precious little light on this question owing, in no small part, to its almost singular preoccupation with results of pupils' activities—as expressed in some sort of test score, and to its tendency to all but ignore what students actually do when confronted with problems of this kind.This study was carried out as one facet of a larger research project designed to gain more insight into some of the ways in which students understand school mathematics. It focuses on the efforts of one pupil, a twelve-year-old girl in grade seven, to come to terms with solving word problems using an algebraic approach. Strategies associated with both the structured and the unstructured clinical interview were used in order to reveal what was involved in her attempts to make sense of the word problems in her grade seven mathematics textbook.Based on the information gained in the interview, a rational reconstruction of the student's problem-solving strategy is proposed, and compared with the strategies normally prescribed in contemporary school mathematics textbooks. What emerges from this comparison is the finding that, while there appear to be systematic and fundamental differences between the procedures prescribed by the text and those actually used by the pupil in working through certain problems, these differences are undetectable in the finished product; either in the answer itself or in the rough or finished work. What this suggests, among other things, is that if, as educators and/or researchers, we limit our attempts to understand how students go about learning to solve word problems (or how they approach any other part of the school mathematics curriculum, for that matter) to examining what they commit to paper, we are apt to be seriously misled concerning what they genuinely understand and what they fail to understand. In short, if we are to learn more about why pupils experience difficulties with word problems we must begin to pay serious attention to what they say and do as they work their way through them.This study was supported by a Research and Development Grant from the Faculty of Education, Queen's University. 相似文献
19.
Adrian Treffers 《Educational Studies in Mathematics》1991,22(4):333-352
Innumeracy, as understood here, is the inability to handle numbers and numerical data decently and to evaluate statements regarding sums and situations which invite mental processing and estimating. Innumeracy is quite frequent at primary school, as experience shows, and particularly, where open problems ask for numerical data to be supplied and substituted by the pupils themselves.Innumeracy may be caused by a structuralist design of the instruction: from the beginning onwards, emphasis is on teaching the algorithms of column arithmetic, and no room is yielded to context problems.The alternative, as here presented, to the structuralist approach is the realistic one. Here arithmetic starts as an informal context-bound activity of the children, who, via model situations, gradually develop more formal methods; these, in turn, remain tied to mental arithmetic and arithmetic by estimate, both in bare sums and in context situations. 相似文献
20.
In mathematical word problem solving, a relatively well-established finding is that more errors are made on word problems in which the relational keyword is inconsistent instead of consistent with the required arithmetic operation. This study aimed at reducing this consistency effect. Children solved a set of compare word problems before and after receiving a verbal instruction focusing on the consistency effect (or a control verbal instruction). Additionally, we explored potential transfer of the verbal instruction to word problems containing other relational keywords (e.g., larger/smaller than) than those in the verbal instruction (e.g., more/less than). Results showed a significant pretest-to posttest reduction of the consistency effect (but also an unexpected decrement on marked consistent problems) after the experimental verbal instruction but not after the control verbal instruction. No significant effects were found regarding transfer. It is concluded that our verbal instruction was useful for reducing the consistency effect, but future research should address how this benefit can be maintained without hampering performance on marked consistent problems. 相似文献