小学生解答数学应用题时考虑问题真实情境的研究

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。     

The Performance of Chinese Primary School Students on Realistic Arithmetic Word Problems

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.     

Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties?

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.     

AN INVESTIGATION ON CHINESE TEACHERS�� REALISTIC PROBLEM POSING AND PROBLEM SOLVING ABILITY AND BELIEFS

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.     

PERFORMANCE IN MATHEMATICAL PROBLEM SOLVING AS A FUNCTION OF COMPREHENSION AND ARITHMETIC SKILLS

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.     

REAL-WORLD PROBLEMS: TEACHERS’ EVALUATION OF PUPILS’ SOLUTIONS

This article scrutinizes the solutions of real-world problems by pupils and the evaluations of these by their teachers in a semi-rural school in Zimbabwe. Generally, real-world problems are solved as if these are standard problems expecting a solution and a correct answer. In most cases, the solutions of the pupils are considered correct by the teachers thereby suggesting teachers’ unfamiliarity with the nature of these problems. There is not much variation in the solution approaches among pupils as well as between pupils and teachers. As assessment in many ways dictates teaching, it is suggested to incorporate continuous assessment into the system, which should include more open ended tasks from real-world contexts. This may encourage teachers to include the same in their day to day teaching.     

The acquisition of problem-solving skills in mathematics: How animations can aid understanding of structural problem features and solution procedures

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations would be most effective for acquiring these prerequisites, because they show the continuous transition from a concrete, but superficial problem representation to a more abstract, mathematical problem model that forms a basis for solving a problem. An experiment was conducted, where N = 32 pupils from a German high school studied either only text-based worked examples explaining different problem categories from the domain of algebra or worked examples augmented with hybrid animations. Learners with hybrid animations showed superior problem-solving performance for problems of different transfer distance relative to those in the text-only condition.     

Word problems and mathematical reasoning-A study of children''s mastery of reference and meaning in textual realities

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.     

小学生解题方法单一性原因与对策

小学生解题方法单一性导致了学生的思维由发散走向统一,阻碍了创新能力的形成和发展.通过对教师日常教学方式、评价方式的分析得出:"填鸭式"教学、运用"规定"方法训练学生解题以及"标准化"考试是造成小学生解题方法单一性的主要原因.改变小学生解题方法单一性为多样化的策略是:要尊重非标准答案;鼓励学生的求异思维;建立以创新为导向的评价体系.     

Modelling reality in mathematics classrooms: The case of word problems

An abundance of recent research, in many countries, has documented a very widespread tendency of children to answer school mathematics word problems with apparent disregard for the reality of the situations described by the text of these problems. Analysis of this behaviour strongly suggests that an explanation is not to be found in some cognitive deficit of the children, but rather in the culture of the classroom wherein word problems are presented in stereotyped fashion, with an implicit assumption that a solution involving the application of one or more of the basic arithmetical operations to the numbers mentioned in the text is appropriate and unproblematical. Taking such contextual influences into account, the observed behaviour of the children may be considered a reasonable response. An alternative conceptualisation of word problems, as situations calling for mathematical modelling taking into account real-world knowledge where appropriate, is proposed, with suggestions as to how it could be implemented.     

Realistic considerations in mathematical modeling of school arithmetic word problems

The aim of the present study was to collect in a systematic way empirical data about the (lack of) activation of real-world knowledge during elementary school pupils' understanding and solution of school arithmetic word problems. Ten pairs of word problems were collectively administered to 75 fifth-graders during a typical mathematics lesson. While the first item of each pair could be modeled and solved in a straightforward and unproblematic way by one or two simple arithmetic operations with the given numbers, the second problem could not be modeled and solved in such a way, at least if one seriously takes into account the realities of the context called up by the problem statement. An analysis of the pupils' reactions to these problematic word problems shows an alarmingly small number of realistic responses or additional comments based on realistic considerations.     

The school staff's perception of their ability to teach special educational needs pupils in inclusive settings in Finland

Recent studies have suggested that the professional training received by general educators does not adequately prepare them to properly implement inclusion-based practices. The idea of inclusion in practice has not significantly changed the situation of teaching pupils with special educational needs (SENs) in mainstream classes. This study's primary intent is to examine the factors that identify the school staff's ability to meet the needs of SEN pupils in their daily teaching situations. A total of 187 elementary school teachers, principals and teaching assistants in a Finnish city completed a structured questionnaire that used a self-evaluation method. Two components were generalised according to answers concerning the respondents’ confidence in and knowledge of teaching SEN pupils. The results indicate that teachers’ qualifications constitute the main reason affecting their ability in this area. Pedagogical and practical knowledge, as well as collaborative skills in teaching SEN pupils, is focused on special educators. These findings reveal the need for additional and in-service training and more effective cooperation between special and general education to share the knowledge of teaching SEN pupils in practice.     

Lower secondary school teachers' judgements of pupils' problems

Lower secondary school teachers from six different schools in one Norwegian municipality reported on the prevalence of problems among pupils entering lower secondary school and types of problems among pupils in Grades 8–10. Teachers report that the transition from Elementary to Lower secondary school is problematic for approximately 30% of the pupils. About 70% of the teachers report that 25% or more of pupils transitioning to Grade 8 lack academic experiences and skills and have problems following directions. There is also a tendency for teachers who report higher values on professional (un)certainty about pupils' learning and on two efficacy variables included in the study, to be more favourably inclined towards inclusion of children who are perceived as having learning or behaviour problems. Additionally, teachers who report higher values on efficacy scales tend to report lower values on problems among pupils, and teachers who are less favourable towards inclusion report higher numbers of pupils having problems. The results are discussed in relation to schools as workplaces and professional development for pre‐service and in‐service teachers.     

Les élèves et l'histoire dans l'examen français du certificat d'études primaires entre 1918 et 1926

This article presents the method used to study examination papers written by young pupils. This sort of pupils’ work can give information on who are involved in examinations.

‐ The pupils: what they learn in history and how they produce answers;

‐ The teachers: what they teach in their class and how;

‐ The juries: how they assess by means of a grade the minimum knowledge of most of the pupils who are to leave school.

The problem here is to follow the route from laws and decrees to real teachers and real pupils. Therefore, this research relies on source material such as annual primary inspector reports, annual local teachers’ meetings with model lessons, and, above all, examination papers. For this last source, a popular examination in France at that time was used: the Certificat d'Etudes, which was given at the end of the primary curriculum for 13‐year‐old pupils. By chance, the Departmental Archives of the Somme region still has 4058 history test examination papers from 1918 to 1926.     

Open-ended problem solving in school chemistry: A preliminary investigation

This paper uses a new set of 14 open-ended problems, designed for 14-17-year-old pupils studying chemistry, to attempt to gain some initial insights into the ways pupils solve open-ended chemistry problems. The emphasis is on how concepts and linkages between concepts influence success in solving such open-ended problems. Pupils worked in groups of three attempting to solve the problems and were encouraged to talk freely, to make notes of their progress, and to note their agreed answers. Evaluation sheets were also completed individually by the pupils after each problem. By studying the interactions between pupils by means of written materials, observation and audiotapes, it was possible to build up a picture of the way the pupils approached the problems and to explore some of the reasons for difficulties they experienced. In the light of the evidence, it is suggested that creating the links between 'islands' of knowledge is an important skill in solving open-ended problems and that this skill is not easily achieved by pupils at these ages. The notion that problem solving is a generic skill which can be taught is questioned.     

新课改下小学生数学真实性问题解决能力的调查研究

基于刘儒德的研究,对山东省济南市某小学120位10~13岁的小学生进行了真实性问题的测验.结果表明:(1)被试中对真实数学问题作出真实性解答的人数占总人数的30%,高于02年的结论;(2)作出常规解答的人数占总人数的40%,比2002年的48%略低;(3)高年级的被试中作出真实解答的人数比例要普遍高于低年级,与2002年一致;(4)对于不同类型的真实性问题,被试能够作出真实解答的程度不同;(5)被试在解答真实性问题的过程中,对题目有了自己更多的想法.上述变化与不变,引导我们反思新课程的得失.     

小学生英语写作中母语负迁移问题及其对策

小学生英语写作长期受母语词汇,语篇,字母、标点,句法、词距等母语负迁移干扰,主要原因在于存在语言标记性差异、东西方思维差异、小学生情感过滤过强、教师词块教学存在问题等。有鉴于此,应该引导学生增加可理解性语言输入,超越"最近发展区",实施词块教学法,鼓励小学生借用思维导图串联词块自主作文等。     

小学生心理健康状况的调查研究

本文采用MHT调查了449名小学生心理健康的现状,通过统计分析发现:(1)市区小学生心理健康现状良好,心理健康问题的检出率为2.475‰。(2)各个内容量表标准分>8的学生人数在性别、年级、学校之间均无显著性差异。(3)各个内容量表标准分>8的人数比率在全体学生问存在极其显著性差别。     

学生听力认识调查和耳语测试报告

听力是一项重要的生理指标。听力检查是发现听力问题的一种重要手段。我们对４０８名小学生进行了听力认识问卷调查及耳语测试。结果显示：９５．８％的学生从未做过听力检查;１６．８％的学生自觉有听力问题;１１．０％的学生耳语测查异常;１１．６％的学生对听力检查抱着无所谓的态度;甚至有６．７％的学生不愿意听力检查。警示：家长、学校、社会应关注儿童的听力状况