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1.
The present study examines the effect of three different structured methods, traditional, independent and problem‐solving, of teaching children arithmetic in the beginning of 7th grade in Sweden, age 13 years. The progress made by these students is presented by measures of their arithmetic ability, calculation and quantitative concept, as well as their self‐regulated learning skills in mathematics, characterised as internal and instrumental motivation, self‐concept and anxiety. The results will be discussed with reference to a socio‐cultural perspective. This study has a split‐plot factorial design with time as within‐subject and type of intervention as a between‐subject factor. The results show that there are no significant differences between teaching methods when assessing arithmetic in total and calculation. Students’ progress in quantitative concepts is significantly better if teachers teach traditionally or with a problem‐based curriculum. In order to develop aspects of self‐regulating learning skills, the results show that pupils would benefit in a traditional or problem‐solving curriculum. Problem‐solving seems to be more effective than traditional and independent work for students’ internal motivation. Traditional work and problem‐solving are more effective than independent work for students’ self‐concept.  相似文献   

2.
Undoubtedly the acquisition of mathematical skills for problem solving is critically important in today’s sophisticated technological world. There is growing evidence that meta-cognition application is an important component of academic success in general and impacts on mathematical achievement in particular. Teachers’ application of meta-cognition therefore directs and reflects their teaching-practice behaviour which influences their learners’ learning with understanding in problem-solving. The purpose of the study reported on in this article was to explore teachers’ available meta-cognitive skills in class with the intention of supporting learners’ development of mathematics in problem-solving in some selected rural primary schools in the Eastern Cape, South Africa. The participants were three teachers purposefully selected from three primary schools. Interviews were conducted with the three teachers and three lessons were observed. The interviews, as an extension of observation, focused on the teachers’ knowledge or understanding of available meta-cognitive skills and how they used these skills in helping their learners’ development of mathematics problem-solving. The findings included a detailed exploration of the teachers’ acquisition and use of specific metacognitive skills, either consciously or unconsciously, during teaching and learning processes in order to develop their mathematics learners’ meta-cognitive skills as well as in solving mathematical problems. The results of the observation showed that there was evidence of teachers applying meta-cognitive skills unconsciously in assisting their learners in problemsolving in class. The interviews confirmed this evidence of available meta-cognitive skills which the teachers usually applied in assisting their learners in problem-solving in class. Recommendations have been made regarding teachers’ methods of teaching to improve the development of such skills in the lives of their mathematics learners through problemsolving.  相似文献   

3.
This paper presents a study on mathematical problem solving in third-grade pupils. The relationship between mathematics, metacognition and intelligence was investigated in children with (n = 191) and without mathematical learning disabilities (n = 268). A significant relationship was found between prediction, evaluation, intelligence, procedural and mathematical fact retrieval skills in children without mathematical learning disabilities. In the children with mathematical learning disabilities a relationship was found between metacognitive and procedural skills. No such relationship was found between intelligence and metacognition or between metacognition and mathematical fact retrieval skills. In addition it was investigated if children with mathematical learning disabilities had less adequate metacognitive skills than peers without learning problems. At group level significant differences were found between both groups. However on analyzing these results further, it was found that four out of five children with combined mathematical learning disabilities, half of the children with procedural disabilities and only 5% of the children with a retrieval deficiency had low metacognitive skills. Furthermore, metacognitive problems were found in one out of five children without learning disabilities. Moreover, a majority of the children with mathematical learning disabilities and inadequate metacognitive skills had problems with prediction and evaluation skills. Most third graders with low metacognitive skills only appeared to have problems predicting the level of difficulty of tasks. Inaccurate evaluations were found on a more regular basis in children with mathematical learning disabilities and inadequate metacognitive skills as opposed to the sample of children with inadequate metacognitive skills but without learning difficulties, where their occurrence was rather a one off. The implications of this study for diagnosis and treatment will be discussed later in this paper.  相似文献   

4.
Playing games is an important part of our social and mental development. This research was initiated to identify the game type most suitable to our teaching environment and to identify game elements that students found interesting or useful within the different game types. A group of twenty students played four commercial games (SimIsle, Red Alert, Zork Nemesis and Duke Nukem 3D). Results suggest that students prefer 3D-adventure (Zork Nemesis) and strategy (Red Alert) games to the other types ("shoot-em-up", simulation) with Zork Nemesis ranked as the best. Students rated game elements such as logic, memory, visualisation and problem solving as the most important game elements. Such elements are integral to adventure games and are also required during the learning process. We present a model that links pedagogical issues with game elements. The game space contains a number of components, each encapsulates specific abstract or concrete interfaces. Understanding the relationship between educational needs and game elements will allow us to develop educational games that include visualisation and problem solving skills. Such tools could provide sufficient stimulation to engage learners in knowledge discovery, while at the same time developing new skills.  相似文献   

5.
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   

6.
The first purpose of this study was to investigate whether the visuospatial working memory (VSWM) skills of 15–16‐year‐old pupils with difficulties in mathematics differ from those of their normally achieving peers. The goal was to broaden the view of the complex system of VSWM. A set of passive and active VSWM tasks was used. The study’s second purpose was to investigate whether pupils with mathematical difficulties differed in their VSWM skills based on whether they had signs of reading deficits or not. Results indicate that the pupils with poor performance in maths showed poorer performance on certain VSWM tasks. The group with deficits only in maths had less capacity for storing passive visual simultaneous information, while the group with difficulties both in maths and reading had deficits in both storing (passive visual and visuospatial information) and processing, and had less ability to control irrelevant visuospatial information compared to their peers of the same age. The results indicate a general VSWM deficit in pupils with both mathematics and reading problems and a specific VSWM deficit in pupils with only mathematics problems.  相似文献   

7.
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   

8.
There is a substantial body of knowledge on the importance of language for learning in general, and for learning mathematics in particular. Hence, language skills and collaborative learning are emphasised in the Norwegian curriculum. Even so, we have few studies on what supports and what impedes mathematical progress in authentic learning situations. In this article, we investigate contrasting dialogues between two pairs of eight-year-old pupils solving mathematical tasks. The analysis in our video-based study shows that both communication skills and use of tools have a profound impact on third graders’ potential to solve tasks as a joint enterprise.  相似文献   

9.
This study offers a view on students’ technology-based problem solving activity through the lens of a theoretical model which accounts for the relationship between mathematical and technological knowledge in successful problem solving. This study takes a qualitative approach building on the work of a 13-year-old girl as an exemplary case of the nature of young students’ spontaneous mathematical problem solving with technology. The empirical data comprise digital records of her approaches to two problems from a web-based mathematical competition where she resorted to GeoGebra and an interview where she explains and describes her usual problem solving activity with this tool. Based on a proposed model for describing the processes of mathematical problem solving with technologies (MPST), the main results show that this student’s solving and expressing the solution are held from the early and continuing interplay between mathematical skills and the perception of the affordances of the tool. The analytical model offers a clear picture of the type of actions that lead to the solution of each problem, revealing the student’s ability to deal with mathematics and technology in problem solving. By acknowledging this as a case of a human-with-media in solving mathematical problems, the students’ efficient way of merging technological and mathematical knowledge is portrayed in terms of her techno-mathematical fluency.  相似文献   

10.
A LOGO teaching period was arranged for 38 eight‐year‐old Finnish pupils. After the teaching period the pupils’ problem‐solving processes were videotaped in an open LOGO problem‐solving situation. The data analysis focused on the occurrence of the pupils’ social problem solving, effectance motivation and information processing. Cluster analysis was used to identify three clusters which are based on the variables present in the problem‐solving processes. The different clusters’ associations with school readiness and school achievement were analysed. The results indicated that during the problem solving the passive pupils (n = 16) needed a lot of teacher support, the independent pupils (n= 10) displayed considerable self‐directivity and rule making, and impulsive pupils (n = 12) had an off‐task behaviour. The school‐readiness and school‐achievement scores were highest among the independent group, moderate among the impulsive group and lowest among the passive group. The results suggest that LOGO promotes the development of problem‐solving skills, if each pupil receives sufficient support from the teacher.  相似文献   

11.
Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively to reduce formal barriers. This education can also be used to enable pupils to access an accurate understanding of some key mathematical concepts. In the field of heuristic knowledge for technical problem solving, experience of programming is no less valuable: it lends itself to promote a discussion of relations between formal procedures and the comprehension of intuitive problem solving and provides examples for the development of heuristic precepts (formulating a plan, subdividing the complexities, etc.). The knowledge gained in programming can also be used for the discussion of concepts and problems of classical mathematics. Finally, it can also facilitate the expansion of mathematical culture to topics in biological and physical sciences, linguistics, etc. The authors describe a programming language called ‘Logo’ adapted to objectify an enduring framework of mathematical experimentation.  相似文献   

12.
Abstract

This paper reviews the situation with regard to the teaching of thinking skills as part of the taught curriculum. The case is made for direct teaching of cognitive skills both to meet the particular learning difficulties of children with special educational needs and also to enhance the learning and thinking of all children. The dangers of ‘recipe’ approaches to teaching this aspect of the curriculum are discussed and a ‘principles’ approach is advocated. Some principles are then described which may be used to underpin the designing of problem‐solving activities, through which thinking skills can be taught across the curriculum.  相似文献   

13.

In most science courses at secondary level, the teaching methods used are not tailored to present different approaches to meet the individual differences in pupils’ learning styles or motivation. Much in the detailed objectives, and blow‐by‐blow worksheet approach, will appeal to the conscientious pupil but may turn off the more creative and curious pupil.

Mini‐projects (problem solving at the bench) were used as a vehicle to motivate the curious pupils. Correlations of factors such as convergence/divergence, field‐dependence/field‐independence and motivational traits with ‘success’ in mini‐projects are set out in this paper. The evidence indicates that those who do best in practical problem solving of the mini‐project type are the curious, field‐independent and divergent pupils. However, all categories of pupils were stimulated to varying degrees by the projects.  相似文献   

14.
The subject of this article is the structure and evolution of skills developed by pupils at primary level. Starting from an analysis of the panel data provided by the French Ministry of Education, the main object of this paper is an original measurement of skills using structural models. The findings of this research raise two complementary issues. The first issue concerns the cross‐curricular nature of skills suggesting a logic of disciplinary interdependence. The acquisition of a skill may be strongly correlated to the acquisition of other skills belonging to the same subject area or to other subject areas. The notion of a set of skills is used to account for the connections between the different aspects of acquired skills. The second issue concerns the evolution of skills over time. Here the aim will be to identify the kinds of skills that are the most predictive of subsequent educational success. This issue is highly relevant for educational policy‐making. It is hoped that the results presented in this paper will improve one’s understanding of the ways in which schools might provide pupils with the best chances of success in the earliest stages of their educational career.  相似文献   

15.
Abstract

Emotional awareness programmes and initiatives in education have a high profile. Training courses in emotional literacy and emotional literacy projects are being promoted nationwide. However, whilst many successful projects and programmes have taken place in the context of mainstream school settings, by comparison relatively fewer projects have been reported in special school settings. A seven-week emotional awareness project was designed for seven pupils in a Year 8 form group (12–13 years of age) who were presenting with emotional and emotional/behavioural difficulties in Durants School, which caters for pupils with moderate learning difficulties. The project drew upon principles of circle time and placed emphasis on multisensory activities and role play. The purpose of the project was to identify whether an emotional awareness programme would lead to an increase in the pupils’ awareness and understanding of their own emotions, and whether an awareness of other people’s feelings/emotions could be integrated as a core module of the school’s personal, social and health education curriculum. This project illustrates that an emotional awareness programme can be adapted creatively for pupils with special educational and learning needs without involving expensive resources, and can give pupils life skills that can be applied both in and out of the classroom.  相似文献   

16.
Abstract

Research shows that students face a range of difficulties when using the Internet to solve information problems. Using a quasi-experimental design, we tested a strategy to improve Chilean 10th graders’ skills for information problem solving using the Internet (IPS-I). The intervention was based on a workshop in which students learned IPS-I strategies and solved information problems using a customized Internet search software package. Results showed that members of the experimental group changed their search behavior and improved the quality of their products. However, no correlation between the number of search actions and product quality was found. Based on this, we highlight the potential of combining teaching strategies to improve specific search skills and the use of customized search tools with embedded functionalities that foster good search techniques.  相似文献   

17.
This study explored what kind of mathematics is needed in cabinetmakers’ everyday work and how problem solving is intertwined in it. The informants of the study were four Finnish cabinetmakers and the data consisted of workshop observations, interviews, photos, pictures and sketches made by the participants during the interviews. The data was analysed using different qualitative techniques. Even though the participants identified many areas of mathematics that could be used in their daily work, they used mathematics only if they were able to. The cabinetmakers’ different mathematical skills and knowledge were utilized to their skill limit. Cabinetmakers were found to constantly face problem solving situations along with the creative processes. Being able to use more advanced mathematics helped them to solve those problems more efficiently, without wasting time and materials. Based on the findings, the paper discusses the similarities and differences between problem solving and creative processes. It is suggested that the combination of craftsmanship, creativity, and efficient problem solving skills together with more than basic mathematical knowledge will help cabinetmakers in adapting and surviving in future unstable labour markets.  相似文献   

18.
阐述了解题课的基本功能,指出了目前中学数学教育中解题课存在的问题。通过对一道平面几何题的分析,讨论了解题课环节如何创设一系列探究式问题,引导学生从问题的条件出发通过特例、试错等方法猜测一般规律并找到解决问题的方法,反思是如何想到这样的方法的?进一步对解题方法的优劣进行评判。通过方法的探究过程培养学生的元认知以及提升学生对数学方法的价值与审美判断能力。  相似文献   

19.
This article from a pedagogical viewpoint deals with the problem of how to promote meaningful learning in distance education. In correspondence courses, major problems arise from individual learning difficulties which are caused, e.g. by ineffective teaching methods, deficient individual prerequisites, and/or lack of social facilitation because of isolation. Dealing with those problems experts have been using various technical facilities (e.g., computers for administration and management) and media. Nevertheless, learning difficulties can be solved only by students themselves, but not by mere manipulation of technology, educational methods, or students’ activities. Methods to enhance individual engagement and learning cannot be based well on existing pedagogical theories, since these address direct teaching of children or youth in classroom. Search for theories and methods appropriate to distance teaching reveals as a major goal the development of problem‐solving skills and related abilities. Learning activities corresponding to that goal obviously cohere to working on problem‐like tests. Thus, a conceptual model of how to effect meaningful learning by tests is being proposed. Based on that model special modular components of tests are being described which should be apt for enhancing meaningful learning, and for computer‐based application.  相似文献   

20.
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.  相似文献   

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