首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 31 毫秒
1.
One theoretical framework which addresses students’ conceptions and reasoning processes in mathematics and science education is the intuitive rules theory. According to this theory, students’ reasoning is affected by intuitive rules when they solve a wide variety of conceptually non-related mathematical and scientific tasks that share some common external features. In this paper, we explore the cognitive processes related to the intuitive rule more A–more B and discuss issues related to overcoming its interference. We focused on the context of probability using a computerized “Probability Reasoning – Reaction Time Test.” We compared the accuracy and reaction times of responses that are in line with this intuitive rule to those that are counter-intuitive among high-school students. We also studied the effect of the level of mathematics instruction on participants’ responses. The results indicate that correct responses in line with the intuitive rule are more accurate and shorter than correct, counter-intuitive ones. Regarding the level of mathematics instruction, the only significant difference was in the percentage of correct responses to the counter-intuitive condition. Students with a high level of mathematics instruction had significantly more correct responses. These findings could contribute to designing innovative ways of assisting students in overcoming the interference of the intuitive rules.  相似文献   

2.
In the international community of mathematics and science educators the intuitive rules theory developed by the Israeli researchers Tirosh and Stavy receives much attention. According to this theory, students' responses to a variety of mathematical and scientific tasks can be explained in terms of their application of some common intuitive rules. Two major intuitive rules are manifested in comparison tasks: ‘More A—more B’ and ‘Same A—same B’. In this paper, we address two important questions for which the existing literature on intuitive rules does not provide a convincing research-based answer: (1) are the reasoning processes of students who respond in line with a given intuitive rule actually affected by that rule or by essentially other misconceptions (leading to the same answer), and (2) are individual students consistent in their choice of one of the intuitive rules when confronted with different, conceptually unrelated tasks? A test consisting of five comparison problems from different mathematical subdomains was administered collectively to 172 Flemish students from Grades 10 to 12. An analysis of students' written calculations and justifications suggested that the students were considerably less affected by the intuitive rules than their multiple-choice answers actually suggested. Instead, essentially different misconceptions and errors were found. With respect to the issue of individual consistency, we found that students who made many errors did not answer systematically in line with one of the two intuitive rules.  相似文献   

3.
During the last two decades many researchers in mathematics and science education have studied students’ conceptions and ways of reasoning in mathematics and science. Most of this research is content‐specific. It was found that students hold alternative ideas that are not always compatible with those accepted in science. It was suggested that in the process of learning science or mathematics, students should restructure their specific conceptions to make them conform to currently accepted scientific ideas. In our work in mathematics and science education it became apparent that some of the alternative conceptions in science and mathematics are based on the same intuitive rules. We have so far identified two such rules: “More of A, more of B”, and “Subdivision processes can always be repeated”. The first rule is reflected in subjects’ responses to many tasks, including all classical Piagetian conservation tasks (conservation of number, area, weight, volume, matter, etc.) in all tasks related to intensive quantities (density, temperature, concentration, etc.) and in all tasks related to infinite quantities. The second rule is observed in students’, preservice and inservice teachers’ responses to tasks related to successive division of material and geometrical objects and in seriation tasks. In this paper, we describe and discuss these rules and their relevance to science and mathematics education.  相似文献   

4.
  相似文献   

5.
This paper indicates that prospective teachers’ familiarity with theoretical models of students’ ways of thinking may contribute to their mathematical subject matter knowledge. This study introduces the intuitive rules theory to address the intuitive, same sides-same angles solutions that prospective teachers of secondary school mathematics come up with, and the proficiency they acquired during the course “Psychological aspects of mathematics education”. The paper illustrates how drawing participants’ attention to their own erroneous applications of same sides-same angles ideas to hexagons, challenged and developed their mathematical knowledge.  相似文献   

6.
This paper addresses the accumulating knowledge of prospective teachers of secondary school mathematics and their acquired proficiency during the course “Psychological aspects of mathematics education,” in which we discussed theoretical models including the intuitive rules theory. Participants’ performances are examined by means of an extensive report of two episodes, one during the course and one afterwards. These episodes marked different stages in the prospective teachers’ analysis of their own and of students’ solutions, which led me to conclude that exposing prospective teachers to the intuitive rules theory is important, since their familiarity with the theory provided them with a tool to reflect on their own mathematical solutions (subject matter knowledge; SMK), on others’ solutions, and on the tasks (pedagogical content knowledge; PCK).  相似文献   

7.

This paper is a part of an extensive project on the role of intuitive rules in science and mathematics education. First, we described the effects of two intuitive rules ‐‐ ‘Everything comes to an end’ and ‘Everything can be divided’ ‐‐ on seventh to twelfth grade students’ responses to successive division tasks related to mathematical and physical objects. Then, we studied the effect of an intervention, which provided students with two contradictory statements, one in line with students’ intuitive response, the other contradicting it, on their responses to various successive division tasks. It was found that this conflict‐based intervention did not improve students’ ability to differentiate between successive division processes related to mathematical objects and those related to material ones. These results reconfirmed that intuitive rules are stable and resistant to change. Finally, this paper raised the need for additional research related to the relationship between intuitive rules and formal knowledge.  相似文献   

8.
Background:?The study investigated a small range of cognitive abilities, related to visual-spatial intelligence, in adolescents. This specific range of cognitive abilities was termed ‘graphic abilities’ and defined as a range of abilities to visualise and think in three dimensions, originating in the domain of visual-spatial intelligence, and related to visual perception and the ability to represent space. The educational importance of graphic abilities has received minimal attention from the educational community and, consequently, plays a limited role in educational practice.

Purpose:?In order to understand the particular educational importance of this range of cognitive abilities, we investigated how graphic abilities are connected with the performance and the subject preference of adolescents in several academic areas. Our hypotheses were, first, that there is a high degree of correlation between developed graphic abilities and high performance in mathematics and science, and second, that there is a high degree of correlation between developed graphic abilities and personal subject preference in these two areas.

Sample:?The sample consisted of 60 14-year-old students (30 girls and 30 boys) attending a public secondary school in a small town in northern Greece. The entire sample had followed the same mathematics courses, which did not involve any geometry or spatial representation tasks.

Design and methods:?We identified and defined a specific range of three graphic abilities, related to visual-spatial intelligence, and we investigated these abilities in the sample through several visual-spatial tasks designed for the study and measured the sample's performance in these tasks. The degree of adolescents' graphic performance (that is, the performance in these visual-spatial tasks) was correlated with their performance in mathematics and science and with their subject preference (mathematics, science and language).

Results:?Our findings confirmed both hypotheses. A high degree of correlation was found between developed graphic abilities and high performance in mathematics, and a lower but still significant degree of correlation was found between developed graphic abilities and high performance in science. The findings support the second hypothesis as well, suggesting that children with developed graphic abilities reported that their favourite subject was mathematics and second favourite subject was science.

Conclusions:?The research suggested that there is a particular relation between the level of graphic abilities performance and children's performance and in preference for mathematics and science. That is, children with developed visual perception, visual thought and representational skills are actually better with numbers and physical concepts. This particular relation might be relevant to the overall cognitive development of children, especially with respect to the increasingly developing communication technologies, and it would seem to deserve more attention and extended research from the educational community. The authorial position is that education would gain from a better understanding of: the nature of graphic abilities, how we can develop this range of abilities and how the development of visual thought and graphic expression contributes to several curriculum subjects.  相似文献   

9.

In the last twenty years researchers have studied students’ mathematical and scientific conceptions and reasoning. Most of this research is content‐specific. It has been found that students often hold ideas that are not in line with accepted scientific notions. In our joint work in mathematics and science education it became apparent that many of these alternative conceptions hail from the same intuitive rules. We have so far identified two such rules: ‘The more of A, the more of B’ and, ‘Everything can be divided by two’. The first rule is reflected in students’ responses to many tasks, including all classical Piagetian conservation tasks (conservation of number, area, weight, volume, matter, etc.), in all tasks related to intensive quantities (density, temperature, concentration, etc.), and in tasks related to infinite quantities. The second rule is observed in responses related to successive division of material and geometrical objects, and in successive dilution tasks. In this paper we describe and discuss the first rule and its relevance to science and mathematics education. In a second paper (Tirosh and Stavy, in press) we shall describe and discuss the second rule.  相似文献   

10.
  相似文献   

11.

In the last twenty years, researchers have studied students’ mathematical and scientific conceptions and reasoning. Most of this research is content‐specific. It has been found that students often hold ideas that are not in line with accepted scientific notions. In our joint work in mathematics and science education, it became apparent that many of these alternative conceptions hail from a small number of intuitive rules. We have so far identified two such rules: ‘The more of A, the more of B’, and, ‘Everything can be divided by two’. The first rule is reflected in students’ responses to many tasks, including all classical Piagetian conservation tasks (conservation of number, area, weight, volume, matter, etc.), all tasks related to intensive quantities (density, temperature, concentration, etc.), and tasks related to infinite quantities. The second rule is observed in responses related to successive division of material and geometrical objects, and in seriation tasks. In this paper we describe and discuss the second rule and its relevance to science and mathematics education. In a previous paper (Stavy and Tirosh 1995, in press) we described and discussed the first rule.  相似文献   

12.
A working memory model applied to mathematical word problem solving   总被引：1，自引：0，他引：1  
The main objective of this study is (a) to explore the relationship among cognitive style (field dependence/independence), working memory, and mathematics anxiety and (b) to examine their effects on students’ mathematics problem solving. A sample of 161 school girls (13–14 years old) were tested on (1) the Witkin’s cognitive style (Group Embedded Figure Test) and (2) Digit Span Backwards Test, with two mathematics exams. Results obtained indicate that the effect of field dependency, working memory, and mathematics anxiety on students' mathematical word problem solving was significant. Moreover, the correlation among working memory capacity, cognitive style, and students’ mathematics anxiety was significant. Overall, these findings could help to provide some practical implications for adapting problem solving skills and effective teaching/learning.  相似文献   

13.
The present study investigated the effectiveness of a cognitive enrichment programme as a tool for enhancing the chances of immigrant and minority students to be admitted to a technological college. Students received two weekly sessions (four hours) of Instrumental Enrichment (IE) during the second semester of the college preparatory programme. The cognitive principles of IE were ‘bridged’ to mathematics and science curricular material. The mathematics and science tasks were analysed to show the students the underlying cognitive principles essential for their solution. Graduates of the programme were much more successful in being admitted to technological college than students in previous years who received no cognitive enrichment.  相似文献   

14.
Typically, mathematics and science are seen as linked together, where both subjects involve numbers, critical thinking, and problem solving. Our study aims to develop a better understanding of the connections between student’s achievement scores in mathematics and science, student gender, and self-efficacy. We used the Trends in International Mathematics and Science Study 2007 eighth grade data to answer our research questions and were able to demonstrate that when controlling for self-efficacy, there is a statistically significant difference in the achievement scores between males and females by subject, where females score higher Algebra, but males score higher in the other mathematics subjects. Likewise, we were also able to demonstrate that there is a statistically significant difference in the achievement scores in Earth Science, Physics, and Biology, between males and females where males score higher in science subjects. In both mathematics and science examinations, we controlled for self-efficacy where in mathematics females hold lower self-efficacy then males and in science there is no difference between females and males in terms of self-efficacy. We conjecture that mathematics and science classrooms that consider self-efficacy may impact student’s achievement scores by subject, which can ultimately impact career choices in mathematics- and science-based fields.  相似文献   

15.
This study investigates the difficulties students encounter in problem solving in the area of sciences. Contrary to usual approaches of a fundamental psychological basis, the research takes into account the sociological processes of learning and transmission in both the family and the school. The aim of the study is to see the extent to which the students have recognition and realisation rules in the micro‐context of problem solving (specific coding orientation) and to find out the reasons which may underlie their difficulties. Thus the data obtained are related to social class, race and gender and also to pedagogic practices (differing in power and control relations) and school science achievement in high level cognitive competencies. They are also related to children's cognitive level. The results show a strong relation between social class and specific coding orientation to problem solving. The relation is also strong for race and weaker for gender. Specific coding orientation is also strongly related to cognitive development and science achievement. These relations differ for the variables according to realisation and recognition rules and their various indices. The study shows the positive influence of pedagogic practice, which constitutes a crucial finding to pedagogic change.  相似文献   

16.
A growing body of research has examined the experiential grounding of scientific thought and the role of experiential intuitive knowledge in science learning. Meanwhile, research in cognitive linguistics has identified many conceptual metaphors (CMs), metaphorical mappings between abstract concepts and experiential source domains, implicit in everyday and scientific language. However, the contributions of CMs to scientific understanding and reasoning are still not clear. This study explores the roles that CMs play in scientific problem-solving through a detailed analysis of two physical chemistry PhD students solving problems on entropy. We report evidence in support of three claims: a range of CMs are used in problem-solving enabling flexible, experiential construals of abstract scientific concepts; CMs are coordinated with one another and other resources supporting the alignment of qualitative and quantitative reasoning; use of CMs grounds abstract reasoning in a “narrative” discourse incorporating conceptions of paths, agents, and movement. We conclude that CMs should be added to the set of intuitive resources others have suggested contribute to expertise in science. This proposal is consistent with two assumptions: that cognition is embodied and that internal cognitive structures and processes interact with semiotic systems. The implications of the findings for learning and instruction are discussed.  相似文献   

17.
The QUASAR Cognitive Assessment Instrument (QCAI) is designed to measure program outcomes and growth in mathematics. It consists of a relatively large set of open-ended tasks that assess mathematical problem solving, reasoning, and communication at the middle-school grade levels. This study provides some evidence for the generalizability and validity of the assessment. The results from the generalizability studies indicate that the error due to raters is minimal, whereas there is considerable differential student performance across tasks. The dependability of grade level scores for absolute decision making is encouraging; when the number of students is equal to 350, the coefficients are between .80 and .97 depending on the form and grade level. As expected, there tended to be a higher relationship between the QCAI scores and both the problem solving and conceptual subtest scores from a mathematics achievement multiple-choice test than between the QCAI scores and the mathematics computation subtest scores.  相似文献   

18.
This study explores the effects of the presence of external representations of a mathematical object (ERs) on problem solving performance associated with short double-choice problems. The problems were borrowed from secondary school algebra and geometry, and the ERs were either formulas, graphs of functions, or drawings of geometric figures. Performance was evaluated according to the reaction time (RT) required for solving the problem and the accuracy of the answer. Thirty high school students studying at high and regular levels of instruction in mathematics (HL and RL) were asked to solve half of the problems with ERs and half of the problems without ERs. Each task was solved by half of the students with ERs and by half of the students without ERs. We found main effects of the representation mode with particular effect on the RT and the main effects of the level of mathematical instruction and mathematical subject with particular influence on the accuracy of students’ responses. We explain our findings using the cognitive load theory and hypothesize that these findings are associated with the different cognitive processes related to geometry and algebra.  相似文献   

19.
Relational reasoning, the ability to detect meaningful patterns, matures through adolescence. The unique contributions of verbal analogical and nonverbal matrix relational reasoning to science and maths are not well understood. Functional magnetic resonance imaging data were collected during science and maths problem‐solving, and participants (N = 36, 11–15 years) also completed relational reasoning and executive function tasks. Higher verbal analogical reasoning associated with higher accuracy and faster reaction times in science and maths, and higher activation in the left anterior temporal cortex during maths problem‐solving. Higher nonverbal matrix reasoning associated with higher science accuracy, higher science activation in regions across the brain, and lower maths activation in the right middle temporal gyrus. Science associations mostly remained significant when individual differences in executive functions and verbal IQ were taken into account, while maths associations typically did not. The findings indicate the potential importance of supporting relational reasoning in adolescent science and maths learning.  相似文献   

20.
This article is a result of a completed survey of the mainly cognitive science literature on the transferability of those skills which have been described variously as ‘core’, ‘key’, and ‘generic’. The literature reveals that those predominantly cognitive skills which have been studied thoroughly (mainly problem solving) are transferable under certain conditions. These conditions relate particularly to the methods and environment of the learning of these skills. Therefore, there are many implications for the teaching of key skills in higher education, which the article draws out, following a summary of the main findings of the research literature. Learning of principles and concepts facilitates transfer to dissimilar problems, as it creates more flexible mental representations, whereas rote learning of facts discourages transfer. Transfer is fostered when general principles of reasoning are taught together with self-monitoring practices and potential applications in varied contexts. Training in reasoning and critical thinking is only effective for transfer, when abstract principles and rules are coupled with examples. Transfer is promoted when learning takes place in a social context, which fosters generation of principles and explanations. Transfer improves when learning is through co-operative methods, and where there is feedback on performance with training examples. The specificity of the context in which principles are learned reduces their transfer. Transfer is promoted if learners are shown how problems resemble each other, if they are expected to learn to do this themselves, if they are aware of how to apply skills in different contexts, if attention is directed to the underlying goal structure of comparable problems, if examples are varied and are accompanied by rules or principles (especially if discovered by the learners), and if learners’ self-explanations are stimulated. Learning to use meta-cognitive strategies is especially important for transfer.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号