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 41 毫秒
1.

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   

2.

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   

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.
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   

5.
Abstract

This paper explores the epistemological dimensions in the thinking of adolescent girls. Using two different kinds of data ‐‐ (1) typical constructions of moral conflicts reported by adolescent girls that reveal either a justice or care (response) focus; and (2) girls’ responses to a story completion exercise ‐‐ this paper identifies epistemological perspectives in girls’ thinking that link ideas of self, knowing and morality. An hypothesized model of ‘learner's interests and goals’ and ‘approaches to knowing’ related to these conceptions of self and morality is presented and implications for teaching are discussed.  相似文献   

6.
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   

7.
According to the intuitive rules theory, students are affected by a small number of intuitive rules when solving a wide variety of science and mathematics tasks. The current study considers the relationship between students’ Piagetian cognitive levels and their tendency to answer in line with intuitive rules when solving comparison tasks. The findings indicate that the tendency to answer according to the intuitive rules varies with cognitive level. Surprisingly, a higher rate of incorrect responses according to the rule same A–same B was found for the higher cognitive level. Further findings and implications for science and mathematics education are discussed.  相似文献   

8.
ABSTRACT

In theory, both virtual manipulatives and explicit instruction are viable options to support students with disabilities as they learn mathematics. This study explored the effect of a treatment package—an app-based virtual manipulative (Cuisenaire® Rods) in conjunction with explicit instruction—on students’ acquisition and generalization of solving problems involving division of whole numbers with remainders. Three middle school students with disabilities participated in this multiple baseline, multiple probe across participants single case design study. Each of the students acquired the mathematical behavior of being able to solve division with remainders problems. In other words, a functional relation existed between the intervention package of explicit instruction and the Cuisenaire® Rods app-based manipulative and students’ accuracy in solving division with remainders problems. Yet, two students failed to generalize the skill without the explicit instruction and use of the app-based manipulative.  相似文献   

9.
John Paul Cook 《PRIMUS》2015,25(3):248-264
Abstract

This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context, identifying patterns, and venturing conjectures. A sequence of open-ended instructional tasks that aim to capitalize on students’ prior experiences with equation solving is provided along with notes and sample student responses for prospective instructors.  相似文献   

10.
ABSTRACT

The purpose of this study is to identify Medical Leadership Competences among medical students at Hashemite University, and analyze the significant differences in the university participants based on their academic level, gender and GPA. Data collection randomly selected from medical students, the response rate for were (260) students. A 40 items survey covered the five areas of Medical Leadership Competences were used. The responses indicated that the most leadership competences for medical students ascending by means were: ‘Demonstrating personal qualities’, ‘Working with others’, ‘Managing services’, ’Setting direction’, an ‘Improving services’, all of these competencies were in high level. There were no significant differences at the 0.05 level among medical leadership competences of medical students’ at Hashemite University related to their academic year, gender, and GPA.  相似文献   

11.

Constructive reflection is seen as an important ingredient in the professional development of teachers, in order to stimulate significant change in approaches to classroom practice and the general provision of science education in schools. This paper explores the use of pupils’ questions in provoking ‘critical incidents’ in the professional lives of teachers. It is suggested that pupils’ questions can be both indicative of their own conceptual change as well as being sophisticated prompts for teachers to examine their own thinking. Case studies of two teachers ‐‐ one primary and one secondary ‐‐ are used to illuminate how such critical incidents can lead to changes in teacher thinking, resulting then in changes in classroom practice in science. Suggestions are made for the use of pupils’ questions as critical incidents in the professional development of teachers.  相似文献   

12.
Abstract

The theme of the 1987 Conference of the International Council for Educational Media to be held at Cardiff on the 26‐27 October is ‘Communication ‐‐ the Essence of Education’.  相似文献   

13.

This study focuses on the similarities and differences in structure and meaning between pupils’ conceptions about steady state tasks and evolutionary tasks, in which the system under study undergoes changes over time. A nine‐item written questionnaire was given to 197 Greek secondary school pupils. Results showed that the majority of pupils employ causal structures for their predictions. Two models were identified: a ‘give’ model, applied by pupils in steady‐state tasks; and a ‘take’ model, applied in evolutionary tasks. Structural similarities and semantic differences were identified between these models. In the light of these results, the study also examined the types of experiments in introductory electricity that would or would not obtain a counter‐intuitive reaction in pupils.  相似文献   

14.
Abstract

HANDYNET is a live and vigorous project with a large ‘family’ of participants. Details of HANDYNET, and other European Commission projects for the handicapped, were published in the Commission of the European Communities Directorate General for Employment, Social Affairs and Education publication Social Europe ‐‐ supplement 7/86 directed towards ‘The Social Integration of Disabled People’. This article on HANDYNET is an edited extract from the above supplement and in particular the splendid paper by Danielle Rimbert.  相似文献   

15.
Summaries

English

The concept of a mathematical function is applied widely in science to describe phenomena in which time, frequency, distance, temperature, and other continuous variables depend on one another. Two tasks were designed to test students’ conceptualization of such relations. Each task involved one independent and one dependent variable in a real‐world context (bacterial growth, spacecraft design). Information about the function was provided in the form of a table of paired values that exhibited a clear non‐linearity. The almost 400 subjects, ranging in age from 11 to 18 years, were required to make interpolations between the given values and to explain their procedure. A brief demonstration of graphical curvilinear interpolation was given between the presentation of the two tasks.

Student responses were classified into four categories according to the method of interpolation: curvilinear, combined curvi‐ and rectilinear, rectilinear, and intuitive (estimates, guesses, unsystematic or erroneous calculations). Most of the youngest subjects used the intuitive approach, while most of the older subjects used the rectilinear approach (either in the form of arithmetic averaging or straight lines on a graph). Only a small percentage of the subjects used curvilinear interpolation, considered to be the most appropriate procedure. The numbers of students using a systematic interpolation procedure was increased modestly by the demonstration. Interviews of some students revealed that many were imitating procedures they had seen in their classes, but they did not understand the reasons behind these procedures.  相似文献   

16.
This paper studies differences between girls ‘ and boys ‘ perceptions of mathematical and scientific higher-order thinking, ways of identifying when higher-order thinking occurs, and methods of mathematical and scientific inquiry that assist in developing higher-level thinking in both young students and pre-service teachers. Participants included 17 pre-service teacher candidates (16 female, 1 male) enrolled in an integrated elementary mathematics and science methods course, and 102 elementary students from large, metropolitan schools (52 females and 50 males from lower-middle- and high-middle-class homes). A 15-item Likert-style rating scale instrument was used. Qualitative measures including observations, interviews and reflections were completed in conjunction with the more quantitative rating scale measure to triangulate the design. Pre-service teacher candidates rated the significance of childrens’ responses and reflected on findings. Results revealed similar ratings between genders and significance on items relating to perceptions of what science and mathematics are, whether girls should be scientists, and objects/manipulatives versus paper/pencil tasks in mathematics.  相似文献   

17.

In this study, we investigate two principals’ learning in a progressive district in the southern United States. Both principals talked about ‘ownership’ and ‘continuous progress'as key to education reform, yet their words carried different meanings for learning. Principals’ use of reform terminology was embedded within two distinctly different communities of principal's practice ‐‐ Total Quality Management and ‘whole language’. We conclude by discussing ways to bridge such gaps in understanding among principals and communities by creating opportunities for learning and discourse. Educational administrators might thereby talk about and explore the different nuances of meaning they bring to their practice.

  相似文献   

18.
Abstract

In this paper I take the opportunity to explore some ideas about the work‐related curriculum which arise, both directly and indirectly, out of several projects with which I have recently been involved, namely, the national evaluations of the Lower Attaining Pupils Programme (Stradling and Saunders, 1991), the management of TVEI Extension (Saunders et.al. 1991), and the operation of Compacts (Saunders and Morris, 1992). The initiatives are (or were) all concerned with providing a work‐related curriculum for young people in their last two years of compulsory schooling, with the aim of easing the transition to adult and working life.

But these evaluations show that if the principle of ‘entitlement’ is not built into work‐related provision, its key messages ‐‐ on relevance and incentives ‐‐ are likely to be unrealised. That the work‐related curriculum needs to be developed through partnership between education and industry is now almost a truism; but partnership is harder to achieve than to eulogise. In particular, clear and precise objectives and consequent criteria of partnership success need to be established, together with a recognition that partners do not necessarily share the same starting points or compatible perspectives. Some process of ‘power‐broking’ may be called for, in order to mediate and match their different needs.  相似文献   

19.
This paper arises from a study of how concepts related to understanding functions develop for students across the years of secondary/high school, using small samples from two different curricula systems: England and Israel. We used a survey consisting of function tasks developed in collaboration with teachers from both curriculum systems. We report on 120 higher achieving students, 10 from each of English and Israeli, 12–18 years old. Iterative and comparative analysis identified similarities and differences in students’ responses and we conjecture links between curriculum, enactment, task design, and students’ responses. Towards the end of school, students from both curriculum backgrounds performed similarly on most tasks but approached these by different routes, such as intuitive or formal and with different understandings, including correspondence and covariational approaches to functions.  相似文献   

20.
Background: Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define the knowledge needed by teachers to teach mathematics effectively. A plethora of terms, such as mathematical content knowledge, pedagogical content knowledge, horizon content knowledge and specialised content knowledge, have been used to describe aspects of such knowledge.

Purpose: This paper proposes a model for teacher knowledge in mathematics that embraces and develops aspects of earlier models. It focuses on the notions of contingent knowledge and the connectedness of ‘big ideas’ of mathematics to enact what is described as ‘powerful teaching’. It involves the teacher’s ability to set up and provoke contingent moments to extend children’s mathematical horizons. The model proposed here considers the various cognitive and affective components and domains that teachers may require to enact ‘powerful teaching’. The intention is to validate the proposed model empirically during a future stage of research.

Sources of evidence: Contingency is described in Rowland’s Knowledge Quartet as the ability to respond to children’s questions, misconceptions and actions and to be able to deviate from a teaching plan as needed. The notion of ‘horizon content knowledge’ (Ball et al.) is a key aspect of the proposed model and has provoked a discussion in this article about students’ mathematical horizons and what these might comprise. Together with a deep mathematical content knowledge and a sensibility for students and their mathematical horizons, these ideas form the foundations of the proposed model.

Main argument: It follows that a deeper level of knowledge might enable a teacher to respond better and to plan and anticipate contingent moments. By taking this further and considering teacher knowledge as ‘dynamic’, this paper suggests that instead of responding to contingent events, ‘powerful teaching’ is about provoking contingent events. This necessarily requires a broad, connected content knowledge based on ‘big mathematical ideas’, a sound knowledge of pedagogies and an understanding of common misconceptions in order to be able to engineer contingent moments.

Conclusions: In order to place genuine problem-solving at the heart of learning, this paper argues for the idea of planning for contingent events, provoking them and ‘setting them up’. The proposed model attempts to represent that process. It is anticipated that the new model will become the framework for an empirical research project, as it undergoes a validation process involving a sample of primary teachers.  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