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1.
This study examined standard 6 and 8 (Standards 6 and 8 are the sixth and eighth years, respectively, of primary level schooling in Kenya.) students’ perceptions of how they use mathematics and science outside the classroom in an attempt to learn more about students’ everyday mathematics and science practice. The knowledge of students’ everyday mathematics and science practice may assist teachers in helping students be more powerful mathematically and scientifically both in doing mathematics and science in school and out of school. Thirty-six students at an urban school and a rural school in Kenya were interviewed before and after keeping a log for a week where they recorded their everyday mathematics and science usage. Through the interviews and log sheets, we found that the mathematics that these students perceived they used outside the classroom could be classified as 1 of the 6 activities that Bishop (Educ Stud Math 19:179–191, 1988) has called the 6 fundamental mathematical activities and was also connected to their perception of whether they learned mathematics outside school. Five categories of students’ perceptions of their out-of-school science usage emerged from the data, and we found that 4 of our codes coincided with 2 activities identified by Lederman & Lederman (Sci Child 43(2):53, 2005) as part of the nature of science and 2 of Bishop’s categories. We found that the science these students perceived that they used was connected to their views of what science is.  相似文献   

2.
Particularly in mathematics, the transition from school to university often appears to be a substantial hurdle in the individual learning biography. Differences between the characters of school mathematics and scientific university mathematics as well as different demands related to the learning cultures in both institutions are discussed as possible reasons for this phenomenon. If these assumptions hold, the transition from school to university could not be considered as a continuous mathematical learning path because it would require a realignment of students’ learning strategies. In particular, students could no longer rely on the effective use of school-related individual resources like knowledge, interest, or self-concept. Accordingly, students would face strong challenges in mathematical learning processes at the beginning of their mathematics study at university. In this contribution, we examine these assumptions by investigating the role of individual mathematical learning prerequisites of 182 first-semester university students majoring in mathematics. In line with the assumptions, our results indicate only a marginal influence of school-related mathematical resources on the study success of the first semester. In contrast, specific precursory knowledge related to scientific mathematics and students’ abilities to develop adequate learning strategies turn out as main factors for a successful transition phase. Implications for the educational practice will be discussed.  相似文献   

3.
This article contributes to the discussion on mathematics teacher reflection. Reflection was included in a study of the didactisation practices of primary school mathematics teachers as one of nine didactisation practices. The study involved five volunteer primary school mathematics teachers. A qualitative design-research approach was designed which employed model-eliciting tasks to create new experiences for teachers. This article reports on the nature and development of mathematics teacher reflection. Teacher reflection was gauged at various times during the programme through written responses to open-ended reflective questionnaires. Teachers were involved in three types of sessions for a period of one year: 1) modelling sessions whereby they collaboratively solved a mathematical modelling task; 2) observing primary school students/learners solve the same problems; and 3) sessions discussing traditional and problem-centred teaching and learning. It was found that modelling tasks provided reflective platforms and a window to teacher resources, orientations and goals. It is recommended that further research into mathematics teacher reflection be conducted where teachers specifically implement modelling in their own classrooms.  相似文献   

4.
We report on a project currently in progress that aims to identify through research the range of factors (individual, school and out-of-school, including home) and their interactions that influence post-16 (i.e. post-compulsory) participation in mathematics and physics in the UK and to assess their relative importance among different student populations. In this project, we are beginning to elucidate the views of students and examine the sources of these views by exploring the contexts in which both school and university students experience barriers or opportunities and form their identities with regard to participation in mathematics and physics. Our focus in this paper is on our methodology, the reasons for it and how and why our approach to data collection developed during the project. We situate our work within a mixed-methods approach, using multilevel modelling and discourse analysis to analyse and interpret our findings that derive from our own questionnaires, interviews and ethnography and from existing large-scale datasets. We argue that greater acknowledgement in the education literatures that investigate student participation in mathematics and science needs to be made than is usual of the range of factors, including unconscious forces that may affect participation.  相似文献   

5.
Drawing on socio-cultural theory, we understand the norms regulating the practices within the mathematics classroom as resulting from the social representations of the socially dominant groups and of the school culture related to what constitutes learning mathematics. Immigrant studients, having their own personal histories as members of particular social groups, and having been in school traditions other than the one predominant in the host society, have their own images of what mathematics in school is about. Individuals interacting in the classroom are all re-interpreting the different episodes from the perspective of the social representations of the larger groups with which they identify themselves. In multiethnic classrooms different re-interpretations of the same norms clash. The lack of negotiation gives rise to obstacles to immigrant students’ participation in the mathematical conversations and, therefore, interferes with the students’ learning process.  相似文献   

6.
This research examined the use of visual-spatial representation by deaf and hearing students while solving mathematical problems. The connection between spatial skills and success in mathematics performance has long been established in the literature. This study examined the distinction between visual-spatial "schematic" representations that encode the spatial relations described in a problem versus visual-spatial "pictorial" representations that encode only the visual appearance of the objects described in a problem. A total of 305 hearing (n = 156) and deaf (n = 149) participants from middle school, high school, and college participated in this study. At all educational levels, the hearing students performed significantly better in solving the mathematical problems compared to their deaf peers. Although the deaf baccalaureate students exhibited the highest performance of all the deaf participants, they only performed as well as the hearing middle school students who were the lowest scoring hearing group. Deaf students remained flat in their performance on the mathematical problem-solving task from middle school through the college associate degree level. The analysis of the students' problem representations showed that the hearing participants utilized visual-spatial schematic representation to a greater extent than did the deaf participants. However, the use of visual-spatial schematic representations was a stronger positive predictor of mathematical problem-solving performance for the deaf students. When deaf students' problem representation focused simply on the visual-spatial pictorial or iconic aspects of the mathematical problems, there was a negative predictive relationship with their problem-solving performance. On two measures of visual-spatial abilities, the hearing students in high school and college performed significantly better than their deaf peers.  相似文献   

7.
中学生数学能力的培养是中学数学的主要教学目标之一，一直是广大基础教育工作关心的问题。而中国是一个多民族的国家，各民族由于化背景和语言的差异，所受家庭教育、学校教育的不同，加上学生的学习动机、兴趣和对数学的爱好的千差万别，都会对学生的数学能力带来影响。  相似文献   

8.
Current reform efforts call for an emphasis on the use of representation in the mathematics classroom across levels and topics. The aim of the study was to examine teachers’ conceptions of representation as a process in doing mathematics, and their perspectives on the role of representations in the teaching and learning of mathematics at the middle-school level. Interviews with middle school mathematics teachers suggest that teachers use representations in varied ways in their own mathematical work and have developed working definitions of the term primarily as a product in problem solving. However, teachers’ conception of representation as a process and a mathematical practice appears to be less developed, and, as a result, representations may have a peripheral role in their instruction as well. Further, the data suggested that representation is viewed as a topic of study rather than as a general process, and as a goal for the learning of only a minority of the students—the high-performing ones. Implications for mathematics teacher education, prospective and practicing, are discussed.  相似文献   

9.
In this study, 12 pre-service mathematics teachers worked in teams to develop their knowledge and skills in using teacher-led spreadsheet demonstrations to help students explore mathematics concepts, stimulate discussions and perform authentic tasks through activity-based lessons. Pre-service teachers’ lesson plans, their instruction of the lessons designed, experiences and lesson enactment outcomes were examined. The pre-service teachers in the study were able to develop and demonstrate their knowledge and skill adequately in designing and enacting activity-based mathematical lessons supported with spreadsheets. The results also showed that the pre-service teachers’ use of the spreadsheet as an instructional tool promoted student in-depth mathematical concept formation and an activity-based learning approach to make lessons less teacher centred and more interactive.  相似文献   

10.
ABSTRACT

Crosscutting concepts such as scale, proportion, and quantity are recognised by U.S. science standards as a potential vehicle for students to integrate their scientific and mathematical knowledge; yet, U.S. students and adults trail their international peers in scale and measurement estimation. Culturally based knowledge of scale such as measurement units may be built on evolutionarily-based systems of number such as the approximate number system (ANS), which processes approximate representations of numerical magnitude. ANS is related to mathematical achievement in pre-school and early elementary students, but there is little research on ANS among older students or in science-related areas such as scale. Here, we investigate the relationship between ANS precision in public school U.S. seventh graders and their accuracy estimating the length of standard units of measurement in SI and U.S. customary units. We also explored the relationship between ANS and science and mathematics achievement. Accuracy estimating the metre was positively and significantly related to ANS precision. Mathematics achievement, science achievement, and accuracy estimating other units were not significantly related to ANS. We thus suggest that ANS precision may be related to mathematics understanding beyond arithmetic, beyond the early school years, and to the crosscutting concepts of scale, proportion, and quantity.  相似文献   

11.
数学文化是指数学的思想、精神、语言、方法、观点以及它们的形成与发展,还包括数学在人类生活、科学技术、社会发展中的贡献和意义,以及与数学相关的人文活动。与纯粹的数学知识相比较,数学文化体现了人文性与科学性交融、开放性与包容性并存、民族性与统一性共生,以及价值理性与工具理性互推的特点。适合小学生学习的数学文化内容主要有数学知识的发展历史、数学家的成长故事、数学的游戏活动、数学的生活应用和学科应用。小学生学习数学文化有助于他们理解数学知识、掌握数学思想方法、提高数学思维水平、加强数学应用意识和培养数学精神。  相似文献   

12.
The challenge that we address concerns teachers’ shifts toward student-centered instruction. We report on a yearlong professional development study in which two United States elementary school teachers engaged in a teaching experiment, as described by Steffe and Thompson (in: Lesh and Kelly (eds) Research on design in mathematics and science education, 2000). The teaching experiment involved close mathematical interactions with a pair of students after school, in the context of solving fractions tasks. By conducting a teaching experiment, we anticipated that each teacher would have more opportunity to develop insight into students’ mathematics. We also anticipated that these insights would influence the teachers’ classroom practice, even without explicit support for such a shift. Indeed, the teachers found that they began asking more probing questions of their students and spending more time listening to students’ explanations, but shifts to classroom practice were limited by constraining factors such an inflexible curriculum.  相似文献   

13.
The importance of actively engaging in mathematics discourse in order to learn mathematics is well recognized. In this paper, I use Basil Bernstein’s concepts of pedagogic discourse to document and analyse academic learning time of students in Years 8 and 9 at a suburban lower secondary school: in particular, for what proportion of class time students reported being academically engaged, their explanations for this engagement and how they felt about the discourse. It was found that many students had disengaged from mathematical endeavour as a result of the failure of the instructional discourse either to engage students or to serve the purpose of developing discipline-specific content knowledge. The reasons for this relate to the overemphasis on mundane mathematics resulting in some students lacking the cognitive tools to engage with the concepts and having neither the intrinsic nor instrumental motivation to persist with secondary school esoteric mathematics. The implications for mathematics curriculum development are discussed.  相似文献   

14.
In an innovative, progressive school, students were asked to solve a fairly routine mathematical problem using real money in a “real-world” scenario. Even though the school values students’ ideas, the reaction of the teacher to one student’s alternative modelling of the problem suggests that he was expecting a particular answer to be provided using routine mathematical models and thinking while not being interested in exploring the student’s unexpected alternative. We place his reasoning for doing so within broad pedagogical discourses that we think define the “allowable” responses of teachers and students in ways that inhibit meaning-making for both. These broad discourses are defined as the progressive constructivist approach, the scaffolding discursive approach, the situation modelling approach and the dialogic approach. We consider the advantages and the potential consequences each might bring to the case. We suggest that extensive consideration of pedagogical discourses in mathematics classes must be reconsidered both for how we understand students’ mathematical meaning-making and how we construct student agency in relationship to culture, whether as apprentices or authors.  相似文献   

15.
《全日制义务教育数学课程标准(实验稿)》明确提出,在数学教学中应当引导学生感悟建模过程,发展"模型思想"。在小学,进行数学建模教学具有鲜明的阶段性、初始性特征,即要从学生熟悉的生活和已有的经验出发,引导他们经历将实际问题初步抽象成数学模型并进行解释与运用的过程,进而对数学和数学学习获得更加深刻的理解。就其教学实施的一般程序而言,教师先行琢磨、通过教学不断建模、学生在体验和感悟中为之着魔是小学数学建模教学的关键所在。  相似文献   

16.
数学思维能力的培养对学生的数学学习及其他理科科目的学习有很好的促进作用。但是在目前的初中数学教学环境中,很多学生在数学的学习上更注重解题的结果而忽视解题的思路以及一些做题技巧,这对于初中生的学习及将来的发展十分不利的。因此,针对初中生的实际情况,教师在教学过程中应注重培养学生的数学思维能力。学生学习能力的培养与提升,从而很好地促进学生的全面发展,为学生将来的学习打下良好的基础。  相似文献   

17.
There is a growing concern that governmental calls for parental involvement in children's school mathematics learning have not been underpinned by research. In this article the authors aim to offer a contribution to this debate. Links between children's home and school mathematical practices have been researched in sociocultural studies, but the origins of differences within the same cultural group are not well understood. The authors have explored the notion that parents' representations of school mathematics and associated practices at home may play a part in the development of these differences. This article reports an analysis of interviews with parents of 24 children of Pakistani and White origin enrolled in primary schools in England, including high and low achievers in school mathematics. The extent to which the parents represented their own school mathematics and their child's school mathematics as the ‘same’ or ‘different’ are examined. In addition, ways in which these representations influenced how they tried to support their children's learning of school mathematics are examined. The article concludes with reflections on the implications of the study for education policy.  相似文献   

18.
This paper replicates and extends my earlier work on productive failure in mathematical problem solving (Kapur, doi:, 2009). One hundred and nine, seventh-grade mathematics students taught by the same teacher from a Singapore school experienced one of three learning designs: (a) traditional lecture and practice (LP), (b) productive failure (PF), where they solved complex problems in small groups without any instructional facilitation up until a teacher-led consolidation, or (c) facilitated complex problem solving (FCPS), which was the same as the PF condition except that students received instructional facilitation throughout their lessons. Despite seemingly failing in their collective and individual problem-solving efforts, PF students significantly outperformed their counterparts in the other two conditions on both the well-structured and higher-order application problems on the post-test, and demonstrated greater representation flexibility in working with graphical representations. The differences between the FCPS and LP conditions did not reach significance. Findings and implications of productive failure for theory, design of learning, and future research are discussed.  相似文献   

19.

Project Ga‐GEMS (Georgia's Project for Gifted Education in Math and Science) viewed the effect that placement in an integrated, hands‐on mathematics and science curriculum had on the achievement of academically talented high school students. For a two‐year period of time, students gifted in the areas of mathematics and science participated in a curriculum which incorporated higher‐level thinking skills and more real life laboratory experiences into mutually reinforcing mathematics and science lessons. After the conclusion of the two‐year program, Ga‐GEMS participants and a control group were given the mathematics and science sections of the ACT as they exited the tenth grade. The Ga‐GEMS students scored significantly higher on the Science Math Total, Pre‐Algebra/Elementary Algebra, Intermediate Algebra/Coordinate Geometry and Plane Geometry/Trigonometry sections of the ACT. To determine if the Ga‐GEMS students retained their higher scores throughout high school the SAT scores of both groups were compared as the students exited high school. Significant differences in the areas of total score and mathematics were noted. This study lends support for the use of a differentiated curriculum for educating gifted students in science and mathematics.  相似文献   

20.
While many semiotic and cognitive studies on learning mathematics have focused primarily on students, this study focuses mainly on teachers, by seeking to bring to light their awareness of the semiotic and cognitive aspects of learning mathematics. The aim is to highlight the degree of awareness that teachers show about: (1) the distinction between what the institution (school, university, society, etc.) proposes as a mathematical object (not in itself but as the content to be learned) and one of its semiotic representations; (2) the different aspects of a semiotic representation that the student able to handle the representation and the student who handles the representation with difficulty may focus on; (3) the semiotic conflicts generated by the contents of semiotic representations that are similar to each other in some respect. For this purpose, in this study, the semio-cognitive approach introduced by Raymond Duval was complemented with the semiotic-interpretative approach of the Peircean tradition. By embracing the pragmatist research paradigm, the methodology was based on the research questions, which guided the selection of the research methods within a qualitatively driven mixed methods design. The research results clearly show the need for a review of professional teacher training programs, as regards the role the semiotic handling plays in the cognitive construction of the mathematical objects and the learning assessment.  相似文献   

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