中学数理融合教学的概念、体系和实施

中学数理融合教学是新课程改革国家要求“改变课程结构过于强调学科本位、科目过多和缺乏整合的现状”前提下产生的一种教学形式。中学数理融合教学过程强调多样性、聚合性和创新性,具有多元化的教学特征,是学科整合背景下对数学和物理的知识、思维、方法的再组织和提炼。中学数理融合教学体系的功能是筛选和整合教学对象、教学内容、课程设置、呈现方式、教学范式、教学评价和教学保障等要素,促进数理学科融合教学活动的有效实施,提升学生的创新性素养。中学数理融合教学的实施路径为:探索新的学科融合教学方法,优化课程设计;开发建设数理融合校本课程;组建融合型创新学习团队,实行“联合培养”模式;开展数理融合科研课题研究,产学研相结合发展创新能力;建立促进学科融合发展的教学机制。     

学科问题解决策略研究的沿革及走向探析

随着知识领域问题研究的深入。学科问题解决策略成为学习策略研究的热点问题之一。其中数学、物理、化学的问题解决策略的研究成果丰富,而人文学科的研究较弱。同时学科问题解决策略的研究受到传统问题研究范式的影响往往难以突出其学科特色。存在一些不足之处。可以通过以下方面改进：把握学科问题解决策略研究的系统性,突出学科问题解决策略研究的“学科”特色,重视中间学生在学科问题解决策略研究阶段中的地位。重视知识获得过程,拓宽各学科问题解决策略的研究领域。     

Essential Characteristics for a Professional Development Program for Promoting the Implementation of a Multidisciplinary Science Module

Teachers involved in the implementation of a curriculum innovation can be prepared for this task through a professional development program. In this paper, we describe essential characteristics (identified empirically and theoretically) for such a professional development program that promotes the acquisition of competences by these teachers. The innovation deals with the introduction of modules from a new multidisciplinary subject, in which elements from physics, chemistry, biology, mathematics, and physical geography are integrated. A 3-step approach was used to identify the essential characteristics: (a) evidence from classroom practice, (b) characteristics of the new subject, and (c) theoretical and empirical evidence from curriculum implementation studies. Analysis of the data showed that 5 characteristics need particular attention in a professional development program.     

Axioms, Essences, and Mostly Clean Hands: Preparing to Teach Chemistry with Libavius and Aristotle

Andreas Libavius’ (c. 1555–1616) three part collection of letters, the Rerum chymicarum epistolica forma ... liber (1595–1599) is a particularly important text in fashioning the subject of chemistry as a demonstrative science and as a didactic discipline. Where Libavius’ Alchemia, which some have claimed to be the first textbook of chemistry, had mostly a humanist agenda, the Rerum chymicarum ... liber more directly sought to wrest the subject of “chemistry” away from Paracelsian adepts, and established the methodological basis for a specific form of knowledge suitable to the university. Making use of Aristotle’s Posterior analytics Libavius created a “floor-plan” for chemistry that integrated practical experience with natural philosophy, and could thus, he claimed, penetrate more deeply into the structure of nature than other academic disciplines.     

Modelling Mathematical Reasoning in Physics Education

Many findings from research as well as reports from teachers describe students’ problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.     

Impact of Interdisciplinary Undergraduate Research in Mathematics and Biology on the Development of a New Course Integrating Five STEM Disciplines

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a course for first-year students that integrates the material in the first course of the major in each of biology, chemistry, mathematics, computer science, and physics.     

Perceptions of the relevance of mathematics and science: Further analysis of an Australian longitudinal study

The media portray girls' achievement in mathematics and science as equal to or better than male performance. This paper reports on a longitudinal study based on Years 7–12. One of the disturbing features of these data is the extremely poor perceptions that students, both male and female, have of performance in mathematics and science in the earlier years of high school. These data suggest the need to examine students' changing perceptions in the transition years from primary school to high school. Despite there having been substantial improvement in girls' perceptions of how they have performed in mathematics and science, proportionately fewer females elect to undertake studies at the higher levels of mathematics, physics and chemistry. The data suggest that year 9 is crucial. The perspective that girls have unequivocally arrived has been challenged.     

Dawn of science

In mankind’s quest for knowledge, spanning the last four thousand years, certain developments stand out as milestones in the progress of science. This new series, intended for the general reader, will highlight such key events in the growth of mathematics, physics, chemistry, biology and engineering in an approximately chronological manner.     

Teachers' beliefs about school mathematics and mathematicians' mathematics and their relationship to practice

There is broad acceptance that mathematics teachers’ beliefs about the nature of mathematics influence the ways in which they teach the subject. It is also recognised that mathematics as practised in typical school classrooms is different from the mathematical activity of mathematicians. This paper presents case studies of two secondary mathematics teachers, one experienced and the other relatively new to teaching, and considers their beliefs about the nature of mathematics, as a discipline and as a school subject. Possible origins and future developments of the structures of their belief systems are discussed along with implications of such structures for their practice. It is suggested that beliefs about mathematics can usefully be considered in terms of a matrix that accommodates the possibility of differing views of school mathematics and the discipline.     

How Will We Understand What We Teach? - Primary Student Teachers’ Perceptions of their Development of Knowledge and Attitudes Towards Physics

The research outlined in this paper investigated how student teachers perceived the development of their knowledge and attitudes towards physics through video recorded practical workshops based on experiments and subsequent group discussions. During an 8-week physics course, 40 primary science student teachers worked in groups of 13–14 on practical experiments and problem-solving skills in physics. The student teachers were video recorded in order to follow their activities and discussions during the experiments. In connection with every workshop, the student teachers participated in a seminar conducted by their physics teachers and a primary science teacher; they watched the video recording in order to reflect on their activities and how they communicated their conceptions in their group. After the 8 weeks of coursework a questionnaire including a storyline was used to elicit the student teachers’ perceptions of their development of subject matter knowledge from the beginning to the end of the course. Finally, five participants were interviewed after the course. The results provided insight into how aspects such as self-confidence and the meaningfulness of knowledge for primary teaching were perceived as important factors for the primary science student teachers’ development of subject matter knowledge as well as a positive attitude towards physics.     

Identity: a complex structure for researching students’ academic behavior in science and mathematics

This article is a response to Pike and Dunne’s research. The focus of their analysis is on reflections of studying science post-16. Pike and Dunne draw attention to under enrollments in science, technology, engineering, and mathematics (STEM) fields, in particular, in the field of physics, chemistry and biology in the United Kingdom. We provide an analysis of how the authors conceptualize the problem of scientific career choices, the theoretical framework through which they study the problem, and the methodology they use to collect and analyze data. In addition, we examine the perspective they provide in light of new developments in the field of students’ attitudes towards science and mathematics. More precisely, we draw attention to and explicate the authors’ use of identity from the perspective of emerging theories that explore the relationships between the learner and culture in the context of science and mathematics.     

New Avenues for History in Mathematics Education: Mathematical Competencies and Anchoring

The paper addresses the apparent lack of impact of ‘history in mathematics education’ in mathematics education research in general, and proposes new avenues for research. We identify two general scenarios of integrating history in mathematics education that each gives rise to different problems. The first scenario occurs when history is used as a ‘tool’ for the learning and teaching of mathematics, the second when history of mathematics as a ‘goal’ is pursued as an integral part of mathematics education. We introduce a multiple-perspective approach to history, and suggest that research on history in mathematics education follows one of two different avenues in dealing with these scenarios. The first is to focus on students’ development of mathematical competencies when history is used a tool for the learning of curriculum-dictated mathematical in-issues. A framework for this is described. Secondly, when using history as a goal it is argued that an anchoring of the meta-issues in the related in-issues is essential, and a framework for this is given. Both frameworks are illustrated through empirical examples.     

小学数学教学生活化的有效策略

数学是一门与生活紧密相连的学科,俗语有云:“学会数理化,走遍全天下。”其中数学位于首位,足以见得数学知识能够很好地解决实际问题。利用生活化教学策略进行数学教学,能够让小学生对数学内容产生一定的学习兴趣与好奇心,并且能够有效提升学生对数学知识的重视程度,学生愿意主动学习数学,其综合能力才能够有效提升起来。为了实现上述教学效果,本文主要研究小学数学教学生活化的有效策略。     

Developing a ‘leading identity’: the relationship between students’ mathematical identities and their career and higher education aspirations

The construct of identity has been used widely in mathematics education in order to understand how students (and teachers) relate to and engage with the subject (Kaasila, 2007; Sfard & Prusak, 2005; Boaler, 2002). Drawing on cultural historical activity theory (CHAT), this paper adopts Leont’ev’s notion of leading activity in order to explore the key ‘significant’ activities that are implicated in the development of students’ reflexive understanding of self and how this may offer differing relations with mathematics. According to Leont’ev (1981), leading activities are those which are significant to the development of the individual’s psyche through the emergence of new motives for engagement. We suggest that alongside new motives for engagement comes a new understanding of self—a leading identity—which reflects a hierarchy of our motives. Narrative analysis of interviews with two students (aged 16–17 years old) in post-compulsory education, Mary and Lee, are presented. Mary holds a stable ‘vocational’ leading identity throughout her narrative and, thus, her motive for studying mathematics is defined by its ‘use value’ in terms of pursuing this vocation. In contrast, Lee develops a leading identity which is focused on the activity of studying and becoming a university student. As such, his motive for study is framed in terms of the exchange value of the qualifications he hopes to obtain. We argue that this empirical grounding of leading activity and leading identity offers new insights into students’ identity development.     

The Impact of Sustained, Standards-Based Professional Learning on Second and Third Grade Teachers’ Content and Pedagogical Knowledge in Integrated Mathematics

This 3 year longitudinal study reports the feasibility of an Improving Teacher Quality: No Child Left Behind project for impacting teachers’ content and pedagogical knowledge in mathematics in nine Title I elementary schools in the southeastern United States. Data were collected for 3 years to determine the impact of standards and research-based teacher training on these aspects of teacher quality. Content knowledge for the scope of this research study refers to the knowledge that teachers have about subject matter. Teacher quality is directly related to teachers’ “highly qualified” status, as defined by the No Child Left Behind mandate. According to this mandate, every classroom should have a teacher qualified to teach in his subject area and be able to “raise the percentage of students who are proficient in reading and math, and in narrowing the test-score gap between advantaged and disadvantaged students.” Participants were six second grade and seven third grade teachers of mathematics from nine schools within one failing school district. The implementation of standards-based methods in the nine Title I Schools increased teacher quality in elementary school mathematics. In fact, qualitative and quantitative data revealed significant gains in teachers’ mathematics content and pedagogical knowledge at both grade levels.     

Conceptions for relating the evolution of mathematical concepts to mathematics learning—epistemology, history, and semiotics interacting To the memory of Carl Menger (1902–1985)

There is an over-arching consensus that the use of the history of mathematics should decidedly improve the quality of mathematics teaching. Mathematicians and mathematics educators show here a rare unanimity. One deplores, however, and in a likewise general manner, the scarcity of positive examples of such a use. This paper analyses whether there are shortcomings in the—implicit or explicit—conceptual bases, which might cause the expectations not to be fulfilled. A largely common denominator of various approaches is some connection with the term “genetic.” The author discusses such conceptions from the point of view of a historian of mathematics who is keen to contribute to progress in mathematics education. For this aim, he explores methodological aspects of research into the history of mathematics, based on—as one of the reviewers appreciated—his “life long research.”     

Where's the Math? Prospective Teachers Visit the Workplace

The integration of academic and vocational subject matter is offered in response to efforts to make the study of mathematics meaningful and engaging for all students,as well as aid in the preparation of a mathematically literate workforce. Yet,teachers often come to mathematics education with more ‘pure’ than ‘applied’ backgrounds making it difficult for them to draw upon their own experiences to make subject matter meaningful. This paper analyses prospective teachers' opportunities to connect subject matter with workplace contexts. It examines the degree of importance prospective teachers place on workplace connections and the ways in which they incorporate these connections in classroom lesson plans. Results suggest that given opportunities to visit workplace sites, it is not a trivial task for prospective teachers to: 1) make the mathematics in work explicit, and 2) keep the mathematics contextualized when designing activities and problems for students. These results have implications for teacher education and the support prospective teachers require in building networks connecting mathematics, pedagogy,and work. This revised version was published online in July 2006 with corrections to the Cover Date.     

Elementary Teachers’ Mathematics Subject Knowledge: the Knowledge Quartet and the Case of Naomi

This paper draws on videotapes of mathematics lessons prepared and conducted by pre-service elementary teachers towards the end of their initial training at one university. The aim was to locate ways in which they drew on their knowledge of mathematics and mathematics pedagogy in their teaching. A grounded approach to data analysis led to the identification of a ‘knowledge quartet’, with four broad dimensions, or ‘units’, through which mathematics-related knowledge of these beginning teachers could be observed in practice. We term the four units: foundation, transformation, connection and contingency. This paper describes how each of these units is characterised and analyses one of the videotaped lessons, showing how each dimension of the quartet can be identified in the lesson. We claim that the quartet can be used as a framework for lesson observation and for mathematics teaching development.     

Physics Teaching in the Search for Its Self

The crisis in physics education necessitates searching for new relevant meanings of physics knowledge. This paper advocates regarding physics as the dialogue among discipline-cultures, rather than as a cluster of disciplines to be an appropriate subject of science education. In a discipline-culture one can distinguish elements of knowledge as belonging to either (1) central principles and paradigms – nucleus, (2) normal disciplinary area – body of knowledge or (3) rival knowledge of the subject – periphery. It appears that Physics cannot be represented as a simple dynamic wholeness, that is, cannot be arranged in a single tripartite (triadic) structure (this result presents a deconstruction), but incorporates several discipline-cultures. Bound together by family similarity, they maintain a conceptual discourse. Teaching physics as a culture is performed in polyphonic space of different worldviews; in other words, it is performed in a Kontrapunkt. Implications of the tripartite code are suggested with regard to representation of scientific revolutions, individual conceptual change, physics curricula and the typology of students learning science.