Hans Freudenthal: A mathematician on didactics and curriculum theory

The main ideas in the work of Hans Freudenthal (1905-1990), the Dutch mathematician and mathematics educator, related to curriculum theory and didactics are described. Freudenthal's educational credo, 'mathematics as a human activity', is explored. From this pedagogical point of departure, Freudenthal's criticism of educational research and educational theories is sketched and fleshed out. Freudenthal's approaches to mathematics education, developmental research and curriculum development can be seen as alternatives to the mainstream 'Anglo-Saxon' approaches to curriculum theory.     

‘Voodoo maths’, asymmetric dependency and maths blame: why collaboration between school science and mathematics teachers is so rare

Mathematical reasoning and tools are intrinsic to science, yet the close and dependent relationship science has to mathematics is not reflected in either school education or science education research. This paper asks what the barriers are to a mutually beneficial relationship between the two disciplines. A two-phase qualitative interview study was used to explore the relationship between school science and mathematics education through the perspectives of science and mathematics education policy-makers and of teachers in departments which are unusual in collaborating. In total there were 36 participants. Interview data were analysed using thematic analysis. Findings show that there is an asymmetry in the dependency between school science and mathematics: science is dependent on mathematics but the reverse is not true. We discuss three consequences of this asymmetric dependency: there is greater benefit for science from any collaboration; ‘maths blame’ can arise from science teacher frustration; and science educators may believe they should have some ownership of the mathematics curriculum. Asymmetry of dependency, and therefore of benefit, will make it very difficult for mathematics and science to work together in a way which is genuinely mutually beneficial.     

走向数学教育哲学研究

数学教育的深入研究面临一些挑战,所涉及到的问题已超出了传统数学教育研究的范围.解决这些问题需要改变数学教育研究的视角,需要对数学教育的问题做出哲学的分析与批判.数学教育哲学研究是一个开拓性的工作,开展数学教育哲学研究,有助于推动数学教育学科理论的纵向发展;有助于数学教育改革走出误区.     

Social Values Associated with Cross-national Differences in Mathematics and Science Achievement: A cross-national analysis

This study explores several factors that account for cross-national differences in mathematics and science achievement for middle-school students from 39 countries based on the Third International Mathematics and Science Study. The results suggest that economic development level, as measured by GNP per capita, has a positive but relatively weak association with mathematics and science achievement. In contrast, variables reflecting a society's value on education, specifically the education of mathematics and science, demonstrates strong effects on students' achievement. These variables include students' perceived rigour of mathematics and science - a proxy of academic standards of mathematics and science, students' school attendance, the length of a school year, students' educational aspiration, and the average number of parents living with the student. The evidence presented in this study supports the argument that education reform aiming at improving mathematics and science achievement can hardly be successful without the efforts of the whole society.     

The Impact of Design-Based STEM Integration Curricula on Student Achievement in Engineering,Science, and Mathematics

The new science education reform documents call for integration of engineering into K-12 science classes. Engineering design and practices are new to most science teachers, meaning that implementing effective engineering instruction is likely to be challenging. This quasi-experimental study explored the influence of teacher-developed, engineering design-based science curriculum units on learning and achievement among grade 4–8 students of different races, gender, special education status, and limited English proficiency (LEP) status. Treatment and control students (n = 4450) completed pretest and posttest assessments in science, engineering, and mathematics as well as a state-mandated mathematics test. Single-level regression results for science outcomes favored the treatment for one science assessment (physical science, heat transfer), but multilevel analyses showed no significant treatment effect. We also found that engineering integration had different effects across race and gender and that teacher gender can reduce or exacerbate the gap in engineering achievement for student subgroups depending on the outcome. Other teacher factors such as the quality of engineering-focused science units and engineering instruction were predictive of student achievement in engineering. Implications for practice are discussed.     

小学数学教学中人文数学的实施策略

在数学教育中渗透人文教育,弘扬人文精神,是素质教育的要求,是我国新课程改革所规定的数学教育的目的,更是数学教育发展的必然。人文数学是数学与人文的结合,是用数学的精神、原则、思想和方法对学生进行文化陶冶和人格塑造,让数学教育在传授科学的同时起到提高人的文化素养和教化人格的作用。教育者可从创设特色人文课堂情境、引导学生自主学习、重视学生的个体差异三个方面实现人文教育在数学教学中的渗透,进而实现科学与人文在数学教学中有机的结合,进而促进学生人文素养的提升。     

Hating school, loving mathematics: On the ideological function of critique and reform in mathematics education

Students’ engagement with fictions in the form of “word problems” plays an important role in classroom practice as well as in theories of mathematical learning. Drawing on the Dutch historian Johan Huizinga and the Austrian philosopher Robert Pfaller, I show that this activity can be seen as a form of play or game, where it is pretended that mathematics is useful in real life in a way that it is not. With Pfaller, I argue that play can take hold of the imagination of the players, infusing everyday life with meaning borrowed from the imagery of the play and that these effects are more powerful when the play is forced and takes an institutionalized form. I show that mathematics education does in fact have these characteristics, including sophisticated mechanisms for translating in-game performance (test scores) to real-life goods (grades and examinations). A central theme of the article is the perceived discrepancy between mathematics education as it is, and how it supposedly could and should be in light of the properties of mathematics. The analysis implies that this gap actually is an effect of play and thus an inherent property of mathematics education itself.     

数学教育与科学人文精神的培养

从数学的特点、我国广大民众的科学人文精神素质情况、社会进步需要看,科学人文精神应是数学教育的最重要内涵之一。数学教育培养科学人文精神,应将数学教育置于社会的文化背景之中来考虑。数学教师要有数学文化的观念,需要注意到学生所具有的观念及其对数学教学活动的影响。     

从京师同文馆算学试题看早期的新式数学教学

京师同文馆是中国近代科技水平最高的学府。其中于1867年成立的天文算学馆成为当时中国新型的专业系科,也促进了中国新式教育诞生。1872年出现的京师同文馆壬申岁考算学试题,是目前我们见到的中国近代最早的新式教育数学试题。说明中国现代数学教学的开端要早于1872年,应在1868年左右。也说明中国学校教育课程结构发生了质的变化,数学开始作为一个独立的学科进入了中国的课堂。试题与答案用的是汉语,涉及代数、几何、三角等数学知识,与现在教学层次比较,其中高中部分试题比例为55%,初中部分试题比例占45%。它折射出我国现代科学技术教育的起点和科学技术兴起的足迹;标志着近代新式数学教学的开始,现代数学知识的传播;同时反映了当时中国数学教学水平的低下。     

数学教育与人文教育的融合

数学是科学文化的重要组成部分,数学科学在提高民族科学和文化素质中处于极其重要的地位。数学教育中富含人文教育的成分,如数学理性、数学思想方法、数学史、数学美等,要重视数学教育的人文价值,将数学教育与人文教育融合是当代国际教育的发展趋势。     

试论弗莱登塔尔的数学教育思想及其启示

我国的基础教育正逐步由应试教育向素质教育全面推进 ,由此带来了教育观念、教育思想等方面的转变。荷兰数学家弗莱登塔尔指出 :数学教育应该是现实数学的教育 ;数学教育的目标应该是学会“数学化”。他的这些数学教育思想对我国数学素质教育有一定的启示。     

数学教育中的素质教育分析

数学从小学到高中被作为三大主科,在大学时,又是理工类学生必修之课,由此可见数学是非常重要的。我国提倡素质教育,因此数学教学中也要进行素质教育。本文从数学教育中创新思维能力的培养、数学教育中学生智力发展的培养、数学教育中德育的培养、数学教育中人文素质的培养以及数学教育中美育价值的培养这几个方面对数学教育中的素质教育进行了分析。     

STEM in England: meanings and motivations in the policy arena

STEM, an acronym for Science, Technology, Engineering and Mathematics, is widely used in science education. There is confusion, however, as to its provenance and meaning which is potentially problematic. This study examines the purpose of STEM practice in education in England and asks if there are differences in perceptions of STEM between science and mathematics educator stakeholders. The study’s contribution to the literature is its unusual focus on those who were responsible for making and enacting national STEM policy. A two-phase qualitative approach was followed comprising an analysis of government documentation together with semi-structured interviews with key contributors to the science and mathematics education discourse. Findings suggest that there is a disconnect between the interpretations of the science and mathematics educators with a danger-advantage dichotomy to participation in STEM being perceived by the mathematics educators. Early aims of the STEM agenda, including increasing diversity, gave way to a focus on numbers of post-16 physics and mathematics students. We conclude that if the term STEM is to continue to be used then there is a need for greater clarity about what it represents in educational terms and a wider debate about its compatibility with the aims of science education for all.     

数学实验教学的探索与实践

传统数学教学模式是理论教育，学生从定义至定理，从推导到结论，无一不是纸上演算的结果。在不断普及与迅速发展的计算机等先进科技支持下，数学教育应改变传统的教学模式，走进实验室。“数学实验”课的开设，使这一设想变为可能。“数学实验”课程主要内容分为：基本实验、专题实验和综合实验，采用模块实验法与案例实验法相结合的方法进行教学。“数学实验”课程的开设应注意以下问题：提高学生学习的兴趣；挖掘学生学习的动力；培养学生科研意识与创造能力。     

The Role of Intuitive Rules in Science and Mathematics Education

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.     

Research on Learners and Teachers of Mathematics and Science: Forerunners to a Focus on Teacher Educator Professional Growth

This introductory paper first reflects the genesis of research in mathematics and science teacher education. The analyses show a movement from foci of research in mathematics and science education from students to teachers, and then to teacher educators. Next, an overview of research in mathematics and science teacher education and its development is provided, including teacher educators’ growth. This is followed by a comparative look at the seven papers in this special issue through three lenses, focusing on who the teacher educators in these papers are, the practices which are the focus for development, and the contexts in which the professional growth is situated. The seven papers not only exemplify how teacher educators might critically and systematically reflect on their own growth, educate new teacher educators, and do corresponding research, but also demonstrate the considerable progress the research community has made with respect to the professional growth of mathematics and science teacher educators in the last decade. Finally, challenges and questions are raised, in particular in relation to raising the quality and quantity of proficient teacher educators in order to strengthen teacher education research, and to have enough human resources to offer more and better professional development opportunities and to support schools.

     

现代科学教育的特点

科学教育指的是数学与自然科学教育以及在它们的基础上形成的各种交叉科学、综合科学和技术科学的教育。各级各类学校中进行的科学教育具有系统性、客观性、抽象性和继承性等特点     

Some Recent Developments in Teacher Education in Mathematics and Science: A Review and Commentary

Teacher preparation in science and mathematics will be best served, says the author of this roundup, by improvements both in the pedagogy and content of the undergraduate science and mathematics courses required of future teachers and in the reform of required science and mathematics methods courses. In a review of the history and politics of teacher education, the author underscores the twin goals of achieving program coherence and higher standards. She compares the place of mathematics education in mathematics departments with that of science education in science departments and recommends the replacement of bare bones methods courses with those combining pedagogy and content. Included is a selective bibliography.     

论数学教学中渗透德育的五个层面

数学教学中的德育．在理论上以前主要局限于三个方面：通过数学史培养爱国主义精神，通过数学内容培养辩证唯物主义世界观；通过数学演练形成良好的个性品质。在实践中也存在许多认识上的误区。在新世纪．数学教学中的德育必须拓展新视野、充实新内涵．注重五个层面：爱国主义教育．马克思主义哲学观教育．现代公民道德教育．科学精神教育和数学美学教育。     

信息与计算科学专业《数学分析》课程的教学改革与实践

在分析<数学分析>课程特点和信息与计算科学专业需要的基础上,围绕素质教育的要求,给出了对信息与计算科学专业<数学分析>课程教学改革的一些体会,提出了一些建议.