Researching research: mathematics education in the Political

We discuss contemporary theories in mathematics education in order to do research on research. Our strategy consists of analysing discursively and ideologically recent key publications addressing the role of theory in mathematics education research. We examine how the field fabricates its object of research by deploying Foucault’s notion of bio-politics—mainly to address the object “learning”—and ?i?ek’s ideology critique—to address the object “mathematics”. These theories, which have already been used in the field to research teaching and learning, have a great potential to contribute to a reflexivity of research on its discourses and effects. Furthermore, they enable us to present a clear distinction between what has been called the sociopolitical turn in mathematics education research and what we call a positioning of mathematics education (research) practices in the Political.     

“自然化的现象学”是否可行——从当代认知科学的视角看

现象学家丹·扎哈维近年来在“自然化的现象学”论题下提出了这样一种观点,该观点认为现象学能够为认知科学提供更有价值的对人心智活动的解释模型,并且现象学对意识的种种先验分析能够对当代认知科学的研究有所助益。文章将以“物体恒常性”以及“拥有感”为案例,通过对比现象学与认知科学对这两个具体人类心智现象的解说方式,审视扎哈维的这一观点在具体事实层面是否可行。并由此指出现象学解释模式与当今时代立足于脑影像技术之上的当代认知科学的解释模式之间并无法兼容。     

Cognitive Research and Elementary Science Instruction: From the Laboratory,to the Classroom,and Back

Can cognitive research generate usable knowledge for elementary science instruction? Can issues raised by classroom practice drive the agenda of laboratory cognitive research? Answering yes to both questions, we advocate building a reciprocal interface between basic and applied research. We discuss five studies of the teaching, learning, and transfer of the “Control of Variables Strategy” in elementary school science. Beginning with investigations motivated by basic theoretical questions, we situate subsequent inquiries within authentic educational debates—contrasting hands-on manipulation of physical and virtual materials, evaluating direct instruction and discovery learning, replicating training methods in classroom, and narrowing science achievement gaps. We urge research programs to integrate basic research in “pure” laboratories with field work in “messy” classrooms. Finally, we suggest that those engaged in discussions about implications and applications of educational research focus on clearly defined instructional methods and procedures, rather than vague labels and outmoded “-isms.”     

Teaching units as the integrating core of mathematics education

How to integrate mathematics, psychology, pedagogy and practical teaching within the didactics of mathematics in order to get unified specific theories and conceptions of mathematics teaching? This problem—relevant for theoretical and empirical studies in mathematics education as well as for teacher training—is considered in the present paper. The author suggests an approach which is based on teaching units (Unterrichtsbeispiele). Suitable teaching units incorporate mathematical, pedagogical, psychological and practical aspects in a natural way and therefore they are a unique tool for integration.     

From Grounding Metaphors to Technological Devices: A Call for Legitimacy in School Mathematics

The mutual relationship between real objects and mathematical constructions is at the very base of studies concerned with making sense in mathematics. In this wider perspective recent research studies have been concerned with the cognitive roots of mathematical concepts. Human perception and movement and, more generally, interaction with space and time are recognized as being of crucial importance for knowledge construction. A new approach to the cognitive science of mathematics, based on the notion of ‘embodied cognition’ assumes that mathematics cannot be considered as mind free. Accordingly, mathematical concepts derive from the cognitive activities of subjects and are highly influenced by the body structure. This article reports some examples of teaching experiments based on body-related metaphors. Some of them are carried out by means of technological devices. A call for legitimacy in school mathematics is made, both for an embodied cognition perspective and for a related use of technology. This revised version was published online in July 2006 with corrections to the Cover Date.     

Ernst Mach and George Sarton’s Successors: The Implicit Role Model of Teaching Science in USA and Elsewhere, Part II

George Sarton had a strong influence on modern history of science. The method he pursued throughout his life was the method he had discovered in Ernst Mach’s Mechanics when he was a student in Ghent. Sarton was in fact throughout his life implementing a research program inspired by the epistemology of Mach. Sarton in turn inspired many others in several generations (James Conant, Thomas Kuhn, Gerald Holton, etc.). What were the origins of these ideas in Mach and what can this origin tell us about the history of science and science education nowadays? Which ideas proved to be successful and which ones need to be improved upon? The following article will elaborate the epistemological questions, which Charles Darwin’s “Origin” raised concerning human knowledge and scientific knowledge and which led Mach to adapt the concept of what is “empirical” in contrast to metaphysical a priori assumptions a second time after Galileo. On this basis Sarton proposed “genesis and development” as the major goal of his journal Isis. Mach had elaborated this epistemology in La Connaissance et l’Erreur (Knowledge and Error), which Sarton read in 1911 (Hiebert in Knowledge and error. Reidel, Dordrecht, 1976; de Mey in George Sarton centennial. Communication & Cognition, Ghent, pp. 3–6, 1984). Accordingly for Sarton, history becomes not only a subject of science, but a method of science education. Culture—and science as part of culture—is a result of a genetic process. History of science shapes and is shaped by science and science education in a reciprocal process. Its epistemology needs to be adapted to scientific facts and the philosophy of science. Sarton was well aware of the need to develop the history of science and the philosophy of science along the lines of this reciprocal process. It was a very fruitful basis, but a specific part of it Sarton did not elaborate further, namely the erkenntnis-theory and psychology of science education. This proved to be a crucial missing element for all of science education in Sarton’s succession, especially in the US. Looking again at the origins of the central questions in the thinking of Mach, which provided the basis and gave rise to Sarton’s research program, will help in resolving current epistemic and methodological difficulties, contradictions and impasses in science education influenced by Sarton. The difficulties in science education will prevail as long as the omissions from their Machian origins are not systematically recovered and reintegrated.     

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。     

Embodied cognition as grounding for situatedness and context in mathematics education

In this paper we analyze, from the perspective of 'Embodied Cognition', why learning and cognition are situated and context-dependent. We argue that the nature of situated learning and cognition cannot be fully understood by focusing only on social, cultural and contextual factors. These factors are themselves further situated and made comprehensible by the shared biology and fundamental bodily experiences of human beings. Thus cognition itself is embodied, and the bodily-grounded nature of cognition provides a foundation for social situatedness, entails a reconceptualization of cognition and mathematics itself, and has important consequences for mathematics education. After framing some theoretical notions of embodied cognition in the perspective of modern cognitive science, we analyze a case study – continuity of functions. We use conceptual metaphor theory to show how embodied cognition, while providing grounding for situatedness, also gives fruitful results in analyzing the cognitive difficulties underlying the understanding of continuity. This revised version was published online in July 2006 with corrections to the Cover Date.     

PRESERVICE MATHEMATICS AND SCIENCE TEACHERS IN AN INTEGRATED TEACHER PREPARATION PROGRAM FOR GRADES 7–12: A 3-YEAR STUDY OF ATTITUDES AND PERCEPTIONS RELATED TO INTEGRATION

The purpose of this article is twofold: (a) to describe a unique teacher licensure program for grades 7–12 that integrates mathematics, science, and technology education and (b) to explore the attitudes and perceptions related to the integration of mathematics, science, and technology education of three cohorts of preservice teachers enrolled in the first 3 years of the program. Eighty-one preservice teachers responded to a semantic differential to measure attitudes and perceptions related to “mathematics, science, and technology education integration.” Principal components and internal consistency reliability analyses were computed to provide validity and reliability evidence. Preservice teachers also responded to one open-ended, free-response written question, “What does the integration of mathematics, science, and technology education mean to you?” Multivariate and univariate analyses of variance with repeated measures and Pearson cross-tabulation chi-square analyses were computed to identify pretest–posttest differences for the value and difficulty scales, identified by the principal components analysis. Analytic inductive methods were used to identify emergent themes in student written responses to the open-ended question. Results indicated no change in preservice teacher attitudes and perceptions related to the value of integration—they clearly valued integration at the onset and completion of the program, often citing student benefits. However, a significant change in preservice teacher attitudes and perceptions related to difficulty was noted. Upon completion of the program, preservice teachers perceived integration to be more difficult and identified barriers and challenges—demonstrating a more realistic, practical, and cautious approach to the integration of mathematics, science, and technology education.     

在高职数学教学中关于操作性教学的研究报告

数学作为高职院校理工科重要的一门基础课,既为专业基础课和专业课提供了必要的数学知识和数学方法,又在培养具有良好数学素养的各类创新型人才、应用技术型人才方面起着特别重要的作用。针对高职学生的特点,展开关于＂在高职数学教学进行操作性教学＂的教学尝试,能够在有限的教学时间里,结合学生的个性特质,培养学生既能运用理论、定义等来解决问题,又能利用数学软件来解决数学问题。     

Confessions from the Performatively Confused

“Confessions” begins with an auto-ethnographic account of my learning-through-movement in a relationship that was intimate, therapeutic, embodied and instructive—with a teacher called Annie. It seems sensible to start with a choreographic teacher of Feldenkrais therapies and theatre-movement to think about the meanings I import from my roles as learner, therapist and performer to my roles as educator and feminist—and back again. My work with Annie, as her student, brought choreography back into the social science class rooms in which I teach, along with an acute awareness of my embodied self as a condition/centre of my pedagogical strategies in teaching the social. Amplifying this experience, I present ways of storying and reading my teaching praxis in conventional academic classrooms, as informed by the ways in which I theorise my learning that has occurred outside of them.     

Science and Technology Education in the STES Context in Primary Schools: What Should It Take?

Striving for sustainability requires a paradigm shift in conceptualization, thinking, research and education, particularly concerning the science-technology-environment-society (STES) interfaces. Consequently, ‘STES literacy’ requires the development of students’ question asking, critical, evaluative system thinking, decision making and problem solving capabilities, in this context, via innovative implementable higher-order cognitive skills (HOCS)-promoting teaching, assessment and learning strategies. The corresponding paradigms shift in science and technology education, such as from algorithmic teaching to HOCS-promoting learning is unavoidable, since it reflects the social pressure, worldwide, towards more accountable socially- and environmentally-responsible sustainable development. Since most of the STES- and, recently STEM (science-technology-engineering-mathematics)-related research in science education has been focused on secondary and tertiary education, it is vital to demonstrate the relevance of this multifaceted research to the science and technology teaching in primary schools. Our longitudinal STES education-related research and curriculum development point to the very little contribution, if any, of the traditional science teaching to “know”, to the development of students’ HOCS capabilities. On the other hand, there appears to be a ‘general agreement’, that the contemporary dominant lower-order cognitive skills (LOCS) teaching and assessment strategies applied in science and technology education are, in fact, restraining the natural curiosity and creativity of primary school (and younger?) pupils/children. Since creative thinking as well as evaluative system thinking, decision making, problem solving and … transfer constitute an integral part of the HOCS conceptual framework, the appropriateness of “HOCS promoting” teaching, and the relevance of science and technology, to elementary education in the STES context, is apparent. Therefore, our overriding guiding purpose was to provide any evidence-based research to the vital LOCS-to-HOCS paradigm shift in STES education. The findings of, and conclusions derived from our longitudinal research on HOCS development within STES-oriented and traditional education, suggest that both—science and technology education (STE) and STES education—are relevant to primary school education. Based on this, what it should take to insure success in this context, is thoroughly discussed.     

电子书包与初中数学教学深度融合的模式与策略研究

本文结合电子书包的课堂教学应用实践,提炼电子书包与初中数学教学深度融合的课堂教学模式,明确了新授课及练习课、复习课的基本教学流程;提出电子书包与初中数学教学深度融合的"电子书包多组件参与探究"等教学策略,以及电子书包与初中数学教学深度融合的"班级空间与微信平台融合"等家校互联学习策略,以期为电子书包环境下创新教师的教学...     

双重认知外语教学策略的数学建模评价

文章将数学、统计学和心理学等基础理论应用于外语教学研究,从跨学科的角度,应用数学建模对发展双重认知的外语教学策略进行评价研究,仿真实验表明了该方法的实用性和有效性。     

What If We Look at the Body? An Embodied Perspective of Collaborative Learning

The bodily experiences and implications of understanding the functioning of the human brain–body mechanism has been a center of attention in the field of cognitive neurosciences for over two decades. Research in this field has enlarged the theories of learning and development, and contributed to changes in educational practices involving language processing, mathematics, and spatial thinking; however, these changes have not yet been applied to the analysis of transversal competencies such as collaborative learning. The aim of this paper is to bridge the theoretical and applied advances in the field of embodied cognition, specifically collaborative learning. The definitions, theoretical frameworks, and current methodological approaches in the field of collaborative learning are reviewed, with a particular focus on those studies that have investigated interactive dynamics in collaborative situations. The need to take the field further by exploring the theoretical perspective of embodied cognition as a possibility that can open the field is also presented. The relevance of investigating learning in groups by analyzing bodily engagements and intersubjectivity is demonstrated and methodological considerations are raised.

     

Quasi-appropriation of dialectical materialism: a critical reading of Marxism in Vygotskian approaches to cultural studies in science education

In this review essay we examine five categories of dialectical materialism proposed by Paulo Lima Junior, Fernanda Ostermann, and Flavia Rezende in their study of the extent to which the articles published in Cultural Studies of Science Education, that use a Vygotskian approach, are committed to Marxism/dialectical materialism. By closely examining these categories (“thesis, antithesis and synthesis,” “unity of analysis,” “History,” “revolution,” “materialism”) we expect to enrich the general discussion about the possible contributions of Marxism to science education. We perceive part of science education practice as orientating toward positivism, which reduces human beings—teachers, learners and researchers—to isolated individuals who construct knowledge by themselves. The very same approach aggravates the inner contradiction of the capitalist society demanding commitments from researchers to continually build innovative science education from human praxis. Nevertheless, it is necessary to situate ourselves beyond a formal commitment with dialectical materialism and hence reach the heart of this method. Besides understanding the researchers’ commitments, we question the extent to which the respective research helps to radically refresh the current view on science, science education practice, and research in science education.     

The beliefs and perceptions of pre-service teachers enrolled in a subject-area dominant teacher education program about “Effective Education”

Teacher educators and researchers have studied the improvement of teacher education programs so that pre-service teachers may be well prepared. Research has shown that not only teachers’ knowledge but also their beliefs have major influence on their approach to teaching. This present research examined the mathematics and science pre-service teachers’ beliefs and perceptions in Turkey. Specifically, the study focused on the student–teachers’ perspectives on “effective education” at the end of their subject area dominant program before the student teaching and the changes in those beliefs after having teaching experience. Many pre-service teachers described the teacher-centered environment as effective, and those who supported a student-centered environment discussed difficulties they faced in creating it during student and full-time teaching.