Epistemic schemes and epistemic states. A study of mathematics convincement in elementary school classes

The paper introduces an interpretative framework that contains a characterization of epistemic schemes (constructs that are used to explain how class agents themselves are able to gain convincement in or promote convincement of mathematical statements) and epistemic states (a person’s internal states, such as convincement or certainty related to the person’s beliefs and to the schemes that explain them); a taxonomy for the epistemic schemes is also proposed. On the basis of the interpretative framework, an analysis is made of an excerpt of a regular elementary school class, a school level at which explicit mathematics reasoning rarely arises. The paper contends that teachers and students use schemes based on reasons in order to make mathematical statements credible, but that they also resort–perhaps unconsciously–to epistemic schemes that are governed by extra-rational considerations.     

High school students’ approaches to learning physics with relationship to epistemic views on physics and conceptions of learning physics

Background and purpose : Knowing how students learn physics is a central goal of physics education. The major purpose of this study is to examine the strength of the predictive power of students’ epistemic views and conceptions of learning in terms of their approaches to learning in physics. Sample, design and method : A total of 279 Taiwanese high school students ranging from 15 to 18?years old participated in this study. Three questionnaires for assessing high school students’ epistemic views on physics, conceptions of learning physics and approaches to learning physics were developed. Step-wise regression was performed to examine the predictive power of epistemic views on physics and conceptions of learning physics in terms of their approaches to learning physics. Results and conclusion: The results indicated that, in general, compared to epistemic views on physics, conceptions of learning physics are more powerful in predicting students’ approaches to learning physics in light of the regression models. That is, students’ beliefs about learning, compared with their beliefs about knowledge, may be more associated with their learning approaches. Moreover, this study revealed that the higher-level conceptions of learning physics such as ‘Seeing in a new way’ were more likely to be positively correlated with the deep approaches to learning physics, whereas the lower-level conceptions such as ‘Testing’ were more likely to positively explain the surface approaches, as well as to negatively predict the deep approaches to learning physics.     

Radical Constructivism, and the Sin of Relativism

The epistemology of relativism that is featured by the theory of radical constructivism is addressed. In particular, I examine several objections, all based on this epistemic position of relativism, that are often raised by critics of the theory: the charge of reality denial (which, it is often claimed, must lead ultimately to the epistemically problematic position of solipsism), the assertion of self-referential contradiction (a theory that rejects the notion of truth cannot itself claim to be true), and the accusation that the theory must lead to a position of ethical indifference. It is demonstrated that these objections do not hold: they arise, to a large extent, from the failure to distinguish properly between different knowledge domains – specifically, between the notions of cognitive and non-cognitive knowledge. Some concrete examples, specifically pertaining to the conflict between natural science and creationism, are addressed; and their relevance for science education is discussed.     

Of connections and fields - I

We describe some instances of the appearance of Chern’s mathematical ideas in physics. By means of simple examples, we bring out the geometric and topological ideas which have found application in describing the physical world. These applications range from magnetic monopoles in electrodynamics to instantons in quantum chromodynamics to the geometric phase of quantum mechanics. The first part of this article is elementary and addressed to a general reader. The second part is somewhat more demanding and is addressed to advanced students of mathematics and physics.     

Realism vs. Constructivism in Contemporary Physics: The Impact of the Debate on the Understanding of Quantum Theory and its Instructional Process

In the present study we attempt to incorporate the philosophical dialogue about physical reality into the instructional process of quantum mechanics. Taking into account that both scientific realism and constructivism represent, on the basis of a rather broad spectrum, prevalent philosophical currents in the domain of science education, the compatibility of their essential commitments is examined against the conceptual structure of quantum theory. It is argued in this respect that the objects of science do not simply constitute ‘personal constructions’ of the human mind for interpreting nature, as individualist constructivist consider, neither do they form products of a ‘social construction’, as sociological constructivist assume; on the contrary, they reflect objective structural aspects of the physical world. A realist interpretation of quantum mechanics, we suggest, is not only possible but also necessary for revealing the inner meaning of the theory’s scientific content. It is pointed out, however, that a viable realist interpretation of quantum theory requires the abandonment or radical revision of the classical conception of physical reality and its traditional metaphysical presuppositions. To this end, we put forward an alternative to traditional realism interpretative scheme, that is in harmony with the findings of present-day quantum theory, and which, if adequately introduced into the instructional process of contemporary physics, is expected to promote the conceptual reconstruction of learners towards an appropriate view of nature.     

Tables turned: Physics in the service of mathematics

E T Bell, the famous author of ‘Men of Mathematics’, has described mathematics as the ‘Queen of Arts and Servant of Science’. What he meant is that mathematics serves science by entering into the picture as soon as a proper mathematical model is set up by the scientist, and then after a purely mathematical analysis of the model, the final mathematical step is interpreted scientifically. The purpose of the present article is to convince the readers that sometimes the roles of science and mathematics are reversed, and a mathematical problem is interpreted as a physics problem; the laws of physics are utilized for a physical analysis, and the final result of the physical analysis is interpreted mathematically. We shall illustrate this by means of few examples.     

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.     

Constructivisms and Objectivity: Disentangling Metaphysics from Pedagogy

We can distinguish the claims of cognitive constructivism from those of metaphysical constructivism, which is almost entirely irrelevant to science education. Cognitive constructivism has strong empirical support and indicates important directions for changing science instruction. It implies that teachers need to be cognizant of representational, motivational and epistemic dimensions which can restrict or promote student learning. The resulting set of tasks for a science teacher are considerably larger and more complex than on the older more traditional conception, but the resources of cognitive sciences and the history of science can provide important parts of the teachers intellectual tool kit. A critical part of this conception of science education is that students must develop the skills to participate in epistemic interchanges. They must be provided opportunities and materials to develop those skills and the classroom community must have the appropriate features of an objective epistemic community.     

Designing Complexity

This article considers the nature of complexity and design, as well as relationships between the two, and suggests that design may have much potential as an approach to improving human performance in situations seen as complex. It is developed against two backgrounds. The first is a world view that derives from second order cybernetics and radical constructivism. What is particular about this view is that it accepts that our understanding of the world is made by us, regardless of whether it originates in an external reality or not. Indeed, it regards the question of whether an external reality can ever be known by us as essentially undecidable, which is part of its power. In terms of complexity, this leads to the position that we choose the complexity we see in the world. The second is design. Design is a way of behaving that approaches complexity in a different way (and expecting a different type of outcome) than we have conventionally used. Designers work in a way (a conversation with the self via the medium of drawing) that allows them to deal with very complex, ill‐defined and ambiguous situations that would probably be inaccessible using conventional approaches. The outcomes of design are generally novel but can never be argued to be the best solution. Design is necessarily a constructivist, second order cybernetic activity. It is suggested that, as second order cybernetics and radical constructivism give us new insights into the nature of complexity, design gives us a way of acting that comprehends these insights.     

The Mathematics of High School Physics

In the seventeenth and eighteenth centuries, mathematicians and physical philosophers managed to study, via mathematics, various physical systems of the sublunar world through idealized and simplified models of these systems, constructed with the help of geometry. By analyzing these models, they were able to formulate new concepts, laws and theories of physics and then through models again, to apply these concepts and theories to new physical phenomena and check the results by means of experiment. Students’ difficulties with the mathematics of high school physics are well known. Science education research attributes them to inadequately deep understanding of mathematics and mainly to inadequate understanding of the meaning of symbolic mathematical expressions. There seem to be, however, more causes of these difficulties. One of them, not independent from the previous ones, is the complex meaning of the algebraic concepts used in school physics (e.g. variables, parameters, functions), as well as the complexities added by physics itself (e.g. that equations’ symbols represent magnitudes with empirical meaning and units instead of pure numbers). Another source of difficulties is that the theories and laws of physics are often applied, via mathematics, to simplified, and idealized physical models of the world and not to the world itself. This concerns not only the applications of basic theories but also all authentic end-of-the-chapter problems. Hence, students have to understand and participate in a complex interplay between physics concepts and theories, physical and mathematical models, and the real world, often without being aware that they are working with models and not directly with the real world.     

Constructivism in Practice: an Exploratory Study of Teaching Patterns and Student Motivation in Physics Classrooms in Finland,Germany and Switzerland

For the last three decades, moderate constructivism has become an increasingly prominent perspective in science education. Researchers have defined characteristics of constructivist-oriented science classrooms, but the implementation of such science teaching in daily classroom practice seems difficult. Against this background, we conducted a sub-study within the tri-national research project Quality of Instruction in Physics (QuIP) analysing 60 videotaped physics classes involving a large sample of students (N?=?1192) from Finland, Germany and Switzerland in order to investigate the kinds of constructivist components and teaching patterns that can be found in regular classrooms without any intervention. We applied a newly developed coding scheme to capture constructivist facets of science teaching and conducted principal component and cluster analyses to explore which components and patterns were most prominent in the classes observed. Two underlying components were found, resulting in two scales—Structured Knowledge Acquisition and Fostering Autonomy—which describe key aspects of constructivist teaching. Only the first scale was rather well established in the lessons investigated. Classes were clustered based on these scales. The analysis of the different clusters suggested that teaching physics in a structured way combined with fostering students’ autonomy contributes to students’ motivation. However, our regression models indicated that content knowledge is a more important predictor for students’ motivation, and there was no homogeneous pattern for all gender- and country-specific subgroups investigated. The results are discussed in light of recent discussions on the feasibility of constructivism in practice.     

关于当代国外数学教育观的综述

本文对当代国外数学教育家所主张的数学文化观、大众数学观、数学意义建构观、数学层次序列观、数学智力结构观、数学实验活动观以及数学情感育德观作了全面综述,揭示了其对我国当前的中小学数学新课程及教学改革的启发意义。     

Using Computer Assisted Instruction to Compare the Inventive Model and the Radical Constructivist Approach to Teaching Physics

This paper introduces a new way of evaluating instructional strategies by using computers. Two basic theories, instructivism and constructivism, are discussed and critically evaluated in terms of their effectiveness in conceptual learning. Despite the current popularity of constructivism, the radical form of it is criticized in this paper. The advantages and limitations of these two approaches, especially the radical forms of constructivism, are outlined. After borrowing some ideas from other effective conceptual change models, an integrative model for conceptual learning (the Inventive Model) is introduced. Two versions of multimedia physics software are developed by the authors. The first version is based on the Inventive Model and the second version based on a radical constructivist model. The effectiveness of the Inventive Model was compared with the radical constructivist approach and conventional science instruction. Students' log files were analyzed to investigate the nature and the processes of the conceptual change. A conceptual test and a knowledge test were used to compare the groups. The quantitative results showed the superiority of the Inventive Model over the other models in conceptual learning and the superiority of conventional instruction in learning the basic knowledge. The qualitative analysis showed that only the Inventive Model lead to coherent conceptual learning. It was concluded that the process of conceptual change is gradual and continuous. Analysis of students' log files revealed no moments of dramatic change in students' conceptions.     

Students' mathematical modeling of motion

We present results of an investigation of university students' development of mathematical models of motion in a physical science course for preservice teachers and graduate students in science and mathematics education. Although some students were familiar with the standard concepts of position, velocity, and acceleration from physics classes, most students had difficulty using these concepts to characterize actual or hypothetical motions. Furthermore, some students developed their own nonstandard method of describing accelerated motion in terms of changes in the average velocity, from the start of the motion up to a given time. This is in contrast to the physics community's use of the acceleration construct, defined in terms of changes in the instantaneous velocity, to describe such motion. Although the change in average velocity is not typically identified as an important construct in traditional physics texts, some students found it intuitively appealing, and were able to use it successfully to describe and predict motion. We conclude that by focusing on standard constructs, and ignoring possible intuitive ways that students might view motion, standard kinematics instruction may miss an opportunity to maximize student understanding. © 2007 Wiley Periodicals, Inc. J. Res. Sci. Teach 45: 153–173, 2008.     

A Framework for Teaching Epistemic Insight in Schools

This paper gives the rationale and a draft outline for a framework for education to teach epistemic insight into schools in England. The motivation to research and propose a strategy to teach and assess epistemic insight followed research that investigated how students and teachers in primary and secondary schools respond to big questions about the nature of reality and human personhood. The research revealed that there are pressures in schools that dampen students’ expressed curiosity in these types of questions and limit their developing epistemic insight into how science, religion and the wider humanities relate. These findings prompted the construction of a framework for education for students aged 5–16 designed to encourage students’ expressed interest in big questions and develop their understanding of the ways that science interacts with other ways of knowing. The centrepiece of the framework is a sequence of learning objectives for epistemic insight, organised into three categories. The categories are, firstly, the nature of science in real world contexts and multidisciplinary arenas; secondly, ways of knowing and how they interact; and thirdly, the relationships between science and religion. Our current version of the Framework is constructed to respond to the way that teaching is organised in England. The key principles and many of the activities could be adopted and tailored to work in many other countries.     

The match matters: Examining student epistemic preferences in relation to epistemic beliefs about chemistry

Student epistemic preferences have been found to be important in student learning and achievement. The present study proposed a new conceptualization of student epistemic preferences in the epistemic match model, assessed the match between student epistemic beliefs about chemistry and their epistemic preferences, and, most importantly, examined how this epistemic match may be associated with chemistry course achievement. We adopted latent class analysis and found three distinct profiles of epistemic preferences based on the dimensions of simple and certain knowledge, attainable truth, and alternative knowledge claims. Students in Latent Class 3 (Moderate Preferences) demonstrated the closest match between chemistry epistemic beliefs and epistemic preferences, and had more students who obtained higher grades and fewer students who had lower grades in an introductory chemistry course compared to the other two classes. Students in Latent Classes 1 (All Preferred) and 2 (Alternative-Claim Disliked), however, demonstrated certain degrees of epistemic mismatch between chemistry epistemic beliefs and epistemic preferences, and had noticeably lower achievement in the chemistry course. The study findings highlight the importance of achieving a close match between epistemic beliefs and epistemic preferences for higher achievement in a subject domain.     

THE PROCESS OF PHYSICS TEACHING ASSISTANTS’ PEDAGOGICAL CONTENT KNOWLEDGE DEVELOPMENT

This study explored the process of physics teaching assistants’ (TAs) PCK development in the context of teaching a new undergraduate introductory physics course. Matter and Interactions (M&I) has recently adopted a new introductory physics course that focuses on the application of a small number of fundamental physical principles to the atomic and molecular nature of matter. The purpose of this study is to describe how the PCK of physics TAs in the M&I course was developed and enacted. Data collection began during the TA preparation workshop that was held before the semester and continued during the recitation and laboratory classes that the TAs taught during the semester. Through a qualitative, multiple case study research design, data were collected from multiple sources: non-participant observations, digitally recorded video, semi-structured interviews, TAs’ written reflections, and researchers’ field notes. Data analysis consisted of cross-case and within-case analyses. Data were analyzed using a constant comparative method. After data analysis, 2 main themes emerged related to the development of TA’s PCK: (a) TAs’ PCK developed from propositional knowledge to personal practical knowledge and (b) the process of knowledge development consisted of 3 phases: accepting, actualizing, and internalizing. The results of this study will not only contribute to the quest to identify the nature of professional knowledge of science teaching but also help guide preparation for innovative introductory physics courses and other college level science courses in the future.     

Combining issues of “girl-suited” science teaching,STS and constructivism in a physics textbook

This paper outlines the design of a physics textbook that addresses issues of gender-inclusive physics teaching, STS and constructivism. Difficulties of addressing these issues in a textbook for normal classes, which has to compete with other textbooks on the market will be discussed. Specializations: constructivist approaches in science education research and practice. Specializations: gender issues in science instruction. Specializations: primary education, integrated science. Specializations: STS, phenomenological oriented physics instruction. Specializations: peace education within science education.