Igal Galili

The relationship between physics and mathematics is reviewed upgrading the common in physics classes’ perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning.

This study considers the short list of Nature of Science features frequently published and widely known in the science education discourse. It is argued that these features were oversimplified and a refinement of the claims may enrich or sometimes reverse them. The analysis shows the need to address the range of variation in each particular aspect of NOS and to illustrate these variations with actual events from the history of science in order to adequately present the subject. Another implication of the proposal is the highlighting of the central role of science educators who, facing various strong claims of researchers in education and philosophy of science, often have difficulty in making a choice of what to teach about NOS. It is suggested that a representative variation with regard to the traditional NOS claims may be appropriate for a genuine understanding of the subject. In that, using the discipline-culture structure of the fundamental theories of physics and addressing the plurality of scientific methods may be helpful in the actual teaching and learning of NOS.

This study deals with the school instruction of the concept of weight. The historical review reveals the major steps in changing weight definition reflecting the epistemological changes in physics. The latest change drawing on the operation of weighing has been not widely copied into physics education. We compared the older instruction based on the gravitational definition of weight with the newer one based on the operational definition. The experimental teaching was applied in two versions, simpler and extended. The study examined the impact of this instruction on the middle school students in regular teaching environment. The experiment involved three groups of 14-year-old students. The assessment drew on a written questionnaire and personal interviews. The elicited schemes of conceptual knowledge allowed to evaluate the impact on students’ pertinent knowledge. The advantage of the new teaching manifested itself in the significant decrease of the well-known misconceptions such as “space causes weightlessness,” “weight is an unchanged property of the body considered,” and “heavier objects fall faster”. The twofold advantage—epistemological and conceptual—of the operational definition of weight supports the correspondent curricular changes of its adoption.

The essay reviews a new approach to science/physics curriculum. Scientific knowledge is considered as a culture, and the disciplinary content knowledge is upgraded to cultural content knowledge ). Physics disciplinary knowledge is considered as comprised of fundamental theoriesFundamental theory, structure of hierarchically structured in triadic model: nucleus-body-periphery representing discipline-culture. This structure supports displaying major steps of the scientific discourseDiscourses in construction of the particular discipline. By contrast between the fundamentals and their alternatives the conceptual meaning of the former is established and emphasized. As to the epistemologicalEpistemology aspects of knowledge, the cultural approach suggests considering different approaches - rationalist, empiricist and constructivist − as complementary contributions interwoven in the integrated method practiced in science. CCKCultural Content Knowledge based curriculum involves and arranges using history and philosophy of science. It seeks meta-knowledge of science appealing to the broad population of learners of different interests and preferences. Three ways to deliver the CCKCultural Content Knowledge oriented curriculum had been empirically explored. They were briefly described: new curriculum, conceptual excursus and summative lecture. Some epistemological features are addressed within the discipline-culture perspective. Altogether, the suggested curricular perspective provides a paradigm matching the tradition of dissemination of scientific literacy and enlightenment.

Physics textbooks often present items of disciplinary knowledge in a sequential order of topics of the theory under instruction. Such presentation is usually univocal, that is, isolated from alternative claims and contributions regarding the subject matter in the pertinent scientific discourse. We argue that comparing and contrasting the contributions of scientists addressing similar or the same subject could not only enrich the picture of scientific enterprise, but also possess a special appealing power promoting genuine understanding of the concept considered. This approach draws on the historical tradition from Plutarch in distant past and Koyré in the recent history and philosophy of science. It gains a new support in the discipline–culture structuring of the physics curriculum, seeking cultural content knowledge of the subject matter. Here, we address two prominent individuals of Italian Renaissance, Leonardo and Galileo, in their dealing with issues relevant for introductory science courses. Although both figures addressed similar subjects of scientific content, their products were essentially different. Considering this difference is educationally valuable, illustrating the meaning of what students presently learn in the content knowledge of mechanics, optics and astronomy, as well as the nature of science and scientific knowledge.

In his Mechanics of 1883, Ernst Mach opened a specific revision of the classical physics which launched a radical epistemological change in physics. Within this move, Mach introduced operational definition of physical concepts and thus changed the status of measurement in the foundation of physics. The paradigmatic change was introduced in the definition of inertial mass. This paper points to another physical concept, which went through a kind of similar change in definition – the concept of weight. In this perspective, we reviewed the history of conceptual transformation of the weight concept. We speculated for the reason that prevented this change to be performed within the classical physics as required another epistemological change introduced by Einstein in establishing of modern physics. It is within the new physics that Machian introduction of the operational concept definitions could fully develop towards operationalism and logical positivism. The anthropocentric nature of the weight concept left it however behind the frontier of theoretical physics. Yet, for the same nature, this concept remained central in physics education. The paper reviewed the status of the weight concept which divides the world of teaching physics into two big camps of educators those keeping with Newtonian definition and those who argue for the modern definition drawing on the operation of weighing. The paper suggests a new educational approach to teaching weight – disciplinary cultural one. The latter implies exposure of the conceptual dialogue regarding weight definition and making explicit the epistemological reasons for the conceptual change regarding weight being illustrated with a set of representative physical situations. The evidence of the educational priority of the new approach is mentioned.