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, as well as the complexities added by physics itself. 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. (shrink)

Interdisciplinary understanding requires integration of insights from different perspectives, yet it appears questionable whether disciplinary experts are well prepared for this. Indeed, psychological and cognitive scientific studies suggest that expertise can be disadvantageous because experts are often more biased than non-experts, for example, or fixed on certain approaches, and less flexible in novel situations or situations outside their domain of expertise. An explanation is that experts’ conscious and unconscious cognition and behavior depend upon their learning and acquisition of a set (...) of mental representations or knowledge structures. Compared to beginners in a field, experts have assembled a much larger set of representations that are also more complex, facilitating fast and adequate perception in responding to relevant situations. This article argues how metacognition should be employed in order to mitigate such disadvantages of expertise: By metacognitively monitoring and regulating their own cognitive processes and representations, experts can prepare themselves for interdisciplinary understanding. Interdisciplinary collaboration is further facilitated by team metacognition about the team, tasks, process, goals, and representations developed in the team. Drawing attention to the need for metacognition, the article explains how philosophical reflection on the assumptions involved in different disciplinary perspectives must also be considered in a process complementary to metacognition and not completely overlapping with it. (Disciplinary assumptions are here understood as determining and constraining how the complex mental representations of experts are chunked and structured.) The article concludes with a brief reflection on how the process of Reflective Equilibrium should be added to the processes of metacognition and philosophical reflection in order for experts involved in interdisciplinary collaboration to reach a justifiable and coherent form of interdisciplinary integration. An Appendix of “Prompts or Questions for Metacognition” that can elicit metacognitive knowledge, monitoring, or regulation in individuals or teams is included at the end of the article. (shrink)

This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)