How students use mathematics in their physics classes has been studied extensively in the physics education literature. In addition to specific mathematical methods in specific physics contexts, possible effects of more general "cultural" differences between the two disciplines have also been explored. However, there has been little examination of students' own awareness and interpretation of these differences. We explore the undergraduate student experience of these "cultural" contrasts, focusing on how they impact learning and problem-solving. Through a qualitative study, including surveys and interviews with students double-majoring in mathematics and physics (or majoring in one and minoring in the other), we investigate students' awareness of distinct pedagogical approaches, mathematical justifications, and organization of concepts in mathematics versus physics classes. We find that students do recognize and navigate these "cultural" differences, often employing specific coping strategies. We identify specific themes from our data and comment on how students feel that these themes impact their learning. We suggest that increased faculty and student awareness of the identified differences in educational practice could facilitate knowledge transfer between mathematics and physics.
Cultural Astronomy is interdisciplinary connecting the arts, humanities, social & physical sciences. Data collection methods and theories are used from many disciplines and meld with methods and theories within cultural astronomy. The burden on the student is that to do cultural astronomy research it is necessary to be widely read within and across disciplines. I developed a series of courses that divided cultural astronomy content into broad regions such as Africa, North America, and the Pacific. The courses were structured to accommodate students from all parts of the university, but had to …
Cultural differences in answering physics questions: Could they arise from the difference between reasoning expected in answering exam questions in those cultures?
The Force Concept Inventory Across Continents: Testing Q-Matrix Transferability and Cross-Cultural Differences in Mechanics Reasoning
Australian Catholic University（澳大利亚天主教大学）；Technolyceum (Ministry of Education School)（技术学院（教育部学校））；University of Johannesburg（约翰内斯堡大学）；City University Macau（澳门城市大学）；De La Salle University（德拉萨大学）
We investigate introductory physics students' difficulties in translating between mathematical and graphical representations and the effect of scaffolding on students' performance. We gave a typical problem that can be solved using Gauss's law involving a spherically symmetric charge distribution (a conducting sphere concentric with a conducting spherical shell) to 95 calculus-based introductory physics students. We asked students to write a mathematical expression for the electric field in various regions and asked them to graph the electric field. We knew from previous experience that studen…
University students taking introductory physics are generally successful executing mathematical procedures in context, but often struggle with the use of mathematical concepts for sense making. Physics instructors note that their students experience difficulty with basic algebraic reasoning, a foundation on which more advanced mathematical thinking rests. However, little systematic research has been done to measure and categorize such difficulties in this population. This paper describes an investigation of trends in student reasoning with proportions, quantification, and symbolizing in introd…
Expressing physics problems in the form of a mathematical model is one of the most important stages in the problem-solving process. Particularly in algebraic symbolization, understanding the meanings of signs and being able to manipulate them becomes a challenging task for students, especially when more than two elements in the mathematical expression could carry a negative sign. We use Conceptual Blending theory to investigate how students attribute emergent meaning to the signs and how they articulate different signs in their algebraic symbolization. The data for this research is drawn from …
Differentiation is a mathematical skill applied throughout science in order to describe the change of a function with respect to a dependent variable. Thus, an intuitive understanding of differentiation is necessary to work with the mathematical frameworks used to describe physical systems in the higher levels of education. In order to obtain this intuition repeated practice is required. This paper presents the development of DiffGame, which consists of a series of exercises that introduce the basic principles of differentiation for high-school students through game-like elements. DiffGame hav…
Equations are about more than computing physical quantities or constructing formal models; they are also about understanding. The conceptual systems physicists use to think about nature are made from many different resources, formal and not, working together and inextricably linked. By blending mathematical forms and physical intuition, physicists breathe meaning into the equations they use. In contrast, in physics class, novice students often treat mathematics as only a calculational tool, isolating it from their rich knowledge of the physical world. We are interested in cases where students …
This project investigates how to quantitatively measure equity in small student groups. We follow several student groups to operationalize how discourse may be equitable or inequitable. The groups came from a two week, pre-college program that prepares first generation and deaf/hard-of-hearing students to major in a STEM field. In the program, students focus on improving their metacognitive skills and cultural preparation for college life within a context of model building. We use three methods to measure equity. First, we look at speaking time: who talks, when, and to whom. Second, we look to…
Many Physics Education Researchers have discussed the positive correlation between students' incoming mathematics skills and performance in their physics classes. Thus, in order to strengthen their performance gains in their physics courses, professors strive to bolster students' mathematics abilities but in-class time constraints force instructors to focus their lesson plans on physics concepts rather than renewing mathematics material. For the sake of preserving in-class time, many instructors are turning to lecture delivery outside of class by way of flipped classrooms and MOOCs (Massive On…
Secondary school students in the United States continue to underachieve in mathematics and science. Improving teacher quality is a core component of improving student achievement. Here we report on a professional development program, the MAST System, that develops the knowledge and skills for teaching mathematics, including metacognitive knowledge and regulation. In this cognitive apprenticeship program, teachers learn to plan, evaluate and adjust to improve student engagement and achievement. Central is the metacognitive practice of defense of instruction. By practicing this reflective approa…
Over the past decades, researchers have explored the relationship among home resources, school environment, and students' mathematics achievement in a large amount of studies. Many of them suggested that rich home resources for learning were related to higher average academic achievement. Some also suggested that the home background was closely associated with the learning environment, and therefore, influenced students' achievements. Thus, this study hypothesized that students who own more home resources would perform better than students who possess fewer resources and that schools that have…
We present a simple but efficient concept for the realization of blended teaching of mathematics and its applications in theoretical mechanics that was conceived, tested and implemented at the University of Trento, Italy, during the COVID-19 pandemic. The concept foresees traditional blackboard lectures with a reduced number of students present in the lecture hall, while the same lectures are simultaneously made available to the remaining students via high quality low-bandwidth online streaming. Based on our first assumption that traditional blackboard lectures, including the gestures and the …
Collaboration among students is fundamental for knowledge building and competency development. Nonetheless, the effectiveness of student collaboration depends on the extent that these interactions take place under conditions that favor commitment, trust, and decision-making among those who interact. The sanitary situation and the transition to remote teaching has added new challenges for collaboration given that students' interactions are mediated by Information and Communication Technologies (ICTs). In this study we explore the effectiveness of different collaborative relationships on physics…
Mathematical Physics : Problems and Solutions of The Students Training Contest Olympiad in Mathematical and Theoretical Physics (May 21st - 24th, 2010)
该系列的本期<<Modern Problems in Mathematical Physics >>代表了学生训练竞赛奥林匹克数学和理论物理的程序，包括陈述和提供给参与者的问题的解决方案。2010年5月21日至24日，萨马拉国立大学数学物理科学研究实验室、俄罗斯科学院斯捷克洛夫数学研究所和莫斯科物理技术学院（国立大学）合作举办了奥林匹克竞赛。本论文集的目的是供大学物理和机械数学系的学生使用，他们有兴趣获得数学和理论物理方法的更深入的知识，也可能对参与数学和理论物理教学的人员有用。
