An appropriate diagram is a required element of a solution building process in physics problem solving and it can transform a given problem into a representation that is easier to exploit for solving the problem. A major focus while helping introductory physics students learn problem solving is to help them appreciate that drawing diagrams facilitates problem solving. We conducted an investigation in which two different interventions were implemented during recitation quizzes throughout the semester in a large enrollment, algebra-based introductory physics course. Students were either (1) asked to solve problems in which the diagrams were drawn for them or (2) explicitly told to draw a diagram. A comparison group was not given any instruction regarding diagrams. We developed a rubric to score the problem solving performance of students in different intervention groups. We investigated two problems involving electric field and electric force and found that students who drew productive diagrams were more successful problem solvers and that a higher level of relevant detail in a student's diagram corresponded to a better score. We also conducted think-aloud interviews with nine students who were at the time taking an equivalent introductory algebra-based physics course in order to gain insight into how drawing diagrams affects the problem solving process. These interviews supported some of the interpretations of the quantitative results. We end by discussing instructional implications of the findings.
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a give problem into a representation that is easier to exploit for solving it. A major focus while helping introductory physics students learn problem solving is to help them appreciate that drawing a diagram facilitates problem solution. We conducted an investigation in which 111 students in an algebra-based introductory physics course were subjected to two different interventions during recitation quizzes throughout the semester. They were either (1) asked to solve problems in which the diagrams were drawn …
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a given problem into a representation that is easier to exploit for solving it. A major focus while helping introductory physics students learn problem solving is to help them appreciate that drawing diagrams facilitates problem solution. We conducted an investigation in which 111 students in an algebra-based introductory physics course were subjected to two different interventions during recitation quizzes throughout the semester. They were either (1) asked to solve problems in which the diagrams were drawn …
One desired outcome of introductory physics instruction is that students will develop facility with reasoning quantitatively about physical phenomena. Little research has been done regarding how students develop the algebraic concepts and skills involved in reasoning productively about physics quantities, which is different from either understanding of physics concepts or problem-solving abilities. We introduce the Physics Inventory of Quantitative Literacy (PIQL) as a tool for measuring quantitative literacy, a foundation of mathematical reasoning, in the context of introductory physics. We p…
Discussion forums provide a channel for students to engage with peers and course material outside of class, accessible even to commuter and non-traditional populations. As such, forums can build classroom community as well as aid learning, but students do not always take up these tools. We use network analysis to compare three semesters of forum logs from an introductory calculus-based physics course. The networks show dense structures of collaboration that differ significantly between semesters, even though aggregate participation statistics remain steady. After characterizing network structu…
We examined how introductory physics students' attitudes and approaches to problem solving compare to those of introductory astronomy students, using a previously validated survey, the Attitudes and Approaches to Problem Solving (AAPS) survey. In addition, we compared the performance of the introductory physics and astronomy students on the factors which were identified in a factor analysis in the original validation study. We found that introductory astronomy students' overall average AAPS score was significantly more favorable than that of introductory physics students (p < 0.01), and the ef…
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a problem into a representation that is easier to exploit for solving it. One major focus while helping introductory physics students learn effective problem solving is to help them understand that drawing diagrams can facilitate problem solution. We conducted an investigation in which two different interventions were implemented during recitation quizzes in a large enrollment algebra-based introductory physics course. Students were either (i) asked to solve problems in which the diagrams were drawn for them …
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a problem into a representation that is easier to exploit for solving the problem. A major focus while helping introductory physics students learn problem solving is to help them appreciate that drawing diagrams facilitates problem solution. We conducted an investigation in which 118 students in an algebra-based introductory physics course were subjected to two different interventions during the problem solving in recitation quizzes throughout the semester. Here, we discuss the problem solving performance of …
Instruction is unlikely to be effective if instructors do not know the common alternate conceptions of introductory physics students and explicitly take into account common student difficulties in their instructional design. Here, we discuss research involving the Conceptual Survey of Electricity and Magnetism (CSEM) to evaluate one aspect of the pedagogical content knowledge of teaching assistants (TAs): knowledge of introductory students' alternate conceptions in electricity and magnetism as revealed by the CSEM. For each item on the CSEM, the TAs were asked to identify the most common incor…
Electromagnetism (E&M) is often challenging for students enrolled in introductory college-level physics courses. Compared to mechanics, the mathematics of E&M is more sophisticated and the representations are more abstract. Furthermore, students may lack productive intuitions they had with force and motion. In this article, we explore the mathematization of electric charge. Specifically, we explore how difficulties with positive and negative signs can arise for learners who approach integers primarily as positions on a number line.
Group work is becoming increasingly common in introductory physics classrooms. Understanding how students engage in these group learning environments is important for designing and facilitating productive learning opportunities for students. We conducted a study in which we collected video of groups of students working on conceptual electricity and magnetism problems in an introductory physics course. In this setting, students needed to negotiate a common understanding and coordinate group decisions in order to complete the activity successfully. We observed students interacting in several dis…
When students are learning to use math in physics, one of the most important ideas they need to learn is that equations are not just calculational tools; they represent relationships between physical variables that change together (covary). How much a change in one variable or parameter is associated with a change in another depends on how they appear in the equation: their functional dependence. Understanding this sort of relationship is rarely taught in introductory mathematics classes, and students who have not yet learned to blend conceptual ideas with mathematical symbols may not see the …
Mathematics is the language of science. Fluent and productive use of mathematics requires one to understand the meaning embodied in mathematical symbols, operators, syntax, etc., which can be a difficult task. For instance, in algebraic symbolization, the negative and positive signs carry multiple meanings depending on contexts. In the context of electromagnetism, we use conceptual blending theory to demonstrate that different physical meanings, such as directionality and location, could associate to the positive and negative signs. With these blends, we analyze the struggles of upper-division…
Relating two quantities to describe a physical system or process is at the heart of "doing physics" for novices and experts alike. In this paper, we explore the ways in which experts use covariational reasoning when solving introductory physics graphing problems. Here, graduate students are considered experts for the introductory level material, as they often take the role of instructor at large research universities. Drawing on work from Research in Undergraduate Mathematics Education (RUME), we replicated a study of mathematics experts' covariational reasoning done by Hobson and Moore with p…
Assessing student learning is a cornerstone of educational practice. Standardized assessments have played a significant role in the development of instruction, curricula, and educational spaces in college physics. However, the use of these assessments to evaluate student learning is only productive if they continue to align with our learning goals. Recently, there have been calls to elevate the process of science ("scientific practices") to the same level of importance and emphasis as the concepts of physics ("core ideas" and "crosscutting concepts"). We use the recently developed 3D-LAP to in…
We describe a study in which introductory physics students engage in reflection with peers about problem solving. The recitations for an introductory physics course with 200 students were broken into the "Peer Reflection" (PR) group and the traditional group. Each week in recitation, students in the PR group reflected in small teams on selected problems from the homework. The graduate and undergraduate teaching assistants (TAs) in the PR group recitations provided guidance and coaching to help students learn effective problem solving heuristics. In the recitations for the traditional group, st…
We describe a study in which introductory physics students engage in reflection with peers about problem solving. The recitations for an introductory physics course with 200 students were broken into the "Peer Reflection" (PR) group and the traditional group. Each week in recitation, students in the PR group reflected in small teams on selected problems from the homework and discussed why solutions of some students employed better problem solving strategies than others. The graduate and undergraduate teaching assistants (TAs) in the PR group recitations provided guidance and coaching to help s…
Model-Based Reasoning in the Upper-Division Physics Laboratory: Framework and Initial Results
我们回顾和扩展现有的框架建模，开发一个新的框架，描述了基于模型的推理在上师物理实验室。构建和使用模型是核心科学实践，在K-12和高等教育中获得了极大的关注。虽然建模是一个广泛适用的过程，但在物理教育中，它已优先应用于广泛适用原理的迭代开发（例如，牛顿运动定律（Newton's laws of motion in introduction mechanics）新框架的一个重要特征是，测量工具（除了正在研究的物理系统）进行建模的过程。有声思维访谈被用来完善的框架，并证明其实用性，通过记录的例子，基于模型的推理在实验室。当应用于有声思维访谈时，该框架捕捉和区分学生的基于模型的推理，并有助于确定未来的研究领域。访谈显示了学生如何有效地将建模的相似方面应用于物理系统和测量工具：构建，预测，数据解释，模型限制的识别和修订。最后，我们记录了学生在构建实验系统模型时明确阐述假设的挑战，以及由于学生先前概念理解不足而在模型构建中面临的进一步挑战。建模的角度重新构建了测量工具和仪器的许多看似任意的技术细节，作为真实和引人入胜的科学意义的机会。
It's Not the Tool, It's the Task: A Framework for Cognitively Activated AI Augmentation in Physics Instruction
Ludwig-Maximilians-Universität München (LMU Munich), Faculty of Physics/Chair of Physics Education Research（慕尼黑路德维希-马克西米利安大学物理学院/物理学教育研究讲席）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Heidelberg University of Education, Institute of Physics（海德堡师范大学物理研究所）
