It is well-known that introductory physics students often have alternative conceptions that are inconsistent with established physical principles and concepts. Invoking alternative conceptions in quantitative problem-solving process can derail the entire process. In order to help students solve quantitative problems involving strong alternative conceptions correctly, appropriate scaffolding support can be helpful. The goal of this study is to examine how different scaffolding supports involving analogical problem solving influence introductory physics students' performance on a target quantitative problem in a situation where many students' solution process is derailed due to alternative conceptions. Three different scaffolding supports were designed and implemented in calculus-based and algebra-based introductory physics courses to evaluate the level of scaffolding needed to help students learn from an analogical problem that is similar in the underlying principles but for which the problem solving process is not derailed by alternative conceptions. We found that for the quantitative problem involving strong alternative conceptions, simply guiding students to work through the solution of the analogical problem first was not enough to help most students discern the similarity between the two problems. However, if additional scaffolding supports that directly helped students examine and repair their knowledge elements involving alternative conceptions were provided, students were more likely to discern the underlying similarities between the problems and avoid getting derailed by alternative conceptions when solving the targeted problem. We also found that some scaffolding supports were more effective in the calculus-based course than in the algebra-based course. This finding emphasizes the fact that appropriate scaffolding support must be determined via research in order to be effective.
Previously we discussed how well students in an introductory physics course diagnosed their mistakes on a quiz problem with different levels of scaffolding support. In that case, the problem they self-diagnosed was unusually difficult. We also discussed issues related to transfer, particularly the fact that the transfer problem in the midterm that corresponded to the self-diagnosed problem was a far transfer problem. Here, we discuss a related intervention in which we repeated the study methodology with the same students in the same intervention groups, using a new quiz problem which was more …
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…
In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred and sixty two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the recitation in which they had to first learn from a solved problem provided and take advantage of what they learned from it to solve another problem (which we call the quiz problem) which was isomorphic. Previous research suggests that the multiple-c…
In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred and eighty two students from a calculus-based and an algebra-based introductory physics course were asked to learn from a solved problem provided and take advantage of what they learned from it to solve another isomorphic problem (which we call the quiz problem). The solved problem provided has two sub-problems while the quiz problem has three sub-problems, which is…
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…
Prior research suggest that introductory physics students have difficulty with graphing and interpreting graphs. Here, we discuss an investigation of student difficulties in translating between mathematical and graphical representations for a problem in electrostatics and the effect of increasing levels of scaffolding on students' representational consistency. Students in calculus-based introductory physics were given a typical problem that can be solved using Gauss's law involving a spherically symmetric charge distribution in which they were asked to write a mathematical expression for the e…
"Self-diagnosis tasks" aim at fostering diagnostic behavior by explicitly requiring students to present diagnosis as part of the activity of reviewing their problem solutions. We have been investigating the extent to which introductory physics students can diagnose their own mistakes when explicitly asked to do so with different levels of scaffolding support provided to them. In our study in an introductory physics class with more than 200 students, the recitation classes were split into three different experimental groups in which different levels of guidance were provided for performing the …
Prior research suggests that many students believe that the magnitude of the static frictional force is always equal to its maximum value. Here, we examine introductory students' ability to learn from analogical reasoning (with different scaffolding supports provided) between two problems that are similar in terms of the physics principle involved but one problem involves static friction, which often triggers the misleading notion. To help students process through the analogy deeply and contemplate whether the static frictional force was at its maximum value, students in different recitation c…
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): the 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 (1) identify the most common incorrect answer choice of introductory physics students and (2) predict the percentage of introductory students who would answer the question correctly in a post-test. Then, we used the CSEM post-test data from approximately 40…
It has been reported that students often leave the introductory physics classroom believing that physics is less connected to the real world than when they entered. In this paper we aim to complicate that narrative by considering students' experiences in an introductory physics for the life-sciences course that leverages students' disciplinary expertise in biology and chemistry as they learn physics. In a case study of three students, we probed the role of physics in their lives to challenge the typical interpretation of PER attitudinal and epistemological measures that aim to assess how stude…
The Force Concept Inventory (FCI) has been widely used to assess student understanding of introductory mechanics concepts by a variety of educators and physics education researchers. One reason for this extensive use is that many of the items on the FCI have strong distractor choices that correspond to students' alternate conceptions in mechanics. Instruction is unlikely to be effective if instructors do not know the common alternate conceptions of introductory physics students and explicitly take into account students' initial knowledge state in their instructional design. Here, we discuss re…
Identifying the relevant physics principles is a central component of problem solving. A major goal of most introductory physics courses is to help students discern the deep similarities between problems based upon the physics principles so that they can transfer what they learned by solving one problem to solve another problem which involves the same principle. We conducted an investigation in which 251 calculus- and algebra-based introductory physics students were asked explicitly in the recitation quiz to learn from a solved problem and then solve another problem that has different surface …
Quantum field theory has formed the conceptual framework of most of physics for more than sixty years. It incorporates a complete revision of our conception of the nature of matter and existence itself. Yet it is rarely taught, or even mentioned, in introductory physics---from high school, college, and university survey courses through upper-division "modern physics" courses. This omission is not necessary: This paper describes an approach through which the fundamental concepts and consequent insights of quantum field theory can be grasped, building upon familiar notions from classical and qua…
The Force Concept Inventory (FCI) has been widely used to assess student understanding of introductory mechanics concepts by educators and physics education researchers. Many of the items on the FCI have strong distractor choices corresponding to students' alternate conceptions in mechanics. Instruction is unlikely to be effective if instructors do not explicitly take into account students' initial knowledge state in their instructional design. We discuss research involving the FCI to evaluate the pedagogical content knowledge of instructors of varying teaching experience. For each item on the…
We discuss the development of interactive video tutorial-based problems to help introductory physics students learn effective problem solving heuristics. The video tutorials present problem solving strategies using concrete examples in an interactive environment. They force students to follow a systematic approach to problem solving and students are required to solve sub-problems (research-guided multiple choice questions) to show their level of understanding at every stage of prob lem solving. The tutorials are designed to provide scaffolding support at every stage of problem solving as neede…
The ability to categorize problems is a measure of expertise in a domain. In order to help students learn effectively, instructors and teaching assistants (TAs) should have pedagogical content knowledge. They must be aware of the prior knowledge of students they are teaching, consider the difficulty of the problems from students' perspective and design instruction that builds on what students already know. Here, we discuss the response of graduate students enrolled in a TA training course to categorization tasks in which they were asked to group problems based upon similarity of solution first…
The Force Concept Inventory (FCI) is a well-established physics education assessment tool used to evaluate students' comprehension of elementary mechanics principles. While it can be used to analyse the effectiveness of instruction if deployed as a pre- and post-test, we utilise the FCI here as pre-test only, to extract insights into first-year students' (mis)conceptions of Newtonian mechanics as they enter university. In this preliminary study, we tested 353 students enrolled at the University of Johannesburg in 2021, across six introductory physics courses. We focus on their responses to six…
A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantum mechanics. Our studies suggest this notoriously difficult task may be frustrated by the intuitively realist perspectives of introductory students, and a lack of ontological flexibility in their conceptions of light and matter. We have developed a framework for understanding and characterizing student perspectives on the physical interpretation of quantum mechanics, and demonstrate the differential im…
"Self-diagnosis tasks" aim at fostering diagnostic behavior by explicitly requiring students to present diagnosis as part of the activity of reviewing their problem solutions. The recitation classes in an introductory physics class (~200 students) were split into a control group and three experimental groups in which different levels of guidance was provided for performing the self-diagnosis activities. We have been a) investigating how students in each group performed on subsequent near and far transfer questions given as part of the exams; and b) comparing student's initial scores on their q…
