The cyclic format of the undergraduate physics curriculum depends on students' ability to recall and utilize material covered in prior courses in order to reliably build on that knowledge in later courses. However, there is evidence to suggest that people often do not retain all, or even most, of what they learned previously. How much information is retained appears to be dependent both on the individuals' approach to learning as well as the style of instruction. In particular, there is evidence to suggest that active engagement techniques in the classroom can improve students' retention of the material over time. Here, we report the findings of a longitudinal investigation of students' retention of conceptual understanding as measured by the Force and Motion Conceptual Evaluation (FMCE) following a first-semester, calculus-based introductory physics course, which features significant active engagement in both lecture and recitation. By administering the FMCE at the end of a first-semester physics course and again at the beginning of the subsequent second-semester physics course, we examine students' knowledge retention over time periods ranging from 1-15 months. We find that the shift in students' FMCE scores between these two courses is positive but corresponds to a small effect size, indicating that students retained effectively all of their conceptual learning (as measured by the FMCE). This finding largely persists even as the length of the gap between the two courses increases. We also find that, when breaking out students' performance on individual questions, the majority of students maintain their score on individual questions. Averaged over all questions, roughly a fifth of the students switched their answers from right to wrong or wrong to right on any given item.
There is some evidence that conceptual inquiry-based introductory physics lab curricula, such as RealTime Physics, may improve students' understanding of physics concepts. Thus, these curricula may be attractive for instructors who seek to transform their physics labs to improve student learning. However, the impact of conceptual inquiry-based lab instruction on students' attitudes and beliefs about experimental physics, as measured by the E-CLASS survey, is not yet fully understood. We present data from three curricular approaches over four semesters ($n=701$). We saw no change in E-CLASS sco…
We discuss the effect of administering conceptual and quantitative isomorphic problem pairs (CQIPP) back to back vs. asking students to solve only one of the problems in the CQIPP in introductory physics courses. Students who answered both questions in a CQIPP often performed better on the conceptual questions than those who answered the corresponding conceptual questions only. Although students often took advantage of the quantitative counterpart to answer a conceptual question of a CQIPP correctly, when only given the conceptual question, students seldom tried to convert it into a quantitati…
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…
We discuss the development and validation of a conceptual multiple-choice survey instrument called the Survey of Thermodynamic Processes and First and Second Laws (STPFaSL) suitable for introductory physics courses. The survey instrument uses common student difficulties with these concepts as resources in that the incorrect answers to the multiple-choice questions were guided by them. After the development and validation of the survey instrument, the final version was administered at six different institutions. It was administered to introductory physics students in various traditionally taugh…
We have developed and implemented a low-cost peer-mentoring program that blends personal and academic support to help students achieve academic success in the introductory courses required for the Physics Major or the Dual-Degree Program in Engineering. As a result of this program, retention has increased among entering science, technology, engineering and mathematics students at Albion College as they move through the introductory classes, as shown by a 20 per cent increase in retention from first-semester to third-semester physics courses compared to years when this program was not in place.
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…
Increasing student retention (successfully finishing a particular course) and persistence (continuing through a sequence of courses or the major area of study) is currently a major challenge for universities. While students' academic and social integration into an institution seems to be vital for student retention, research into the effect of interpersonal interactions is rare. We use network analysis as an approach to investigate academic and social experiences of students in the classroom. In particular, centrality measures identify patterns of interaction that contribute to integration int…
We present a model for competency-based grading for calculus-based introductory physics that encourages students to obtain proficiency with all course content. By allowing students to continually improve their proficiency with skills and content throughout the semester, this formative grading system is designed to create a more flexible learning environment that better accommodates the varying schedules and needs of students. While all students show improvement in their performance following the implementation of this grading system, the largest gains were found for women and first generation …
In this companion paper, we explore the use of isomorphic problem pairs (IPPs) to assess introductory physics students' ability to solve and successfully transfer problem-solving knowledge from one context to another in mechanics. We call the paired problems "isomorphic" because they require the same physics principle to solve them. We analyze written responses and individual discussions to a range of isomorphic problems. We examine potential factors that may help or hinder transfer of problem-solving skills from one problem in a pair to the other. For some paired isomorphic problems, one cont…
We have investigated the long-term effect of student-centered instruction at the freshman level on juniors' performance on a conceptual survey of Electricity and Magnetism (E&M). We measured student performance on a research-based conceptual instrument -- the Brief Electricity & Magnetism Assessment (BEMA) -- over a period of 8 semesters (2004-2007). Concurrently, we introduced the University of Washington's Tutorials in Introductory Physics as part of our standard freshman curriculum. Freshmen took the BEMA before and after this Tutorial-based introductory course, and juniors took it after co…
Several prior studies in introductory physics have found a gender gap on conceptual assessments such as the Force Concept Inventory (FCI) and the Conceptual Survey of Electricity and Magnetism (CSEM) with male students performing better than female students. Moreover, prior studies in the context of mathematics have also found that activation of a negative stereotype about a group can lead to deteriorated performance of the stereotyped group. Here, we describe two studies in which we investigated the impact of interventions on the gender gap on the FCI and CSEM in large introductory physics co…
Recently there have been multiple calls for curricular reforms to develop new pathways to the science, technology, engineering and math (STEM) disciplines. The Marble Game answers these calls by providing a conceptual framework for quantitative scientific modeling skills useful across all the STEM disciplines. The approach actively engages students in a process of directed scientific discovery. In a "Student Assessment of their Learning Gains" (SALG) survey, students identified this approach as producing "great gains" in their understanding of real world problems and scientific research. Using…
Increasing student retention and persistence -- in particular classes or in their major area of study -- is a challenge for universities. Students' academic and social integration into an institution seems to be vital for student retention, yet, research on the effect of interpersonal interactions is rare. Social network analysis is an approach that can be used to identify patterns of interaction that contribute to integration into the university. We analyze how students position within a social network in a Modeling Instruction (MI) course that strongly emphasizes interactive learning impacts…
Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied meanings. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. The mathematics education research literature documents the cognitive challenge of conceptualizing negative numbers as mathematical objects--both for experts, histor…
We examine the difficulties that introductory physics students, undergraduate physics majors, and physics graduate students have with concepts related to conductors and insulators covered in introductory physics by giving written tests and interviewing a subset of students. We find that even graduate students have serious difficulties with these concepts. We develop tutorials related to these topics and evaluate their effectiveness by comparing the performance on written pre-/post-tests and interviews of students who received traditional instruction vs. those who learned using tutorials.
Mathematical reasoning flexibility across physics contexts is a desirable learning outcome of introductory physics, where the math world and physical world meet. Physics Quantitative Literacy (PQL) is a set of interconnected skills and habits of mind that support quantitative reasoning about the physical world. The Physics Inventory of Quantitative Literacy (PIQL), which we are currently refining and validating, assesses students proportional reasoning, covariational reasoning, and reasoning with signed quantities in physics contexts. In this paper, we apply a Conceptual Blending Theory analys…
Physics education researchers have developed many evidence-based instructional strategies to enhance physics students' conceptual learning. These strategies have historically been tested using assessments such as the Force Concept Inventory (FCI) and Force and Motion Conceptual Evaluation (FMCE). We have performed a review and analysis of FCI and FMCE data published between 1995 and 2014. We confirm previous findings that interactive engagement teaching techniques are significantly more likely to produce high student learning gains than traditional lecture-based instruction. We also establish …
Single particle models are sufficient for many topics in introductory physics courses, but become misleading when applied to situations involving changes in internal energy. This paper merges two parallel attempts to reform the teaching of energy in the introductory physics curriculum, resulting in an approach to internal energy that is conceptually correct, mathematically rigorous, and yet simple enough for the introductory student to understand. It uses diagrams and graphs to provide concrete and visual means to track energy storage and transfer, and takes the smallest possible step in mathe…
Designing a one-hour unit test for an introductory physics class can be quite challenging. We present an efficient format of a one-hour unit test that utilizes question groups for quantitative free-response problems and a binary system (True or False) for conceptual questions. This format promotes coherence and allows the instructor to test a wide variety of topics in a one-hour exam. For the 4 semesters in which the design has been implemented, average unit test scores have increased from 76% using traditional test format, to 79% using the efficient design.
As part of a larger research project into massively open online courses (MOOCs), we have investigated student background, as well as student participation in a physics MOOC with a laboratory component. Students completed a demographic survey and the Force and Motion Conceptual Evaluation at the beginning of the course. While the course is still actively running, we have tracked student participation over the first five weeks of the eleven-week course.
Many prior studies have found a gender gap between male and female students' performance on conceptual assessments such as the Force Concept Inventory (FCI) and the Conceptual Survey of Electricity and Magnetism (CSEM) with male students performing better than female students. Prior studies have also found that activation of a negative stereotype about a group or stereotype threat, e.g., asking test-takers to indicate their ethnicity before taking a test, can lead to deteriorated performance of the stereotyped group. Here, we describe two studies in which we investigated the gender gap on the …
While it is well known which curricular practices can improve student performance on measures of conceptual understanding, the sustaining of these practices and the role of faculty members in implementing these practices are less well understood. We present a study of the hand-off of Tutorials in Introductory Physics from initial adopters to other instructors at the University of Colorado, including traditional faculty not involved in physics education research. The study examines the impact of implementation of Tutorials on student conceptual learning across eight first-semester, and seven se…
Newton's third law is one of the most important concepts learned early in introductory mechanics courses; however, ample studies have documented a wide range of students' misconceptions and fragmented understandings of this concept that are difficult to change through traditional instruction. This research develops a conceptual framework model to investigate students' understanding of Newton's third law through the knowledge integration perspective. The conceptual framework is established with a central idea emphasizing forces as the outcomes of an interaction instead of using the common actio…
We argue here for a more conceptual or qualitative approach in the introductory teaching of Quantum Physics which is built on the basis of epistemological and ontological discussions and as such is a valuable tool mainly in the initial and continued formation of school teachers. We illustrate our point with the analysis of undulatory and corpuscular phenomena of a single photon in a virtual Mach-Zehnder Interferometer - an experimental setup similar to double slits device but simpler - using key ideas of the most known interpretations of quantum formalism, including the many worlds interpretat…
We report on research carried out to improve teaching and student engagement in the introductory astronomy course at the University of Cape Town. This course is taken by a diverse range of students, including many from educationally disadvantaged backgrounds. We describe the development of an instrument, the Introductory Astronomy Questionnaire (IAQ), which we administered as pre- and post-tests to students enrolled in the course. The instrument comprised a small number of questions which probed three areas of interest: student motivation and expectations, astronomy content, and worldview. Amo…
The ability to categorize problems based upon underlying principles, rather than surface features or contexts, is considered one of several proxy predictors of expertise in problem solving. With inspiration from the classic study by Chi, Feltovich, and Glaser, we assess the distribution of expertise among introductory physics students by asking three introductory physics classes, each with more than a hundred students, to categorize mechanics problems based upon similarity of solution. We compare their categorization with those of physics graduate students and faculty members. To evaluate the …
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…
Mechanics Cognitive Diagnostic: Testing Fine-Grained Learning Objectives in Introductory Physics
School of Education, Iowa State University（爱荷华州立大学教育学院）；Department of Physics, Montana State University（蒙大拿州立大学物理系）；School of Engineering Education, Purdue University（普渡大学工程学院）；College of Education, Purdue University（普渡大学教育学院）
This article quantitatively examines the effects that different incentives have on students' homework completion rates in introductory physics courses at the United States Air Force Academy. Our data suggest that no more than 10-15% of the total course points need to be allocated to homework to maximize completion of homework through a grade incentive. In addition, we find that there is a strong relationship between students' perception of the benefits of homework and homework completion rates. Students completed nearly 20% more homework when their average perception of homework increased by 0…
The research presented in this thesis was motivated by the need to improve introductory physics courses. Introductory physics courses are generally the first courses in which students learn to create models to solve complex problems. However, many students taking introductory physics courses fail to acquire a command of the concepts, methods and tools presented in these courses. The reforms proposed by this thesis focus on altering the content of introductory courses rather than content delivery methods as most reforms do. This thesis explores how the performance on a widely used test of conce…
We investigate student understanding of energy and momentum concepts at the level of introductory physics by designing and administering a 25-item multiple choice test and conducting individual interviews. We find that most students have difficulty in qualitatively interpreting basic principles related to energy and momentum and in applying them in physical situations. The test development process and a summary of results are presented.
The Lecture-Tutorials for Introductory Astronomy have been designed to help introductory astronomy instructors actively engage their students in developing their conceptual understandings and reasoning abilities across a wide range of astrophysical topics. The development of the Lecture-Tutorials has been informed by nearly two-decades of research into common learning difficulties students experience when studying astronomy. The results from multiple studies provide evidence that Lecture-Tutorials can help students achieve learning gains well beyond what is typically achieved by lecture alone.…
Studies examining gender differences in introductory physics show a consensus when it comes to a gender gap on conceptual assessments; however, the story is not as clear when it comes to differences in gendered performance on exams. This study examined whether gendered differences exist on midterm and final exams in introductory physics courses and if such differences were correlated with a gender difference in final course grades. The population for this study included more than 10,000 students enrolled in algebra- and calculus-based introductory physics courses between spring 2007 and spring…
This is the third series of the lab manuals for virtual teaching of introductory physics classes. This covers fluids, waves, thermodynamics, optics, interference, photoelectric effect, atomic spectra, and radiation concepts. A few of these labs can be used within Physics I and a few other labs within Physics II depending on the syllabi of Physics I and II classes. Virtual experiments in this lab manual and our previous Physics I (arXiv.2012.09151) and Physics II (arXiv.2012.13278) lab manuals were designed for 2.45 hrs long lab classes (algebra-based and calculus-based). However, all the virtu…
We analyze the effectiveness of working in pairs on the Conceptual Survey of Electricity and Magnetism test in a calculus-based introductory physics course. Students who collaborated with a peer showed significantly larger normalized gain on individual testing than those who did not collaborate. We did not find statistically significant differences between the performance of students who were given an opportunity to formulate their own response before the peer discussions, compared to those who were not. Peer collaboration also shows evidence for co-construction of knowledge. Discussions with …
We discuss the development of a research-based conceptual multiple-choice survey related to magnetism. We also discuss the use of the survey to investigate gender differences in students' difficulties with concepts related to magnetism. We find that while there was no gender difference on the pre-test, female students performed significantly worse than male students when the survey was given as a post-test in traditionally taught calculus-based introductory physics courses (similar results in both the regular and honors versions of the course). In the algebra-based courses, the performance of …
Incorporating computer programming exercises into introductory physics is a delicate task that involves a number of choices that may have an effect on student learning. We present a "hybrid" approach that speaks to a number of common concerns regarding cognitive load which arise when using programming exercises in introductory physics classes where many students are absolute beginner programmers. This "hybrid" approach provides the student with a highly interactive web-based visualization, not unlike a PhET or Physlet interactive, but importantly the student is shown only the subset of the cod…
We occasionally include projects in our learner-centered introductory astronomy college course to enable non-science major students explore some astronomical concepts in more detail than otherwise. Such projects also highlight ongoing or upcoming astronomical events. We hope that students will feel more interested in astronomy through projects tied to astronomical events. In Spring 2012, we offered short essays focused on eclipses, transits and occultations to promote the rare transit of Venus that occurred on June 5th, 2012. We asked students to write two short essays from three that were off…
Incorporating computer programming exercises in introductory physics is a delicate task that involves a number of choices that may have a strong affect on student learning. We present an approach that speaks to a number of common concerns that arise when using programming exercises in introductory physics classes where most students are absolute beginner programmers. These students need an approach that is (1) simple, involving 75 or fewer lines of well-commented code, (2) easy to use, with browser-based coding tools, (3) interactive, with a high frame rate to give a video-game like feel, (4) …
The use of validated conceptual assessments alongside more standard course exams has become standard practice for the introductory courses in many physics departments. These assessments provide a more standard measure of certain learning goals, allowing for comparisons of student learning across instructors, semesters, and institutions. Researchers at the University of Colorado Boulder have developed several similar assessments designed to target the more advanced physics content of upper-division classical mechanics, electrostatics, quantum mechanics, and electrodynamics. Here, we synthesize …
Massive Open Online Courses are an exciting new avenue for instruction and research, yet they are full of unknowns. In the Spring of 2013, MITx released its first introductory physics MOOC through the edX platform, generating a total enrollment of 43,000 students from around the world. We describe the population of participants in terms of their age, gender, level of education, and country of origin, highlighting both the diversity of 8.02x enrollees as well as gender gap and retention. Using three midterm exams and the final as waypoints, we highlight performance by different demographic subp…
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…
Research experience and mentoring has been identified as an effective intervention for increasing student engagement and retention in the STEM fields, with high impact on students from undeserved populations. However, one-on-one mentoring is limited by the number of available faculty, and in certain cases also by the availability of funding for stipend. One-on-one mentoring is further limited by the selection and self-selection of students. Since research positions are often competitive, they are often taken by the best-performing students. More importantly, many students who do not see themse…
As part of a large-scale assessment project at a large university, we administered weekly pre-tests and bi-weekly post-tests in the recitation sections of our introductory classes over four semesters from Spring 2010 through Fall 2011. The post-tests were administered as graded quizzes and were developed to assess problem solving, laboratory, calculational and conceptual skills that had been the focus of instruction in lab, lecture and recitation sessions. They were not comprehensive, but gave us 'snapshots' of students' abilities throughout the semester. They were used in conjunction with oth…
