Saul, PhD Dissertation (1998)

Beyond problem solving: Evaluating introductory physics courses through the hidden curriculum

J. M. Saul, Ph.D. Dissertation, E. F. Redish (advisor), (1998). (html TOC and abstract)

pdfs: Intro, Ch 1, Ch 2, Ch 3, Ch 4, Ch 5, Ch 6, Ch 7, Ch 8, Ch 9, Ch 10, Ch 11

Abstract: A large number of innovative approaches have been developed based on Physics Education Research (PER) to address student difficulties introductory physics instruction. Yet, there are currently few widely accepted assessment methods for determining the effectiveness of these methods. This dissertation compares the effectiveness of traditional calculus-based instruction with University of Washington's Tutorials, University of Minnesota's Group Problem Solving & Problem Solving Labs, and Dickinson College's Workshop Physics. Implementation of these curricula were studied at ten undergraduate institutions. The research methods used include the Force Concept Inventory (FCI), the Maryland Physics Expectation (MPEX) survey, specially designed exam problems, and interviews with student volunteers. The MPEX survey is a new diagnostic instrument developed specifically for this study.

Instructors often have learning goals for their students that go beyond having them demonstrate mastery of physics through typical end-of-chapter problems on exams and homeworks. Because these goals are often not stated explicitly nor adequatelyreinforced through grading and testing, we refer to this kind of learning goal as part of the course's ìhidden curriculum.î In this study, we evaluate two aspects of student learning from this hidden curriculum in the introductory physics sequence: conceptual understanding and expectations (cognitive beliefs that affect how students think about and learn physics).

We find two main results. First, the exam problems and the pre/post FCI results on students conceptual understanding showed that the three research-based curricula were more effective than traditional instruction for helping students learn velocity graphs, Newtonian concepts of force and motion, harmonic oscillator motion, and interference. Second, although the distribution of students' expectations vary for different student populations, the overall distributions differ considerably from what expert physics instructors would like them to have and differ even more by the end of the first year. Only students from two of the research-based sequences showed any improvement in their expectations.

Wittmann, PhD Dissertation (1998)

Making sense of how students come to an understanding of physics: An example from mechanical waves

M. C. Wittmann, Ph.D. Dissertation, E. F. Redish (advisor), (1998). (html TOC and abstract)

pdfs: Intro, Ch 1, Ch 2, Ch 3, Ch 4, Ch 5, Ch 6, Ch 7, Ch 8

Abstract: While physics education research (PER) has traditionally focused on introductory physics, little work has been done to organize and develop a model of how students come to make sense of the material they learn. By understanding how students build their knowledge of a specific topic, we can develop effective instructional materials. In this dissertation, I describe an investigation of student understanding of mechanical and sound waves, how we organize our findings, and how our results lead to the development of curriculum materials used in the classroom.

The physics of mechanical and sound waves at the introductory level (using small-amplitude approximation in the dispersionless system) involves fundamental concepts that are difficult for many students. These include: distinguishing between medium properties and boundary conditions, recognizing local phenomena (e.g. superposition) in extended systems, using mathematical functions of two variables, and interpreting and applying the mathematics of waves in a variety of settings. Student understanding of these topics is described in the context of wave propagation, superposition, use of mathematics, and other topics. Investigations were carried out using the common tools of PER, including free response, multiple choice, multiple-response, and semi-guided individual interview questions.

Student reasoning is described in terms of primitives generally used to simplify reasoning about complicated topics. I introduce a previously undocumented primitive, the object as point primitive. We organize student descriptions of wave physics around the the idea of patterns of associations that use common primitive elements of reasoning. We can describe students as if they make an analogy toward Newtonian particle physics. The analogy guides students toward describing a wave as if it were a point particle described by certain unique parts of the wave. A diagnostic test has been developed to probe the dynamics of student reasoning during the course of instruction.

We have replaced traditional recitation instruction with curriculum materials designed to help students come to a more complete and appropriate understanding of wave physics. We find that the research-based instructional materials are more effective than the traditional lecture setting in helping students apply appropriate reasoning elements to the physics of waves.

Bao, PhD Dissertation (1999)

Using the Context of Physics Problem Solving to Evaluate the Coherence of Student Knowledge

L. Bao, Ph.D. Dissertation, E. F. Redish (advisor), (1999). (html TOC and abstract)

pdfs: Ch 1, Ch 2, Ch 3, Ch 4, Ch 5, Ch 6, Ch 7, Ch 8, Ch 9

Abstract: A good understanding of how students understand physics is of great importance for developing and delivering effective instructions. This research is an attempt to develop a coherent theoretical and mathematical framework to model the student learning of physics. The theoretical foundation is based on useful ideas from theories in cognitive science, education, and physics education. The emphasis of this research is made on the development of a mathematical representation to model the important mental elements and the dynamics of these elements, and on numerical algorithms that allow quantitative evaluations of conceptual learning in physics.

In part I, a model-based theoretical framework is proposed. Based on the theory, a mathematical representation and a set of data analysis algorithms are developed. This new method is called Model Analysis, which can be used to obtain quantitative evaluations on student models with data from multiple-choice questions. Two specific algorithms are discussed in great detail. The first algorithm is the concentration factor. It measures how student responses on multiple-choice questions are distributed. A significant concentration on certain choices of the questions often implies the existence of common student models that are associated to those choices. The second algorithm is model evaluation which analyzes student responses to form student model vectors and student model density matrix. By studying the density matrix, we can obtain quantitative evaluations of specific models used by students. Application examples with data from FCI, FMCE, and Wave Test are discussed. A number of additional algorithms are introduced to deal with unique aspects of different tests and to make quantitative assessment of various features of the tests. Implications on test design techniques are also discussed with the results from the examples.

Based n the theory and algorithms developed in part I, research is conducted to investigate student understandings of quantum mechanics. Common student models on classical prerequisites and important quantum concepts are identified. For exampled, many students interpret the quantum wavefunction as the representation of the energy of a particle. Based on the research results, multiple-choice instruments are developed to probe student models analysis algorithms. A set of quantum tutorials are also developed and implemented instruction. Results from exams and student interviews indicate that the quantum tutorials are effective.

Sabella, PhD Dissertation (1999)

Using the context of physics problem solving to evaluate the coherence of student knowledge

M. S. Sabella, Ph.D. Dissertation, E. F. Redish (advisor), (1999). (html TOC and abstract)

pdfs: Intro, Ch 1, Ch 2, Ch 3, Ch 4, Ch 5, Ch 6, Ch 7, Ch 8, Ch 9

Abstract: We use the context of problem solving to show that students exhibit a local coherence but not global coherence in their physics knowledge. When presented with a problem-solving task, students often activate a coherent set of knowledge called a schema to solve the problem. This schema of strongly related knowledge and procedures. Although the schemas students develop in the physics course are usually sufficient in the class, they are often insufficient for solving complex problems. Complex problems require that students have a deep understanding where they have integrated their qualitative knowledge with their quantitative knowledge and have integrated related physics topics. We show that our students activate schemas consisting of small amounts of knowledge and these schemas are often isolated from other schemas.

Physics Education Research (PER) has shown that students in introductory physics lack a deep understanding of physics principles and concepts. Through research-based curricula, conceptual understanding can be improved. In addition PER has shown that these students can be taught problem solving skills through a modified curriculum. Despite these improvements, students still have difficulty developing a coherent knowledge of physics. In particular, students often have difficulty connecting related physics concepts. In addition, they view quantitative problems and qualitative questions as distinct types of tasks, possessing different types of knowledge and different sets of rules for responding.

We discuss some possible methods that physics instructors and physics education researchers can use to examine coherence in student knowledge. Using these methods, we provide evidence for the local coherence in student physics knowledge by identifying distinct schemas for qualitative and quantitative knowledge. After identifying some of these difficulties in student understanding, we look at how students are connecting their qualitative knowledge to quantitative knowledge after going through concept-based curriculum. The research benefits as well as shortcomings in the concept-based curriculum and talk about possible modifications that may foster coherence. In addition, we compare performance on quantitative questions between a physics class using the traditional problem-solving recitation and a class using Tutorials in Introductory Physics on quantitative problems.

Lippmann, PhD Dissertation (2003)

Students' understanding of measurement and uncertainty in the physics laboratory: Social construction, underlying concepts, and quantitative analysis

R. F. Lippmann, Ph.D. Dissertation, E. F. Redish (advisor), (2003). (html TOC and abstract)(appendices)

Abstract: In the physical sciences and other fields, conclusions are made from experimental data. To succeed in such fields, people must know how to gather, analyze, and draw conclusions from data: not just following steps, but understanding the concepts of measurement and uncertainty. We design the Scientific Community Laboratory (SCL) to teach students to utilize their everyday skills of argument and decision-making for data gathering and analysis. We then develop research tools for studying students’ understanding of measurement and uncertainty and use these tools to investigate students in the traditional laboratory and in the SCL.

For students to apply their everyday skills of argument and decision-making, they must be in a state of mind (a frame) where they consider these skills productive. The laboratory design should create an environment which encourages such a frame. We determine student’s frames through information reported by students in interviews and surveys and through analyzing students’ behavior. We find that the time students spend sense-making in the SCL is five times more than in traditional labs. Students in both labs frequently evaluate their level of understanding but only in the SCL does that evaluation cause a change to more productive behavior.

We analyze lab videotapes to determine underlying concepts commonly used by students when gathering and analyzing data. Our final goal is for students to use these concepts to analyze data in an appropriate manner. We develop a multiple-choice survey which asks students to analyze data from a hypothetical lab context. With this survey we find more students using range to compare data sets after the SCL (from 12% before to 43% after).

For students to understand measurement and uncertainty, we argue that the laboratory must be designed to encourage students to be in a frame where they view resources used to argue and evaluate as appropriate, engage in productive behavior and monitor their behavior, use productive resources to build an understanding of the underlying concepts, and use those concepts to analyze data. We make use of interviews, surveys, and video data to study each of these requirements and to evaluate the SCL curriculum.

Tuminaro, PhD Dissertation (2004)

A cognitive framework for analyzing and describing introductory students' use and understanding of mathematics in physics

J. Tuminaro, Ph.D. Dissertation, E. F. Redish (advisor), (2004). (html TOC and abstract)

Abstract: Many introductory, algebra-based physics students perform poorly on mathematical problem solving tasks in physics. There are at least two possible, distinct reasons for this poor performance: (1) students simply lack the mathematical skills needed to solve problems in physics, or (2) students do not know how to apply the mathematical skills they have to particular problem situations in physics. While many students do lack the requisite mathematical skills, a major finding from this work is that the majority of students possess the requisite mathematical skills, yet fail to use or interpret them in the context of physics.

In this thesis I propose a theoretical framework to analyze and describe studentsí mathematical thinking in physics. In particular, I attempt to answer two questions. What are the cognitive tools involved in formal mathematical thinking in physics? And, why do students make the kinds of mistakes they do when using mathematics in physics? According to the proposed theoretical framework there are three major theoretical constructs: mathematical resources, which are the knowledge elements that are activated in mathematical thinking and problem solving; epistemic games, which are patterns of activities that use particular kinds of knowledge to create new knowledge or solve a problem; and frames, which are structures of expectations that determine how individuals interpret situations or events.

The empirical basis for this study comes from videotaped sessions of college students solving homework problems. The students are enrolled in an algebra-based introductory physics course. The videotapes were transcribed and analyzed using the aforementioned theoretical framework.

Two important results from this work are: (1) the construction of a theoretical framework that offers researchers a vocabulary (ontological classification of cognitive structures) and grammar (relationship between the cognitive structures) for understanding the nature and origin of mathematical use in the context physics, and (2) a detailed understanding, in terms of the proposed theoretical framework, of the errors that students make when using mathematics in the context of physics.

Atkins, PhD Dissertation (2004)

Analogies as categorization phenomena: Studies from scientific discourse

L. J. Atkins, Ph.D. Dissertation, D. Hammer (advisor), (2004). (html TOC and abstract) (pdf links: Chapter 1, Chapter 2, Chapter 3, Chapter 4, Chapter 5, Chapter 6, Chapter 7, Chapter 8)

Abstract: Studies on the role of analogies in science classrooms have tended to focus on analogies that come from the teacher or curriculum, and not the analogies that students generate. Such studies are derivative of an educational system that values content knowledge over scientific creativity, and derivative of a model of teaching in which the teacher's role is to convey content knowledge. This dissertation begins with the contention that science classrooms should encourage scientific thinking and one role of the teacher is to model that behavior and identify and encourage it in her students. One element of scientific thinking is analogy. This dissertation focuses on student-generated analogies in science, and offers a model for understanding these. I provide evidence that generated analogies are assertions of categorization, and the base of an analogy is the constructed prototype of an ad hoc category. Drawing from research on categorization, I argue that generated analogies are based in schemas and cognitive models. This model allows for a clear distinction between analogy and literal similarity; prior to this research analogy has been considered to exist on a spectrum of similarity, differing from literal similarity to the degree that structural relations hold but features do not. I argue for a definition in which generated analogies are an assertion of an unexpected categorization: that is, they are asserted as contradictions to an expected schema.

Gresser, PhD Dissertation (2006)

A Study of Social Interaction and Teamwork in Reformed Physics Laboratories

P. Gresser, Ph.D. Dissertation, E. F. Redish (advisor), (2006). (html TOC and abstract)

Abstract: It is widely accepted that, for many students, learning can be accomplished most effectively through social interaction with peers, and there have been many successes in using the group environment to improve learning in a variety of classroom settings. What is not well understood, however, are the dynamics of student groups, specifically how the students collectively apprehend the subject matter and share the mental workload.

This research examines recent developments of theoretical tools for describing the cognitive states of individual students: associational patterns such as epistemic games and cultural structures such as epistemological framing. Observing small group interaction in authentic classroom situations (labs, tutorials, problem solving) suggests that these tools could be effective in describing these interactions.

Though conventional wisdom tells us that groups may succeed where individuals fail, there are many reasons why group work may also run into difficulties, such as a lack or imbalance of knowledge, an inappropriate mix of learning styles, or a destructive power arrangement. This research explores whether or not inconsistent epistemological framing among group members can also be a cause of group failure. Case studies of group interaction in the laboratory reveal evidence of successful groups employing common framing, and unsuccessful groups failing from lack of a shared frame.

This study was conducted in a large introductory algebra-based physics course at the University of Maryland, College Park, in a laboratory designed specifically to foster increased student interaction and cooperation. Videotape studies of this environment reveal that productive lab groups coordinate their efforts through a number of locally coherent knowledge-building activities, which are described through the framework of epistemic games. The existence of these epistemic games makes it possible for many students to participate in cognitive activities without a complete shared understanding of the specific activity's goal. Also examined is the role that social interaction plays in initiating, negotiating, and carrying out these epistemic games. This behavior is illustrated through the model of distributed cognition.
An attempt is made to analyze this group activity using Tuckman's stage model, which is a prominent description of group development within educational psychology. However, the shortcomings of this model in dealing with specific cognitive tasks lead us to seek another explanation. The model used in this research seeks to expand existing cognitive tools into the realm of social interaction. In doing so, we can see that successful groups approach tasks in the lab by negotiating a shared frame of understanding. Using the findings from these case studies, recommendations are made concerning the teaching of introductory physics laboratory courses.

Russ, PhD Dissertation (2006)

A Framework for Recognizing Mechanistic Reasoning in Student Scientific Inquiry

R. S. Ross, Ph.D. Dissertation, D. Hammer (advisor), (2006). (html TOC and abstract)

Abstract:  A central ambition of science education reform is to help students develop abilities for scientific inquiry. Education research is thus rightly focused on defining what constitutes "inquiry" and developing tools for assessing it. There has been progress with respect to particular aspects of inquiry, namely student abilities for controlled experimentation and scientific argumentation. However, we suggest that in addition to these frameworks for assessing the structure of inquiry we need frameworks for analyzing the substance of that inquiry.

In this work we draw attention to and evaluate the substance of student mechanistic reasoning. Both within the history and philosophy of science and within science education research, scientific inquiry is characterized in part as understanding the causal mechanisms that underlie natural phenomena. The challenge for science education, however, is that there has not been the same progress with respect to making explicit what constitutes mechanistic reasoning as there has been in making explicit other aspects of inquiry.

This dissertation attempts to address this challenge. We adapt an account of mechanism in professional research science to develop a framework for reliably recognizing mechanistic reasoning in student discourse. The coding scheme articulates seven specific aspects of mechanistic reasoning and can be used to systematically analyze narrative data for patterns in student thinking. It provides a tool for detecting quality reasoning that may be overlooked by more traditional assessments.

We apply the mechanism coding scheme to video and written data from a range of student inquiries, from large group discussions among first grade students to the individual problem solving of graduate students. While the primary result of this work is the coding scheme itself and the finding that it provides a reliable means of analyzing transcript data for evidence of mechanistic thinking, the rich descriptions we develop in each case study help us recognize continuity between graduate level learning and elementary school science: part of what students are able to do in elementary school finds its way to graduate school. Thus this work makes it possible for researchers, curriculum developers, and teachers to systematically pursue mechanistic reasoning as an objective for inquiry.

Bing, PhD Dissertation (2008)

An Epistemic Framing Analysis of Upper-Level Physics Students' Use of Mathematics

T. J. Bing, Ph.D. Dissertation, E. F. Redish (advisor), (2008). (html TOC and abstract)

Abstract: Mathematics is central to a professional physicist's work and, by extension, to a physics student's studies. It provides a language for abstraction, definition, computation, and connection to physical reality. This power of mathematics in physics is also the source of many of the difficulties it presents students. Simply put, many different activities could all be described as "using math in physics". Expertise entails a complicated coordination of these various activities. This work examines the many different kinds of thinking that are all facets of the use of mathematics in physics. It uses an epistemological lens, one that looks at the type of explanation a student presently sees as appropriate, to analyze the mathematical thinking of upper level physics undergraduates. Sometimes a student will turn to a detailed calculation to produce or justify an answer. Other times a physical argument is explicitly connected to the mathematics at hand. Still other times quoting a definition is seen as sufficient, and so on. Local coherencies evolve in students' thought around these various types of mathematical justifications. We use the cognitive process of framing to model students' navigation of these various facets of math use in physics.

We first demonstrate several common framings observed in our students' mathematical thought and give several examples of each. Armed with this analysis tool, we then give several examples of how this framing analysis can be used to address a research question. We consider what effects, if any, a powerful symbolic calculator has on students' thinking. We also consider how to characterize growing expertise among physics students. Framing offers a lens for analysis that is a natural fit for these sample research questions. To active physics education researchers, the framing analysis presented in this dissertation can provide a useful tool for addressing other research questions. To physics teachers, we present this analysis so that it may make them more explicitly aware of the various types of reasoning, and the dynamics among them, that students employ in our physics classes. This awareness will help us better hear students' arguments and respond appropriately.