Redish, Wittmann, Bao & Steinberg, NARST Annual Meeting (1999)

The Influence of Student Understanding of Classical Physics when Learning Quantum Physics

E. F. Redish, M. C. Wittmann, L. Bao & R. N. Steinberg, Research on the Teaching and Learning of Quantum Sciences, NARST Annual Meeting, Boston, MA (1999).

Abstract: Understanding quantum mechanics is of growing importance, not just to future physicists, but to future engineers, chemists, and biologists. Fields in which understanding quantum mechanics is important include photonics, mesoscopic engineering, and medical diagnostics. It is therefore not surprising that quantum is being taught more often to more students starting as early as high school. However, quantum mechanics is difficult and abstract. Furthermore, understanding many classical concepts is prerequisite to a meaningful understanding of quantum systems.

In this paper, we describe research results of two examples of the influence of student understanding of classical concepts when learning quantum mechanics. for each example, we describe difficulties students have in the classical regime and how these difficulties seem to impair student learning of quantum concepts. We briefly discuss how these difficulties can be addressed.

Obviously the examples described in this paper are not intended to be exhaustive. Instead, we have two objectives. The first is to highlight the importance of having a strong conceptual base when learning more advanced topics in physics. The second is to illustrate the importance of continuously and systematically probing student learning by using the tools of physics education research.

Bao, Hogg & Zollman, Am J Phys (2002)

Model analysis of fine structures of student models: An Example with Newton's Third Law

L. Bao, K. Hogg & D. Zollman, American Journal of Physics, 70(7), p 766 778 (July 2002). (link to journal article)

Abstract: In problem-solving situations, the contextual features of the problems affect student reasoning. Using Newton's third law as an example, we study the role of context in students' uses of alternative conceptual models. We have identified four contextual features that are frequently used by students in their reasoning. Using these results, a multiple-choice survey was developed to probe the effects of the specific contextual features on student reasoning. Measurements with this instrument show that different contextual features can affect students' conceptual learning in different ways. We compare student data from different populations and instructions and discuss the implications.

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.

Bao & Redish, Am J Phys (2002)

Understanding probabilistic interpretations of physical systems: A prerequisite to learning quantum physics

L. Bao & E. F. Redish, Am J Phys, 70(3), p 210-217 (2002). (html version)

Abstract: Probability plays a critical role in making sense of quantum physics, but most science and engineering undergraduates have very little experience with the topic. A probabilistic interpretation of a physical system, even at a classical level, is often completely new to them, and the relevant fundamental concepts such as the probability distribution and probability density are rarely understood. To address these difficulties and to help students build a model of how to think about probability in physical systems, we have developed a set of hands-on tutorial activities appropriate for use in a modern physics course for engineers. We discuss some student difficulties with probability concepts and an instructional approach that uses a random picture metaphor and digital video technology.

Bao & Redish, UMD preprint (2001)

Model Analysis: Assessing the Dynamics of Student Learning

L. Bao & E. F. Redish, University of Maryland preprint (Mar 2001).

Abstract: In this paper we present a method of modeling and analysis that permits the extraction and quantitative display of detailed information about the effects of instruction on a class’s knowledge. The method relies on a cognitive model of thinking and learning that represents student thinking in terms of patterns of association in long-term memory structures that we refer to as schemas or mental models. As shown by previous research, students frequently fail to recognize relevant conditions that lead to appropriate uses of their mental models and, as a result, can use multiple models inconsistently to treat problems that appear equivalent to an expert. Once the most common mental models have been determined via qualitative research, they can be mapped onto probing instruments such as a multiple-choice test. We have developed Model Analysis to analyze the results of these instruments that treats the student as if he/she were in a mixed state – a state which, when probed with a set of scenarios under diverse contextual settings, gives the probability that the student will choose a particular mental model to analyze the scenario. We illustrate the use of our method by analyzing results from the Force Concept Inventory, a research-based multiplechoice instrument developed to probe student’s conceptual understanding of Newtonian Mechanics in a physics class. Model Analysis allows one to use qualitative research results to provide a framework for analyzing and interpreting the meaning of students’ incorrect responses on a well-designed research-based multiple-choice test. These results can then be used to guide instruction, either for an individual teacher or for developers of reform curricula.

Bao & Redish, PER Suppl to Am J Phys (2001)

Concentration Analysis: A Quantitative Assessment of Student States

L. Bao & E. F. Redish, Physics Education Research Supplement to the American Journal of Physics, 69, S45-S53 (July 2001).

Abstract: Multiple-choice tests such as the Force Concept Inventory (FCI) provide useful instruments to probe the distribution of student difficulties on a large scale. However, traditional analysis often relies solely on scores (number of students giving the correct answer). This ignores what can be significant and important information: the distribution of wrong answers given by the class. In this paper we introduce a new method, concentration analysis, to measure how students’ responses on multiple-choice questions are distributed. This information can be used to study if the students have common incorrect models or if the question is effective in detecting student models. When combined with information obtained from qualitative research, the method allows us to identify cleanly what FCI results are telling us about student knowledge.

Bao & Redish, Conf: Phys Teacher Beyond 2000 (2000)

What can you learn from a (good) multiple choice exam?

L. Bao & E. F. Redish, contributed paper, GIREP Conference: Physics Teacher Education beyond 2000, Barcelona, Spain (2000).

Abstract: The information that a teacher typically extracts from a multiple-choice exam is limited. Basically, one learns: How many students in my class can answer each question correctly? Careful studies of student thinking [1] demonstrate that student responses may reflect strongly held naïve conceptions and that students may function as if they think about a particular topic using contradictory models (typically their naïve model and the scientific one taught in class). We have developed tools for extracting information about the state of knowledge of a class from multiple-choice exams that goes beyond how many students answered each question correctly. First, a mathematical function, the concentration factor, allows one to determine whether a particular question triggers students’ naïve models. Second, by treating the students as if they can exist in “mixed states” of knowledge, we create methods of extracting measures of the state of confusion of the class. By this we mean how likely the students are to used mixed models. Our method assists in the construction of multiple-choice tests that respond to what is known about the difficulties students bring into classes and we provide ways of extracting more detail about what students have learned than traditional analysis tools.