Edward Redish

• PhD
• Professor Emeritus at University of Maryland, College Park

Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to effectively include math in physics in a way that reaches most students remains unsolved. In this paper, we sug...

Organismal biology (OrgBio) comprises the diversity, structures, and functions of all organisms from bacteria to humans. Arguably, OrgBio is often the most poorly taught and least conceptually rigorous section of the introductory biology sequence offered at most U.S. institutions of higher education. This article reports on the successful implement...

Even if students can make the blend, interpret physics correctly in mathematical symbology and graphs, they still need to be able to apply that knowledge in productive and coherent ways. As instructors, we can show our solutions to complex problems in class. We can give complex problems to students as homework. But our students are likely to still...

Learning to use math in physics involves combining (blending) our everyday experiences and the conceptual ideas of physics with symbolic mathematical representations. Graphs are one of the best ways to learn to build the blend. They are a mathematical representation that builds on visual recognition to create a bridge between words and equations. B...

• PPT |• High-resolution 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 (co-vary). How much a change in one variable or parameter is associated with a change in anoth...

Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complicated system with highly simplified or toy models. In introductory physics classes, we tend to use them without comment or motivation. Some students infer that physics is irrelevant to their understanding of t...

An important step in learning to use math in science is learning to see symbolic equations not just as calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and of organizing physics knowledge structures. In this paper, I propose “anchor equations” as a construct to sup...

Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification—that physical quantities can be assigned specific numbers (with a unit). A second is to develop an intuition for scal...

Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think with math. Teaching the dimensionality of measured quantities and dimensional analysis (DA) is a valuable first...

The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even the way we interpret mathematical equations. Learning to think about physics with math instead of just calculating involves a number of general scien...

At many physics departments a significant fraction of teaching is in support of engineers and scientists in other majors. These service courses are thus an automatic crucible of interdisciplinary interaction, and at times, strife. For example, the traditional algebra-based physics course is often considered by both biology faculty and students as h...

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 app...

An important step in learning to use math in science is learning to see physics equations as not just calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and of organizing physics knowledge structures. In this paper I discuss the role of basic anchor equations in intr...

Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complex system with highly simplified or toy models. In introductory physics classes, we tend to use them without comment or motivation. Some students infer that physics is irrelevant to their understanding of the r...

Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification: that physical quantities can be assigned specific numbers. A second is to develop an intuition for scale. One way to...

Making meaning with math in physics requires blending physical conceptual knowledge with mathematical symbology. Students in introductory physics classes often struggle with this, but it is an essential component of learning how to think with math. Teaching dimensional analysis (DA). figuring out what measurements were combined to create a symbolic...

Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification — that physical quantities can be assigned specific numbers. A second is to develop an intuition for scale. One way t...

The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even to the way we interpret mathematical equations. Learning to think about physics with math instead of just calculating involves a number of general sc...

Course syllabi are a required component of college and university courses. Syllabi present both broader course structuring practices, are a valuable “first impression” of what instructors want to offer their students, and are used as tools in course design. While best teaching practices suggest specific recommendations for syllabi development, ther...

Students in one discipline often receive their scientific training from faculty in other disciplines. As a result of tacit disciplinary differences, especially as implemented in courses at the introductory college level, such students can have difficulty in understanding the nature of the knowledge they are learning in a discipline that they do not...

Equations are about more than computing physical quantities or constructing formal models; they are also about understanding. The conceptual systems physicists use to think about nature are made from many different resources, formal and not, working together and inextricably linked. By blending mathematical forms and physical intuition, physicists...

Equations are about more than computing physical quantities or constructing formal models; they are also about understanding. The conceptual systems physicists use to think about nature are made from many different resources, formal and not, working together and inextricably linked. By blending mathematical forms and physical intuition, physicists...

A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of the maths we draw on grows as our students progress through a physics curriculum. Despite much research on th...

A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of the maths we draw on grows as our students progress through a physics curriculum. Despite much research on th...

Energy is an abstract science concept, so the ways that we think and talk about energy rely heavily on ontological metaphors: metaphors for what kind of thing energy is. Two commonly used ontological metaphors for energy are energy as a substance and energy as a vertical location. Our previous work has demonstrated that students and experts can pro...

As interdisciplinary courses are developed, instructors and researchers have to grapple with questions of how students should make connections across disciplines. We explore the issue of interdisciplinary reconciliation (IDR): how students reconcile seemingly contradictory ideas from different disciplines. While IDR has elements in common with othe...

In our Introductory Physics for Life Scientists (IPLS) course at the University of Maryland, we are building interdisciplinary bridges that help students better understand thermodynamics. One aspect of this endeavor involves having students grapple with the physical processes underlying heuristic rules that they bring to our course from their biolo...

Teaching about energy in interdisciplinary settings that emphasize coherence among physics, chemistry, and biology leads to a more central role for chemical bond energy. We argue that an interdisciplinary approach to chemical energy leads to modeling chemical bonds in terms of negative energy. While recent work on ontological metaphors for energy h...

A major curriculum redesign effort at the University of Maryland is infusing all levels of our undergraduate biological sciences curriculum with increased emphasis on interdisciplinary connections and quantitative approaches. The curriculum development efforts have largely been guided by recommendations in the National Research Council's Bio 2010 r...

In an Introductory Physics for Life Science (IPLS) course that leverages authentic biological examples, student ideas about entropy as "disorder" or "chaos" come into contact with their ideas about the spontaneous formation of organized biological structure. It is possible to reconcile the "natural tendency to disorder" with the organized clusterin...

In response to increasing calls for the reform of the curriculum for life science majors and pre-medical students (Bio2010, Scientific Foundations for Future Physicians, Vision & Change), an interdisciplinary team has created NEXUS/Physics: a reinvention of an introductory physics curriculum for the life sciences. The curriculum interacts strongly...

Physics Education Research (PER) applies a scientific approach to the question, "How do our students think about and learn physics?" PER allows us to explore such intellectually engaging questions as, "What does it mean to understand something in physics?" and, "What skills and competencies do we want our students to learn from our physics classes?...

Energy is a complex idea that cuts across scientific disciplines. For life science students, an approach to energy that incorporates chemical bonds and chemical reactions is better equipped to meet the needs of life sciences students than a traditional introductory physics approach that focuses primarily on mechanical energy. We present a curricula...

Much recent work in physics education research has focused on ontological metaphors for energy, particularly the substance ontology and its pedagogical affordances. The concept of negative energy problematizes the substance ontology for energy, but in many instructional settings, the specific difficulties around negative energy are outweighed by th...

An introductory physics course that meets the needs of biology students must recognize that the two disciplines see the world differently.

A common feature of the recent calls for reform of the undergraduate biology curriculum has been for better coordination between biology and the courses from the allied disciplines of mathematics, chemistry, and physics. Physics has lagged behind math and chemistry in creating new, biologically oriented curricula, although much activity is now taki...

Teaching physics to biologists requires far more than making the course for engineers mathematically less rigorous and adding in a few superficial biological problems. What is needed is for physicists to work closely with biologists to learn not only what physics topics and habits of mind that are useful to biologists, but how biologists work is fu...

Research biologists and medical schools are calling for universities to revise and upgrade the undergraduate curriculum for biology and pre-medical students. The critical issues they have identified include modernizing the course, coordinating with other disciplines, and focusing on helping students to develop scientific competencies. As part of th...

We present case-study data of undergraduates describing the relationship between scientific disciplines. Rather than viewing biology, chemistry, and physics as existing in disconnected silos, or as overlapping only in narrow regions of common interest, these students exhibit a range of nuanced views about disciplinary relationships. Some students d...

We present a qualitative analysis of a group of students working through a task designed to build connections between biology, chemistry, and physics. During the discussion, members of the group explicitly index some of the ideas being presented as coming from ``chemistry'' and from ``physics.'' While there is evidence that students seek coherence...

Students' sometimes contradictory ideas about ATP (adenosine triphosphate) and the nature of chemical bonds have been studied in the biology and chemistry education literatures, but these topics are rarely part of the introductory physics curriculum. We present qualitative data from an introductory physics course for undergraduate biology majors th...

The theme of the World Conference on Physics Education 2012 is "Context, Culture, and Representations." In this talk I present a brief outline of a theoretical framework that allows us to discuss these issues using a model based in psychology and sociology: the resources framework. The framework brings together a model of individual behavior based...

Educators and policy-makers have advocated for reform of undergraduate biology education, calling for greater integration of mathematics and physics in the biology curriculum. While these calls reflect the increasingly interdisciplinary nature of biology research, crossing disciplinary boundaries in the classroom carries epistemological challenges...

Energy concepts are fundamental across the sciences, yet these concepts can be fragmented along disciplinary boundaries, rather than integrated into a coherent whole. To teach physics effectively to biology students, we need to understand students' disciplinary perspectives. We present interview data from an undergraduate student who displays multi...

The past 10-15 years have seen numerous calls for curricular reform in undergraduate biology education, most of which focus on changes to curriculum or pedagogy. Data collected from students in a large introductory undergraduate biology course indicate that student expectations about the nature of the knowledge they were learning influence how they...

Physics students can encounter difficulties in physics problem solving as a result of failing to use knowledge that they have but do not perceive as relevant or appropriate. In previous work the authors have demonstrated that some of these difficulties may be epistemological. Students may limit the kinds of knowledge that they use. For example, the...

We appreciate Professor Slotta's responding to our critique (Slotta, this issue) and the editors' providing him and us space in the Journal of the Learning Sciences for this exchange. It is often difficult to understand subtle new ideas without seeing them defended against misinterpretations. If we have misunderstood Chi's ideas, then we believe ot...

The University of Maryland (UMD) Biology Education and Physics Education Research Groups are investigating students' views on the role of physics in introductory biology courses. This paper presents data from an introductory course that addresses the fundamental principles of organismal biology and that incorporates several topics directly related...

When we teach physics to prospective scientists and engineers we are teaching more than the "facts" of physics - more, even, than the methods and concepts of physics. We are introducing them to a complex culture - a mode of thinking and the cultural code of behavior of a community of practicing scientists. This culture has components that are often...

Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But because of the way the cognitive system builds expertise through binding, experts may have difficulty in unpacki...

Developing expertise in physics entails learning to use mathematics effectively and efficiently as applied to the context of physical situations. Doing so involves coordinating a variety of concepts and skills including mathematical processing, computation, blending ancillary information with the math, and reading out physical implications from the...

The University of Maryland Physics Education Research Group (UMd-PERG) carried out a five-year research project to rethink, observe, and reform introductory algebra-based (college) physics. This class is one of the Maryland Physics Department's large service courses, serving primarily life-science majors. After consultation with biologists, we re-f...

Mathematics can serve many functions in physics. It can provide a computational system, reflect a physical idea, conveniently encode a rule, and so forth. A physics student thus has many different options for using mathematics in his physics problem solving. We present a short example from the problem solving work of upper level physics students an...

The Legendre transform is an important tool in theoretical physics, playing a critical role in classical mechanics, statistical mechanics, and thermodynamics. Yet, in typical undergraduate or graduate courses, the power of motivation and elegance of the method are often missing, unlike the treatments frequently enjoyed by Fourier transforms. We rev...

Current concerns over reforming engineering education have focused attention on helping students develop skills and an adaptive expertise. Phenomenological guidelines for instruction along these lines can be understood as arising out of an emerging theory of thinking and learning built on results in the neural, cognitive, and behavioral sciences. W...

We investigate the dynamics of how graduate students coordinate their mathematics and physics knowledge within the context of solving a homework problem for a plasma physics survey course. Students were asked to obtain the complex dielectric function for a plasma with a specified distribution function and find the roots of that expression. While al...

In a series of well-known papers, Chi and Slotta (Chi, 1992; Chi & Slotta, 1993; Chi, Slotta & de Leeuw, 1994; Slotta, Chi & Joram, 1995; Chi, 2005; Slotta & Chi, 2006) have contended that a reason for students' difficulties in learning physics is that they think about concepts as things rather than as processes, and that there is a significant bar...

In a series of well-known papers, Chi and Slotta (Chi & Slotta, 1993; Chi, Slotta & de Leeuw, 1994; Chi, 2005; Slotta & Chi, 2006) have suggested that one reason for students' difficulties in learning physics is that they think about concepts in terms of 'things' rather than 'processes', and that there is a significant barrier between these two 'on...

Symbolic calculators like Mathematica are becoming more commonplace among upper level physics students. The presence of such a powerful calculator can couple strongly to the type of mathematical reasoning students employ. It does not merely offer a convenient way to perform the computations students would have otherwise wanted to do by hand. This p...

Conceptual Knowledge is only one aspect of a good knowledge structure: how and when knowledge is activated and used are also important. We explore knowledge organization in the context of the resources model of student thinking via observations of student problem-solving behavior on a mechanics task that integrates the concepts of force, motion, an...

Although much is known about the differences between expert and novice problem solvers, knowledge of those differences typically does not provide enough detail to help instructors understand why some students seem to learn physics while solving problems and others do not. A critical issue is how students access the knowledge they have in the contex...

Numbers, variables, and equations are used differently in a physics class than in a pure mathematics class. In physics, these symbols not only obey formal mathematical rules but also carry physical ideas and relations. This paper focuses on modeling how this combination of physical and mathematical knowledge is constructed. The cognitive blending f...

Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend to blend conceptual physics with mathematical symbolism in a way that profoundly affects the way equations are...

In this paper, we show an example of students working on a physics problem—an example that demonstrated to us that we had failed to understand the work they needed to do in order to solve a “simple” problem in electrostatics. Our critical misunderstanding was failing to realize the level of complexity that was built into our own knowledge about phy...

Decades of education research have shown that students can simultaneously possess alternate knowledge frameworks and that the development and use of such knowledge are context dependent. As a result of extensive qualitative research, standardized multiple-choice tests such as Force Concept Inventory and Force-Motion Concept Evaluation tests provide...

Without Abstract

In physics education research (PER), we have focused our attention for many years on finding ways to improve our instruction and have achieved some notable successes. In this paper, we suggest that the time has come to embed this activity in a more complete and scientific view of PER, one that builds a coherent understanding of the system of teachi...

Volume 2: Modern Physics The Photoelectric Effect Wave Particle Duality Classical Probability Classical Probability, Advanced Version Fourier Analysis and Uncertainty Potential Energy Diagrams The Shape of the Wave Function Eigenvalues and Bound States Quantum Tunneling (non-computer) Quantum Tunneling (computer) QM Model of Energy Bands QM Model o...

Built on the foundations of Halliday, Resnick, and Walker's Fundamentals of Physics Sixth Edition, this text is designed to work with interactive learning strategies that are increasingly being used in physics instruction (for example, microcomputer-based labs, interactive lectures, etc. ). In doing so, it incorporates new approaches based upon Phy...

Modern instructional advice encourages us to not just tell our students what we want them to know, but to listen to them carefully. This helps us to find out ``where they are'' in order to better understand what tasks to offer them that might help them learn the physics most effectively. Sometimes, listening to students and trying to understand the...

Over the past twenty-five years, educational research on introductory university physics classes has demonstrated that student learning is often significantly less than we hope and expect. Specific con- ceptual difficulties have been identified in a wide variety of topics. Research-based curricula de- signed to improve student conceptual learning c...

Education is a goal-oriented field. But if we want to treat education scientifically so we can accumulate, evaluate, and refine what we learn, then we must develop a theoretical framework that is strongly rooted in objective observations and through which different theoretical models of student thinking can be compared. Much that is known in the be...

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 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 p...

The Activity-Based Tutorials are designed to accompany and enhance lecture instruction. They have been developed using a cycle of physics education research, including investigations into student learning on a given topic, development of materials, and revision of the materials based on evaluation after use in the classroom. Activity-Based Tutorial...

The recent dramatic expansion of activity in physics education research among AAPT members has not been matched by commensurate increases in publication venues. Although the impact of this research field within the broader physics community has sharply increased, the viability of its continued existence is dependent upon substantially expanded publ...

The Activity-Based Tutorials are designed to accompany and enhance lecture instruction. They have been developed using a cycle of physics education research, including investigations into student learning on a given topic, development of materials, and revision of the materials based on evaluation after use in the classroom. Activity-Based Tutorial...

“What should we do when we find students giving inconsistent responses on a measurement instrument?” The answer depends on the cognitive models chosen as the basis for the assessment. The common theoretical basis for many assessment tools assumes that students possess internal models or have general abilities that are responsible for creating the o...

Students in introductory calculus-based physics not only have difficulty understanding the fundamental physical concepts, they often have difficulty relating those concepts to the mathematics they have learned in math courses. This produces a barrier to their robust use of concepts in complex problem solving. As a part of the Activity-Based Physics...

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 congitive model that represents student thinking in terms of mental models. Students frequently fail to recognize relevant conditions...

We report on our study of student understanding of the physics of mechanical waves, specifically the propagation and superposition of simple wavepulses traveling on long, taut strings. We introduce the terms "particle pulses mental model" to describe the reasoning approach that students use to guide their thinking in wave propagation and superposit...

Student learning of sound waves can be helped through the creation of group-learning classroom materials whose development and design rely on explicit investigations into student understanding. We describe reasoning in terms of sets of resources, i.e. grouped building blocks of thinking that are commonly used in many different settings. Students in...

Students are taught several models of conductivity, both at the introductory and the advanced level. From early macroscopic models of current flow in circuits, through the discussion of microscopic particle descriptions of electrons flowing in an atomic lattice, to the development of microscopic nonlocalized band diagram descriptions in advanced ph...

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...

In this talk I consider what physics can offer to students, both as physics majors and in other sciences. The recent increases in the technological character of the workplace appear likely to continue, leading to increasing numbers of individuals who should learn something about science. For many of these people, understanding the character of scie...

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...

this paper is part of an iterative cycle of research, curriculum development, delivery, and evaluation. We do our evaluation using a variety of probes, including videotaped individual demonstration interviews, pretests (short, ungraded quizzes that accompany tutorials) , examination questions, and specially designed diagnostic tests. In interviews,...

This paper reviews the state of the current community of physics education researchers and considers the changes in culture needed to implement reforms of tertiary-level technological education. The recent work of discipline-based educational researchers has some important consequences. The researchers' primary goal is to illuminate and explain wha...

During the past 15 years, physics education research has revealed many surprising things about the difficulties introductory physics students have in learning physics. At the same time, the ongoing revolution in information technology has led to new tools for creating innovative educational environments. In response to these two developments, a wid...

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The purpose of this Resource Letter is to provide an overview of research on the learning and teaching of physics. The references have been selected to meet the needs of two groups of physicists engaged in physics education. The first is the growing number whose field of scholarly inquiry is (or might become) physics education research. The second...