Preparing future teachers to anticipate student difficulties in physicsin a graduate-level course in physics, pedagogy, and education research
John R. Thompson,1 Warren M. Christensen,2 and Michael C. Wittmann1
1Department of Physics and Astronomy and Maine Center for Research in STEM Education, University of Maine, Orono, Maine, USA2Department of Physics, North Dakota State University, Fargo, North Dakota, USA
(Received 10 November 2009; revised manuscript received 4 February 2011; published 20 May 2011)
We describe courses designed to help future teachers reflect on and discuss both physics content and
student knowledge thereof. We use three kinds of activities: reading and discussing the literature,
experiencing research-based curricular materials, and learning to use the basic research methods of
physics education research. We present a general overview of the two courses we have designed as well as
a framework for assessing student performance on physics content knowledge and one aspect of
pedagogical content knowledgeknowledge of student ideasabout one particular content area: electric
circuits. We find that the quality of future teachers responses, especially on questions dealing with
knowledge of student ideas, can be successfully categorized and may be higher for those with a
nonphysics background than those with a physics background.
DOI: 10.1103/PhysRevSTPER.7.010108 PACS numbers: 01.40.J
With the growth of physics education research (PER) asa research field [1,2] and the ongoing desire to improveteaching of introductory physics courses using reform-based approaches , there has been an opportunity tomove beyond an apprenticeship model of learning aboutPER toward a course-driven structure. At the University ofMaine, as part of our Master of Science in Teaching (MST)program, we have developed and are teaching two coursesin Integrated Approaches in Physics Education . Thesecourses are designed to teach physics content, develop PERmethods, and present results of investigations into studentlearning. The goal of our courses is to build a research-based foundation for future teachers at the high school anduniversity level as they move into teaching.
Teachers must satisfy many, many goals in their instruc-tion. In part, teachersmust be able to understand fromwheretheir students are coming, intellectually, as they discuss thephysics. Teachers need to know how their students thinkabout the content. Such an agenda has a long history in PER and is one part of pedagogical content knowledge (PCK). We want to help teachers recognize how investigationsinto student learning and understanding have led to what isknown about student thinking in physics, and how theresults of this research inform curricular materials develop-ment. In order to do this, we expose (future) teachers to, andlet them participate in, the research on student learning;from this, they can learn to properly analyze instructional
materials created based on research. And, to be consistent inour philosophy, we must attend to the future teacherslearningof both physics content and pedagogyasmuch as we wish for them to attend to students learning.The activities described in this paper take part within alarger cycle of research, instruction, and evaluation, muchas has been carried out in the PER community as a wholewhen developing instructional strategies to affect studentlearning.In this paper, we propose to accomplish three tasks; the
first two set the stage for the third. Before we describe ourresearch, we first describe the two courses, the context inwhich they take place, and the activities that make up atypical learning cycle within the courses (elaborating onone such instructional unit from the course sequence insome detail). Second, we describe how we determinewhether the future teachers have gained appropriate knowl-edge of student understanding and the role of differentcurricula. Finally, we draw from several semesters ofdata on future teacher learning of physics, pedagogy, andPER, looking at one topic that has been taught three timesduring this period. We present a framework for analyzingdata on learning of physics content knowledge and of oneaspect of pedagogical content knowledgespecifically,what conceptual difficulties a teacher might encounteramong his or her students when teaching particular con-tent. We then apply this framework to a small data set inorder to provide a concrete example. All three of the taskswe have for this section are summarized in a single over-arching research question: In a course designed to teachboth content and pedagogy, how is future teacher knowl-edge affected by focused instruction with research-basedmaterials and research literature documentation? In thispaper, we present a method of assessment that we feel canbe successfully used to address this question.
Published by the American Physical Society under the terms ofthe Creative Commons Attribution 3.0 License. Further distri-bution of this work must maintain attribution to the author(s) andthe published articles title, journal citation, and DOI.
PHYSICAL REVIEW SPECIAL TOPICS - PHYSICS EDUCATION RESEARCH 7, 010108 (2011)
1554-9178=11=7(1)=010108(11) 010108-1 Published by the American Physical Society
II. PEDAGOGICAL CONTENT KNOWLEDGE ANDKNOWLEDGE OF STUDENT IDEAS
Much of the literature on PER in the U.S.A. over the past30 years deals with identification of student difficultieswith specific physics concepts, models, relationships, orrepresentations . Past results of PER on student learningat the university level have led to the development ofcurricular materials designed to address common incorrector naive student ideas using various pedagogical strategies. These curricular innovations have helped improvestudent learning of physics concepts, as measured by per-formance on specific diagnostic assessments and/or sur-veys. In light of the history of PER, we believe that wemust prepare future physics teachers to have an awarenessof how their students might think about various topics, aswell as an awareness of the kinds of curricular materialsavailable to help guide students to the proper scientificcommunity consensus thinking about the physics. Thisattention to student ideas in the classroom is one compo-nent of what Shulman labeled as pedagogical contentknowledge . Shulman describes PCK as the particu-lar form of content knowledge that embodies the aspects ofcontent most germane to its teachability; this includesknowledge of representations, analogies, etc. that make thecontent comprehensible, and an understanding of whatmakes the learning of specific topics easy or difficult. Thecomponent of the description most relevant to our work,however, is the conceptions and preconceptions that stu-dents of different ages and backgrounds bring with them tothe learning of those most frequently taught topics andlessons. In teaching in a field such as physics, the use ofanalogies and representations are often helpful, if notessential, in developing a coherent and sensible under-standing by students [17,18]. The ways in which studentsmisunderstand, misinterpret, or incorrectly apply priorknowledge to common pedagogical tools need to be rec-ognized by teachers who will be using these tools to teachand want to teach effectively.
In the larger science education research literature, re-search on science teachers PCK has focused on the natureand the development of PCK in general, rather than inves-tigating science teachers PCK about specific topics in adiscipline. van Driel and colleagues noted this issue in anarticle a decade ago . In the context of results on aPCK-oriented workshop, the authors describe their owninterpretation of and framework for PCK. The authorsargue that PCK consists of two key elements: knowledgeof instructional strategies incorporating representations ofsubject matter and understanding of specific learning diffi-culties and student conceptions with respect to that subjectmatter. They state that the value of PCK lies essentially inits relation with specific topics. Our work speaks directlyto this recommendation and emphasizes the second of theirtwo key elements.
van Driel et al. also suggest, based on their work andthe literature review, what features a discipline-basedPCK-oriented course should contain, including exposureto curricular materials and the study of what they refer to asauthentic student responses. Through specific assign-ments and discussions, participants may be stimulated tointegrate these activities and to reflect on both academicsubject matter and on classroom practice. In this way,participants PCK may be improved.In addition, van Driel et al. lament the contemporary
state of research into teachers PCK and make recommen-dations for a research agenda on teachers PCK. From theirreview of the literature, they call for more studies onscience teachers PCK with respect to specific topics.Despite the apparent specificity of this approach, theyargue that the results would benefit teacher preparationand professional development programs and classroompractice beyond any individual topic. As an example ofsuch work, Loughran and colleagues  have conductedlongitudinal studies of teachers in the classroom, and usedthe results to develop a different two-piece framework forPCK, involving content representations and teaching prac-tice. We seek to advance this agenda in physics.Magnusson et al.  present an alternate framework
and discussion. They conceptualize PCK as pulling in andtransforming knowledge from other domains, includingsubject matter, pedagogy, and context. They argue thatthis enables PCK to represent a unique domain of teacherknowledge rather than a combination of existing domains.They state that . . . the transformation of general knowl-edge into pedagogical content knowledge is not a straight-forward matter of having knowledge; it is also anintentional act in which teachers choose to reconstruct theirunderstanding to fit a situation. Thus, the content of ateachers pedagogical content knowledge may reflect aselection of knowledge from the base domains (,p. 111).Magnusson et al. break down PCK for science teaching
further than van Driel et al., into five components. Theirfirst component is orientations toward science teachingand learning, dealing with views about the goals of sci-ence teaching and learning, and how that perspectiveguides the teachers instructional decisions. In PERone might classify this domain as the metacognitive andepistemological aspects of physics education. For example,Magnusson et al. describe the didactic orientation, whosegoal is to transmit the facts of science; the accompany-ing instructional approach would be lecture or discussion,and questions to students would be used for the purposes ofaccountability for the facts. The importance of the orien-tation component is that it acts as the lens through whichany teacheror teacher educator, as they point outviewsother aspects of PCK, especially curricular materials, in-structional strategies, and assessment methods. Magnussonet al.s main argument here is that a teachers orientation
THOMPSON, CHRISTENSEN, AND WITTMANN PHYS. REV. ST PHYS. EDUC. RES. 7, 010108 (2011)
influences, and may even determine, his or her pedagogicalchoices and perspectives. In PER one would present thisargument in terms of a teachers epistemological framingof their science instruction , where epistemologicalframing describes ones (in this case the instructors) ex-pectations for what it means to teach science and how theirstudents learn science, and how these expectations influ-ence their behavior within the classroom.
The other four components deal with knowledge andbeliefs about science curriculum; students understandingof specific science topics; science assessment, includingmethods and referents against which to assess; and science-specific instructional strategies. Most directly relevant toour work here is the student understanding category. Thisis further broken down into two parts. The first deals withrequirements for student learning, which includes prereq-uisite knowledge as well as developmental appropriatenessof particular representations. Developmental appropriate-ness refers to the degree to which students of varyingabilities can successfully work with representations thatrequire higher-order reasoning (e.g., three-dimensionalmodels of atoms). The second component of understandingconcerns areas of student difficulty, which includes diffi-culties with the abstract or unfamiliar nature of the con-cepts, with needed problem-solving skills, or with alternate(prior) conceptions (or specific difficulties) held by stu-dents. Magnusson et al. argue that knowledge of thesestudent ideas, as we are referring to them, will help teach-ers interpret students actions and responses in the class-room and on assessments. From their research and theliterature they cite, they find that even teachers whoknow about student difficulties may lack knowledge abouthow to address these difficulties.
In the domain of mathematics, Ball and colleagues havedeveloped a framework for what they have labeledmathematics knowledge for teaching [23,24]. Theyenvision a set of knowledge split between subject matterknowledge (broken down further into common and speci-alized knowledge) and pedagogical content knowledge.PCK contains three subgroups of knowledge and content:those of teaching, students, and curriculum. This frame-work has only recently been established but is quite similarto the one we have used implicitly. In particular, we havefocused on the knowledge of student ideas (KSI), describedby Ball and collaborators as the knowledge of ideas aboutthe content that students have been documented to have.
Within the PER community, Etkina discussed the build-ing of physics-specific PCKdescribed as an applicationof general, subject-independent knowledge of how peoplelearn to the learning of physicsas a central goal inbuilding an ideal physics teacher preparation program[25,26]. Etkina emphasizes the domain specificity ofPCK, underscoring the need for each discipline to havecontent-tailored PCK learned in teacher preparation pro-grams. She points out that learning about PCK should be
conducted in the same manner as effective content learn-ing, via active learning, or in this case, active teaching. In, Etkina describes an entire graduate program for highschool physics teacher preparation that embodies the prin-ciples of learning PCK, and in which students learn aboutmany aspects of PCK and put them into practice. Etkinasnecessary and careful work is consistent with the agenda ofbuilding a large-scale framework for PCK as describedabove. The lack of available PCK literature in PER isreflected by its absence in Etkinas references, and indi-cates the need for explicit atten...