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Implications of research on learning for the education of prospective science and physics

teachers

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2001 Phys. Educ. 36 44

(http://iopscience.iop.org/0031-9120/36/1/308)

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Implications of research onlearning for the education ofprospective science and physicsteachers†Jose P Mestre

Department of Physics, University of Massachusetts, Amherst, MA 01003, USA

AbstractThis article provides a brief overview of cognitive research findings from thelast 25 years pertinent to the teaching and learning of physics, and discussesthe implications of this research both for structuring the training ofprospective physics instructors, and for reforming physics instruction.

Over the last two decades cognitive research hasmade great strides in helping us understand thelearning process. It should not be surprisingthat findings from research on learning are verysuggestive about the ingredients that should bepresent in effective instruction. Several reviewarticles have done a good job discussing theimplications of this research for the teaching ofphysics (Redish 1994, 2000, Van Heuvelen 1991,McDermott 1984, 1991, 1993, Mestre 1991, 1994,Mestre and Touger 1989). Perhaps the bestsynthesis of research on learning is contained ina recent report from the US National ResearchCouncil (1999) titled How People Learn: Brain,Mind, Experience and School; this report goesbeyond synthesis and provides examples of howlearning research can be applied in teaching. Inthis article I provide a brief review of researchon learning and discuss its implications for thepreparation of prospective science and physicsteachers by departments of physics.

† Based on an invited talk given at ‘The Role of PhysicsDepartments in Preparing K-12 Teachers’ conference, 8–9 June2000, University of Nebraska–Lincoln, USA, and sponsoredby the University of Nebraska, The American Association ofPhysics Teachers, The American Physical Society and TheAmerican Institute of Physics.

Overview of research findings pertinent toteaching and learning physics

The nature of expertise

Much of what is known about knowledgeacquisition, storage in memory and applicationto solving problems has come from studies ofexperts engaged in problem-solving tasks in theirdomain of expertise. Experts have extensiveknowledge that is highly organized and usedefficiently in solving problems, and so cognitivescientists have focused on characterizing theorganization, acquisition, retrieval and applicationof experts’ knowledge (see ch 2 of NationalResearch Council 1999). Among the salientfindings is that experts’ knowledge is highlyorganized (Chi and Glaser 1981, Glaser 1992,Larkin 1979, Mestre 1991). The organizationis hierarchical, with the top of the hierarchycontaining the major principles/concepts of thedomain; ancillary concepts, related facts andequations occupy the middle to lower levels ofthe knowledge pyramid. Because of the highlyorganized nature of their knowledge, expertsare able to access their knowledge quickly andefficiently. Further, procedures for applying the

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major principles and concepts are closely linkedto the principles, and retrieved with relativelylittle cognitive effort when a major principle isaccessed in memory. This allows experts tofocus their cognitive efforts on analysing andsolving problems, rather than on searching forthe appropriate ‘tools’ in memory needed to solvethe problems. Knowing more, by virtue ofhaving an efficient organizational structure of theknowledge, means that it requires relatively littleeffort for the expert to learn even more abouttheir area of expertise since new knowledge isintegrated into the existing knowledge structurewith the appropriate links to make recall andretrieval relatively easy.

Experts also approach problem-solving dif-ferently from novices (Chi et al 1981). Forexample, when asked to categorize problems(without solving them) according to similarity ofsolution, experts categorize according to the majorprinciples that can be applied to solve the problems(e.g., conservation of momentum), whereasnovices categorize according to the superficialattributes of the problems (e.g., according theobjects that appear on the problem statement, suchas ‘pulleys’ and ‘inclined planes’). When asked tostate an approach they would use to solve specificproblems, experts discuss the major principle theywould apply, the justification for why the principlecan be applied to the problem, and a procedurefor applying the principle. In contrast, novicesjump immediately to the quantitative aspects ofthe solution, discussing the equations they wouldapply to generate an answer.

This research suggests that the tacit knowl-edge that experts use to solve problems should bemade explicit during instruction, and that studentsshould actually practise applying this (no longertacit) knowledge while solving problems. If onebelieves that learners learn by constructing knowl-edge (see next section), however, this cannot beaccomplished by simply telling students how ma-jor ideas apply to problems—students need to en-gage actively in applying and thinking about howthe big ideas are relevant for solving problems sothat they become internalized as useful problem-solving tools. Several research studies suggest thatit is possible to get introductory physics studentsto attend to ‘high level’ knowledge (as opposedto simply manipulating equations). For example,studies indicate that students are more likely to

focus on conceptual knowledge in problem cat-egorization and problem-solving tasks following‘treatments’ in which they spent time analysingproblems qualitatively before attempting quanti-tative solutions (Dufresne et al 1992, Eylon andReif 1984, Heller and Reif 1984, Leonard et al1996, Mestre et al 1992, 1993).

Current view of learning

The contemporary view of learning is thatindividuals actively construct the knowledge theypossess. Constructing knowledge is a life-long, effortful process requiring significant mentalengagement from the learner. In contrast tothe ‘absorbing knowledge in ready-to-use formfrom a teacher or textbook’ view of learning, the‘constructing knowledge’ view has two importantimplications for teaching. One is that theknowledge that individuals already possess affectstheir ability to learn new knowledge. When newknowledge conflicts with resident knowledge, thenew knowledge will not make sense to the learner,and is often constructed (or accommodated) inways that are not optimal for long-term recallor for application in problem-solving contexts(Anderson 1987, Schauble 1990, Resnick 1983,Glasersfeld 1989, 1992). For example, whenchildren who believe the Earth is flat are told thatit is round, they accommodate this to mean thatit is round like a pancake, with people standingon top of the pancake (Vosniadou and Brewer1992). When subsequently told that the Earth isnot round like a pancake, but rather round like aball, children envision a ball with a pancake on top,upon which people could stand (after all, studentsreason, people would fall off if standing on theside of a ball!). Thus, prior knowledge and sense-making are prominent in the constructivist view oflearning.

The second implication is that instructionalstrategies that facilitate the construction ofknowledge should be favoured over those that donot. Sometimes this statement is interpreted tomean that we should abandon all lecturing andadopt instructional strategies where students areactively engaged in their learning. Although thelatter goal is certainly desirable, the former is anoverreaction. It is certainly true that, under theright conditions, lecturing could be a very effectivemethod for helping students learn, but wholesale

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lecturing is not an effective means of gettingthe majority of students engaged in constructingknowledge during class time. Hence, instructionalapproaches where students are discussing physics,doing physics, teaching each other physics andoffering problem solution strategies for evaluationby peers will facilitate the construction of physicsknowledge.

The relationship between content expertise andteaching

Expertise in a discipline is a necessary, but notsufficient, condition for teaching that disciplineeffectively. An effective instructor also hasa wealth of ‘pedagogical content knowledge’,which includes knowledge about the typesof difficulties that students experience, typicalpaths that students must traverse to achieveunderstanding and potential strategies for helpingstudents overcome learning obstacles, all of whichare discipline-dependent (Shulman 1986, 1987,National Research Council 1999). Pedagogicalcontent knowledge also differs from knowledgeabout general teaching methods, which are oftentaught within ‘methods’ courses outside of thescience discipline. What cannot be learned inisolated methods courses about teaching a specificdiscipline such as physics are such things asthe types of assignments that are best suited forteaching particular topics, the types of assessmentsthat are best suited to gauge students’ progressand to guide instruction, and the way to structureclassroom discussions to highlight and clarifynew ideas, as well as to integrate them withinthe students’ knowledge structures. In short,there is an interaction between knowledge ofthe discipline and the pedagogy for teachingthat discipline which results, for the experiencedinstructor, in a ‘cognitive road map’ that guidesthe instructor while teaching. All of this raisesthe question of how prospective university physicsprofessors are supposed to develop pedagogicalcontent knowledge when nearly all of the emphasisin PhD graduate training is on content; this is anissue to be discussed in a later section.

Assessment in the service of learning

Most assessment carried out in university sciencecourses is ‘summative’ in that it is intended tosum up the competence of the students and assign

grades. Largely missing from science classrooms,especially large lecture courses, is formativeassessment intended to provide feedback to bothstudents and instructors, so that students have anopportunity to revise and improve the quality oftheir thinking and instructors can tailor instructionappropriately. Perhaps the biggest deterrent tousing formative assessments in science classesis that instructors lack techniques for usingcontinuous formative assessment in ways that areunobtrusive and fit seamlessly with instruction.The age-old technique of asking a question to theclass and asking for a show of hands has beentried by most but does not work well since fewstudents participate in the hand-raising, largelydue to lack of anonymity. Because research onlearning indicates that all new learning dependson the learner’s prior learning and current state ofunderstanding, to ignore students’ current level ofunderstanding during the course of instruction isperilous.

In small classes it is not difficult to shapeteaching so that two-way communication takesplace between the instructor and the student. Forexample, one very effective method of teachingphysics to small classes perfected by Minstrell(1989) involves class-wide discussions led bythe teacher. Students offer their reasoning forevaluation by the class and by the instructor,with the class format taking somewhat the formof a debate among students, with the instructormoderating the discussion and leading it incertain directions by posing carefully craftedquestions. In large enrollment classes theadvent of classroom communication systemshas allowed the incorporation of a workshopatmosphere, with students working collaborativelyon conceptual or quantitative problems, enteringanswers electronically via calculators, and seeingthe entire class’s response in histogram form fordiscussion (Dufresne et al 1996, Mestre et al1997, Wenk et al 1997). With this approach,the histogram serves as a springboard for aclass-wide discussion in which students volunteerthe reasoning that led to particular answers andthe rest of the class evaluates the arguments.The instructor moderates, making sure that thediscussion leads to appropriate understanding.Other approaches, such as Laws’ WorkshopPhysics (Laws 1991) and McDermott’s Physicsby Inquiry (McDermott 1996), are intended for

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small classes where students engage in hands-onlearning and the instructor circulates to ensurethat students make suitable progress; this allowsindividualized formative assessment, since theinstructor can serve as a diagnoser/tutor as s/hecirculates about the room.

Transferring knowledge flexibly across differentcontexts

Transfer, which refers to the ability to applyknowledge learned in one context to a novelcontext, is difficult to achieve with traditionalinstruction (National Research Council 1999).In physics, we have all heard complaints frominstructors that students do not apply what theylearn in maths classes to their physics classes.Research suggests that transfer is not easy toaccomplish (Gick and Holyoak 1980, Bassok andHolyoak 1989). My own work with problem-posing in physics reinforces this (Mestre 2000).I found that when asked to pose their ownsolvable, textbook-like problems from conceptscenarios1 students were quite constrained by theirinability to find multiple contexts in which to applyconcepts. For example, when posing problemsthat incorporated ‘conservation of mechanicalenergy’, students always used the same context,namely an object undergoing free fall in theEarth’s gravitational field. Because of this, itwas often impossible for them to match otherpieces of the concept scenario with a problemposed within this context (e.g., in the conceptscenario in the footnote below, it was impossiblefor students to pose a problem in which afalling object collides and sticks to another object[thus far the first two parts of the scenarioare satisfied, namely conservation of mechanicalenergy followed by conservation of momentum],and then have potential energy increase and kineticenergy decrease). The concept scenario belowcould have been easily satisfied within a contextcontaining a spring, which, besides gravitation,is the other major system studied in introductoryphysics that conserves mechanical energy.

Research suggests that several features oflearning affect transfer (ch 3 of National Research

1 A ‘concept scenario’ is a sequence of concepts that applyto a problem in the order in which they apply. For example:Mechanical energy is conserved, followed by conservation ofmomentum, followed by conservation of mechanical energy,with potential energy increasing and kinetic energy decreasing.

Council 1999). First, the amount of learningclearly affects whether the knowledge is availablefor transfer, and this depends on the time ontask and the student’s interest and motivation tolearn the material. The context in which theknowledge is learned is also pivotal in termsof ability to transfer; if knowledge is learnedsolely in one context, it is unlikely that it willbe transferable to other contexts. This impliesthat as new knowledge is learned, students shouldbe assisted in considering multiple contexts inwhich it applies and in linking the knowledgeto previously learned knowledge. Finally, newlearning involves transfer from previous learning,and often previous learning can interfere withability to transfer knowledge appropriately to newcontexts (the physics education research literatureon ‘preconceptions’ or ‘alternative conceptions’ isan archetypal example of this).

Metacognition: making defensive learners

Research suggests that transfer can be improved,that is, ability to use knowledge in new contextswithout the need for explicit prompting, by theuse of metacognitive strategies (Brown 1975,1980, Flavell 1973). Metacognitive strategiesrefer to strategies for helping learners becomemore aware of themselves as learners, and includeability to monitor one’s understanding throughself-regulation; ability to plan, monitor successand correct errors when appropriate; and ability toassess one’s readiness for high level performancein the field one is studying (National ResearchCouncil 1999). Reflecting about one’s ownlearning is a major component of metacognition,and does not occur naturally in the physicsclassroom, due to lack of opportunity and becauseinstructors do not emphasize its importance. It iscommon to hear physics students comment, ‘I amstuck on this problem’, but when asked for morespecificity about this condition of ‘stuckness’,students are at a loss to describe what it is about theproblem that has them stuck, and often just repeatthat they are just stuck and can’t proceed. If duringinstruction we were to take the time to suggestwhy, and how, students should reflect about theirlearning, there would be fewer incidents of the‘stuck’ condition, since students would be able toidentify what they are missing that would allowthem to proceed.

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Promoting the habit of reflecting on one’sown learning is also pivotal in physics coursesthat deviate from the norm in pedagogy. Despiteresearch evidence that students learn best whenactively engaged, the norm in college physicsinstruction is the lecture, in which most studentsare passively taking notes. Courses that attemptto get students to work collaboratively, or that tryother techniques to engage them, are often viewedby students as being deviant, and thus simplyto be tolerated rather than invested in. In casessuch as these, instructors should communicatewith students why the course is being taught theway it is, and explain how research on learningsuggests that the approach being used is superiorto the teach-by-telling approach. Only by gettingstudents to reflect about their learning, and byaccruing evidence that in fact the ‘active learning’approach is making them learn more than a lectureapproach, will students begin to buy into theapproach and become active participants ratherthan simply tolerant participants.

What this research suggests about physicscourses for prospective science teachers

The research reviewed above carries importantimplications for how instruction for prospectiveteachers (and all students for that matter) shouldbe structured. In this section I provide a list ofdesirable attributes for physics courses suggestedby research on learning. The list of attributes thatI will provide is not intended to be complete, andis very likely somewhat idiosyncratic; someoneelse’s list will likely differ, but if any two lists basedon cognitive research findings are compared, thereshould be considerable overlap. Further, the listis intentionally general and will not differentiatebetween courses aimed at the elementary, middleor high school levels. Finally, no hierarchy ofattributes is implied by this list.

• Physics content and pedagogy should beintegrated.When pedagogy and content are taughtseparately, they are seldom integrated. Anideal course for prospective teachers wouldintegrate the content with effective ways ofteaching that specific content, the goal beingto develop pedagogical content knowledge.A similar goal is desirable for trainingprospective PhD physicists. At nearly all

universities physics PhD training does notinclude courses on cognition, teaching andlearning. In addition, teaching assistantsare usually relegated to teaching traditionallaboratory sections attached to traditionallytaught large lecture courses. This situationis not conducive for developing pedagogicalcontent knowledge, so it is not surprisingthat new professors in physics departmentsteach as they were taught. It is not easyto break out of this cycle. The research onexpertise demonstrates that it takes time tobecome an expert at something, and becominga competent ‘learning coach’ is no exception.Thus, simply giving physics faculty ‘tips’ incrash workshops on teaching and learningmay serve to pique their interest, but itdoes little to promote effective, or lasting,instructional innovations.

• Construction, and sense-making, of physicsknowledge should be encouraged.Although teachers can facilitate learning, re-search indicates that students must do thelearning themselves. Students must also learnscience content in ways that make sense tothem, and their understanding of that sci-ence must be consistent with scientists’ cur-rent models for how the physical and bio-logical world works. Classroom environ-ments in which students are actively engagedand the instructor plays the role of learn-ing coach (e.g., inquiry learning, cooperativegroup learning, hands-on activities) are help-ful in achieving this goal.

• The teaching of content should be a centralfocus.Clearly any physics course for prospectiveteachers has to be based on physics content,but at the same time it should not be so ladenwith content that it becomes a race to surveyas many topics as possible. The emphasisshould be on understanding—in depth—a fewmajor topics rather than the memorization offacts about many topics; the former has lastingvalue, the latter is quickly forgotten after thecourse is over.

• Ample opportunities should be availablefor learning ‘the process of doing science’.Doing science requires not only lots ofcontent knowledge, but also knowledgeabout the processes involved in scientific

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investigation—knowledge of the process ofscience. Students should, therefore, useapparatus, objects, equipment and technologyto design experiments and test hypotheses,rather than performing ‘cookbook’ labs. Justenough guidance should be provided so thatstudents make suitable progress.

• Ample opportunities should be providedfor students to apply their knowledgeflexibly across multiple contexts.Physics is perhaps the only science in which ahandful of concepts can be applied to solveproblems across a wide range of contexts.Unfortunately, the transfer research literaturesuggests that when people acquire knowledgein one context they can seldom apply thisknowledge to situations in related contexts—contexts that look superficially different fromthe original context, but which are relatedby the major idea that could be applied tosolve or analyse them. The implication is thatstudents should learn to apply major conceptsin multiple contexts in order to make theknowledge ‘fluid’.

• Helping students organize content knowl-edge according to some hierarchy shouldbe a priority.To learn lots of things about a topic, to recallthat knowledge efficiently and to apply it flex-ibly across different contexts requires a highlyorganized mental framework. A hierarchicalorganization, in which the major principlesand concepts are near the top of the hierarchy,and ancillary ideas, facts and formulas occupythe lower levels of the hierarchy but are linkedto related knowledge within the hierarchy, isneeded to achieve a high level of proficiencyin a field.

• Qualitative reasoning based on physicsconcepts should be encouraged.Much of the knowledge that scientists possessis referred to as ‘tacit knowledge’; it isknowledge used often but seldom madeexplicit or verbalized (e.g., when applyingconservation of mechanical energy, one mustmake sure that there are no non-conservativeforces doing work on the system). Tacitknowledge should be made explicit to helpstudents recognize it, learn it and apply it. Oneway of making tacit knowledge explicit is byconstructing qualitative arguments using the

physics being learned. By both constructingqualitative arguments and evaluating others’arguments, students can begin to appreciatethe role of conceptual knowledge in ‘doingscience’.

• Metacognitive strategies should be taughtto students.Students should be able to predict not onlytheir ability to perform tasks but also theircurrent levels of mastery and understanding.By helping students to be self-reflective abouttheir own learning, they can learn how tolearn more efficiently. For example, whenstuck trying to solve a problem, asking oneselfquestions such as ‘What am I missing orwhat do I need to know to make progresshere?’, ‘Am I stuck because of a lack ofknowledge or because of an inability toidentify or implement some procedure forapplying a principle/concept?’, are oftenhelpful in deciding on a course of action.After solving a problem, reflecting on thesolution by asking questions such as ‘Whatdid I learn that was new by solving thisproblem?’, ‘What were the major ideas thatwere applied and what is their order ofimportance?’, ‘Am I able to pose a problem inan entirely different context that can be solvedwith the same approach?’, help one monitormastery and understanding of the topics beinglearned.

• Formative assessment should be used fre-quently to monitor students’ understand-ing and to help tailor instruction to meetstudents’ needs.Assessment for the purposes of providingfeedback to both students and instructors tohelp guide teaching and learning providesvaluable information to both students and in-structors; formative assessment helps studentsrealize what they don’t understand, and helpsteachers craft tailored instructional strategiesto help students achieve the appropriate un-derstanding. This practice would also modela very powerful pedagogical strategy thatprospective teachers should adopt when theybecome teachers.

Received 17 August 2000PII: S0031-9120(01)16469-5

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