Helping physics students learn how to learnAndrew Elby

Citation: American Journal of Physics 69, S54 (2001); doi: 10.1119/1.1377283 View online: http://dx.doi.org/10.1119/1.1377283 View Table of Contents: http://scitation.aip.org/content/aapt/journal/ajp/69/S1?ver=pdfcov Published by the American Association of Physics Teachers Articles you may be interested in Millikan Lecture 1999: The Workplace, Student Minds, and Physics Learning Systems Am. J. Phys. 69, 1139 (2001); 10.1119/1.1399043 Student resources for learning introductory physics Am. J. Phys. 68, S52 (2000); 10.1119/1.19520 Another reason that physics students learn by rote Am. J. Phys. 67, S52 (1999); 10.1119/1.19081 What Jamaican students think about physics and how we are adapting AIP Conf. Proc. 399, 827 (1997); 10.1063/1.53184 Choice in upper-level physics: How to serve two student populations AIP Conf. Proc. 399, 745 (1997); 10.1063/1.53166

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Helping physics students learn how to learnAndrew Elbya)

Department of Physics, University of Maryland, College Park, Maryland 20742-4111

~Received 9 February 2000; accepted 26 October 2000!

Students’ ‘‘epistemological’’ beliefs—their views about the nature of knowledge and learning—affect how they approach physics courses. For instance, a student who believes physics knowledgeto consist primarily of disconnected facts and formulas will study differently from a student whoviews physics as an interconnected web of concepts. Unfortunately, previous studies show thatphysics courses, even ones that help students learn concepts particularly well, generally do not leadto significant changes in students’ epistemological beliefs. This paper discusses instructionalpractices and curricular elements, suitable for both college and high school, that helped studentsdevelop substantially more sophisticated beliefs about knowledge and learning, as measured by theMaryland Physics Expectations Survey and by the Epistemological Beliefs Assessment for PhysicalScience. ©2001 American Association of Physics Teachers.

@DOI: 10.1119/1.1377283#

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I. INTRODUCTION

Building upon the line of inquiry initiated in this journaby Redish, Saul, and Steinberg,1 I discuss how teachers cahelp to bring about changes in students’epistemologicalbeliefs—their views about what it means to learn and undstand physics. As Hammer2 shows, some students viephysics as weakly connected pieces of information toseparately learned, whereas others view physics as a coent web of ideas to be tied together. Some students eqlearning physics with retaining formulas and problesolving algorithms, while others think that learning involvrelating fundamental concepts to problem-solving teniques. Some students believe learning consists primarilabsorbing information, while others view learning as buiing one’s own understanding.

Epistemological sophistication is valuable. Previous sties show that students’ epistemological expertise correlwith academic performance and conceptual understandinmath and science.3 These correlations exist even controllinfor confounding factors such as interest in science, maematical aptitude, and socioeconomic status.4 So, we can rea-sonably infer that a sophisticated epistemological stanceports productive study habits and metacognitive practicFor instance, a student who sees physics knowledgecoherent web of ideas has reason to ‘‘switch on’’ the mecognitive practice of monitoring one’s understandingconsistency.5 In addition, helping students to understand timportance of consistency and coherence, and the differebetween rote memorization and deeper understanding, iguably a worthy instructional goal in its own right. After ait’s important that students can solve conservation of mmentum problems; but in the long run, it’s equally importathat their beliefs about knowledge and learning engendsophisticated approach to~re!learning that kind of materialPerhaps, to best prepare students for advanced work inence, engineering, and medicine, instructors of introductphysics courses should focus more on epistemological deopment and less on content coverage.

Of course, this proposal deserves no attention if physclasses inevitably fail to help students develop epistemolcally. Previous research isn’t encouraging: Many of the bresearch-based reformed physics curricula, ones thatstudents obtain a measurably deeper conceptual unders

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ing, generally fail to spur significant epistemologicdevelopment.1 Apparently, students can participate in activties that help them learn more effectivelywithout reflectingupon and changing their beliefs about how to learn efftively. These students may revert to their old learning stregies in subsequent courses.

In this paper, I show that instructional practices and cricular elements explicitly intended to foster epistemologidevelopment can lead to significant improvement in sdents’ views about knowledge and learning. An honors-lecurriculum taught to gifted students at a magnet high schin Virginia, and perhaps more significantly, a nonhonophysics curriculum taught at a comprehensive high schooCalifornia, produced significant pre–post gains in studenscores on the Maryland Physics Expectations Sur~MPEX! and on the Epistemological Beliefs AssessmentPhysical Science~EBAPS!, a similar assessment developefor high school~rather than college-level! physics studentsAlthough different in many respects, both courses contaicommon elements discussed in Sec. IV. Most of thesements are suitable for both high school and college.

After describing in Sec. II how I ‘‘measured’’ my students’ epistemological beliefs, I present the major resultsSec. III. Then, in Sec. IV, I describe elements of the cricula, acknowledging the trade-offs associated with a strofocus on epistemological development.

II. RESEARCH METHODS

A. Subjects and setting

1. California

During the 1997–98 academic year, the subjects werephysics students at a small, comprehensive high school sing a middle-class community in the San Francisco Bay aThe 30-member class consisted of 12th, 11th, and 10th gers. 43% were female. Because the school offers onlyphysics class besides Advanced Placement, the class waverse in terms of interest and ability.6 I had nearly completecontrol over the curriculum. Due to absences and shufflclass schedules,n527 students completed the pre- and poassessment described below.

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2. Virginia

During the 1998–99 academic year, the subjects were76 physics students at a large magnet high school for giand talented students near Washington, DC. 50% of mydents were female. Since the school requires all 11th grato take Physics, I was one of five physics teachers. A Stmandated curriculum required me to cover large numbertopics. This core curriculum was ‘‘enforced’’ by sharedepartment-wide midterm and final exams.~In Sec. IV, I willdiscuss how these exams influenced, and were influencemy actions.! Due to extensive shuffling of class schedulesthe beginning of the year,n555 students took the pre-anpost-assessments.

B. Epistemological assessments

I used two independently developed epistemologicalsessments. The Maryland Physics Expectations Su~MPEX! developed by Redish, Saul, and Steinberg1 andaimed at students taking college-level physics, probesdents’ beliefs by posing statements, such as

In this course, I do not expect to understandequations in an intuitive sense; they just have tobe taken as givens.

Students choose ‘‘strongly agree, agree, neutral, disagrestrongly disagree.’’ The above item probes whether studeview learning in their physics class as absorbing informator as constructing their own understanding~IndependenceofLearning!; and whether they view mathematical equationsdisconnected problem-solving tools or as expressions of cceptual content~Math integration!. The italics denote MPEXsubscales. Since physics experts tend to disagree withstatement, disagreement or strong disagreement gets sas ‘‘favorable,’’ while agreement or strong agreement couas ‘‘unfavorable.’’

MPEX items also explore whether students view physknowledge as a collection of pieces or as a more integrawhole ~Coherence!; whether they view physics as consistinmore of formulas and facts or of concepts~Concepts!; theextent to which they view physics as connected to their lioutside the classroom~Reality Link!; and the extent to whichcertain varieties of sustained effort lead to success in phyclass~Effort!.7

I also used the Epistemological Beliefs AssessmentPhysical Science~EBAPS!, developed by a team at the Unversity of California, Berkeley.8 It differs from MPEX infour ways. First, it targets high-school-level chemistry, phics, and physical science classes, which often involvemath than college-level classes do. Second, as describeSec. III C, EBAPS subscales differ slightly from MPEX suscales. Third, in addition to MPEX-style agree/disagitems, EBAPS poses multiple-choice questions, as welmini-debates. An example:

Brandon: A good science textbook should showhow the material in one chapter relates to thematerial in other chapters. It shouldn’t treat eachtopic as a separate ‘‘unit,’’ because they’re notreally separate.

Jamal: But most of the time, each chapter isabout a different topic, and those different topics

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don’t always have much to do with each other.The textbook should keep everything separate,instead of blending it all together.

With whom do you agree? Read all the choicesbefore circling one.

~a! I agree almost entirely with Brandon.

~b! Although I agree more with Brandon, I thinkJamal makes some good points.

~c! I agree~or disagree! equally with Jamal andBrandon.

~d! Although I agree more with Jamal, I thinkBrandon makes some good points.

~e! I agree almost entirely with Jamal.

Response~b!, like response~a!, gets tallied as ‘‘sophisti-cated,’’ since Jamal makes the good point that a textbookeasily become overwhelming by immediately diving into tdeep, subtle connections between ideas that are still newconfusing to the student.

The fourth way in which EBAPS differs from MPEX ismore subtle. By construction, MPEX probes a combinatof students’epistemologicalbeliefs about knowledge anstudents’expectationsabout their physics course. For instance, consider this MPEX item:

My grade in the course will be primarily deter-mined by how familiar I am with the material.Insight or creativity will have little to do with it.

If a student thinks that understanding physics means kning definitions and algorithms, then his/her agreement wthis item reflects the student’s epistemological orientatiHowever, in a fast-paced course that rewards the quick,application of algorithms, a student may ruefully agree wthe statement even though he/she knows thatunderstandingphysics involves insight and creativity. In this case, tagreement stems not from the student’s epistemologicallook, but rather, from his/herexpectationsabout the exams ina particular class. Again, Redishet al. designed MPEX toprobe both epistemology and expectations. By contrEBAPS was constructed to probe epistemology alone, toextent that it can be teased apart from expectations.www2.physics.umd.edu/;elby/EBAPS/home.htm for the entire assessment, and for more discussion of these issues

C. Administration of the assessments: Pre- andpost-testing

In Virginia ~1998–99!, on the first day of class~Septem-ber! and during the last week of class~June!, MPEX andEBAPS were given as an ‘‘opinion survey’’ homework asignment, with students receiving full credit for handing it iIn California ~1997–98!, I administered EBAPS as a preand post-test in the same way. The California studentsnot take MPEX, which is optimized for college-level matematical physics courses. Since the Virginia students tboth assessments, however, it’s possible to ‘‘cross calibrathe two surveys. By June, in both Virginia and Californistudents had received full credit on numerous ‘‘opinionhomework assignments whether or not their views agrwith mine. In addition, their answers to opinion questiothroughout the year indicated most students’ willingnessdisagree with the teacher.

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III. RESULTS AND DISCUSSION

A. MPEX results

To obtain matched pre–post data, I include only thostudents who took MPEX as both a pre- and a poassessment. Following Redishet al.,1 I present the results byspecifying the percentage of favorable versus unfavoraresponses to items in each subscale. For instance, in Tathe ‘‘Pre, Coherence’’ cell indicates that, in September, 5of students’ responses to items in theCoherencecluster~sub-scale! were favorable, while 21% were unfavorable. Sinstudents sometimes chose ‘‘neutral’’ instead of ‘‘agree’’‘‘disagree,’’ these percentages sum to less than 100%. Fi1 represents the same data in an agree–disagree plot

Table I. Virginia MPEX scores. The first two rows show the pre- apost-percentage of favorable/unfavorable responses for each cluster.student’sgain scoreis the difference between his/her percentage of favable responses on the pre- and post-tests. The fourth row shows the stadeviation of the gain scores, relevant for the paired~matched! samplest-testof statistical significance.~n555 students.!

Overall Independ. Coherence ConceptsReality

link Math Effort

Pre 55/21 49/34 53/21 41/28 57/13 68/16 74/1Post 66/17 60/24 78/11 68/12 78/6 82/8 55/2Meangainscore

11a 11a 25a 27a 21a 14a 218a

s.d. ofgainscores

20 28 32 32 36 33 29

ap,0.01.

Fig. 1. Agree–disagree plot for Virginia MPEX results. For each MPEcluster, the base of the arrow represents the pre-test favorable and unable percentages, while the tip of the arrow represents the post-test peages. ‘‘Coh’’ stands forCoherence. This plot omits theEffort cluster, onwhich the students showed a substantial decline; see Table I.

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every cluster, a matched~paired! samplest-test reveals thepre–post changes in the percentage of favorable responsbe statistically significant top,0.01.

B. MPEX discussion

Redishet al.1 found that students’ overall MPEX scoredo not improve significantly between the beginning and eof the course, even at colleges and universities employresearch-based, reform-oriented curricular elements sucthe University of Washington tutorials,9 the University ofMinnesota context-rich problems,10 and Dickinson CollegeWorkshop Physics.11 These active-learning curricula all leato significantly better conceptual learning than traditioncurricula do, as measured by the Force Concept Invenand other assessments.12 Therefore, Redishet al.’s MPEXresults suggest that students can engage in productive leing without reflecting upon and changing their beliefs abothe nature of knowledge and learning. I will return to thpoint in Sec. IV.

To put my MPEX results in context, it is helpful to reviewthe best MPEX results from Redishet al.’s study. In Dick-inson College’s Workshop Physics, students spend no tin lecture and essentially all their time interactively engagwith the material and with each other. In that class, the pcentage of favorable responses increased slightly for thenitive subscales inspired by Hammer’s work—5% forInde-pendence; 8% for Coherence; and 11% forConcepts, withno changes in the rate of unfavorable responses. The osubscale scores showed no change or a deterioration, leato no change in the Overall MPEX score. I take these resto show that even the best learning environments doautomatically lead students to rethink their epistemologioutlook.

The substantial deterioration in my students’ beliefs aexpectations aboutEffort was typical of the colleges anuniversities studied by Redishet al.

Of course, since the Virginia magnet-school students hunusually high ability and motivation, these MPEX resuon their own do not indicate the effectiveness of my curriclum. In the next section, however, I present evidence that~nonhonors! California students underwent just as muepistemological change as my Virginia students.

A reader could also argue that the MPEX gains stem frthe efforts of a particular instructor, not from widely implementable curricular elements. Section IV H addresses thissue.

C. EBAPS results and discussion

The first three EBAPS subscales roughly correspondMPEX subscales, as shown in italics in Tables II and III13

EBAPS subscale 4,Evolving knowledge, probes the epistemological sophistication that students bring to the tasksorting out which scientific knowledge is more tentative vsus more ‘‘settled.’’ Subscale 5,Source of ability to learn,gets at the following issue: Is success at learning and doscience almost entirely a matter of fixed natural ability? Ocan people become better at learning and doing sciethrough hard work and appropriate strategies?

A student’s response to each EBAPS item receives a sof 0 to 100, with 05very unfavorable, 505neutral, and1005very favorable. Averaging the scores for each item incluster gives the corresponding subscale score. These n

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Table II. Virginia EBAPS scores. The first two rows show the mean pre- and post-scores for each su‘‘Source of ability...’’ stands forSource of Ability to Learn. Because these scores are not percentagefavorable responses, they cannot be compared directly to MPEX scores. Each student’sgain score is thedifference between his/her pre- and post-test score. The fourth row shows the standard deviation of tscores, relevant for the paired~matched! samplest-test of statistical significance.~n555 students.!

Overall

Structure ofknowledge

Concepts, Coh.

Nature oflearning

Independence

Real-lifeapplicabilityReality link

Evolvingknowledge

Source ofability...

Pre 67.4 67.9 66.8 72.4 67.0 67.4Post 71.8 76.1 72.7 77.1 69.5 66.3Mean gainscore

4.4a 8.2a 5.9a 4.7a 2.5 21.1

s.d. of gainscores

7.5 16.2 12.3 14.5 18.3 16.1

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bers are not percentages of favorable or unfavorablesponses; the multiple question types used in EBAPS doinvite this representation of the data.

As Table II shows, the Virginia students’ EBAPS resucorrespond closely to their MPEX results, with the larggain in the subscale corresponding toCoherenceand Con-cepts, and smaller but significant gains in the subscales cresponding toIndependenceandReality link. Table III showsthat, as compared to the Virginia students, the Califorstudents achieved essentially identical gains in the cognsubscales, but not inReal-life applicability. Indeed, this fail-ure in California~1997–98! caused me to use more real-liexamples and to make other modifications when I taughVirginia ~1998–99!.

In both California and Virginia, my curricula failed tochange students’ beliefs aboutSource of Ability to Learn,despite my efforts.

I did not design my curricula to foster development alothe Evolving knowledgesubscale. This decision stemmepartly from personal preference, and partly from the folloing fact: In introductory physical science and math, whethe target knowledge is comparatively settled, a sophisticaapproach to sorting out which knowledge is more tentatand which knowledge is more settled does not necesshelp students learn the material more effectively,Schommer et al. show.14 My own work confirms thisconclusion. For my California students, the correlaticoefficient between their score on a midyear exam coveNewtonian mechanics and their EBAPSNature of Learning

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subscale score was 0.56. ForStructure of knowledge,the correlation was 0.41, also statistically significa(p,0.05). But there was essentiallyno correlation (r50.01) between the exam score andTentativenesssubscalescore.

D. Summary of results

In California ~1997–98! and Virginia~1998–99!, I taughttwo different curricula to two different sets of students—nonhonors, slower-paced course versus an honors, fapaced course. Both curricula contained common elemediscussed in the next section. The California and Virginstudents achieved significant—and according to EBAPcomparable—gains in the sophistication of their belieabout the coherence and ‘‘conceptual-ness’’ of physknowledge and about the constructive nature of learnishowing that an epistemology-focused course can wfor both average and talented students. In additithe Virginia students also acquired more favorable beliabout the link between physics and real life outside the claroom, and about the meaningfulness of mathematequations. These results came at the expense of contenterage, but not at the expense of basic concepdevelopment.15 By contrast, even the best curricula aimedconceptual developmentbut not aimed explicitly at epistemological developmentdo not produce comparable epistemlogical results.

scales,ificant

Table III. California EBAPS scores. See the caption of Table II caption for an explanation. On most subthe average California gain was greater than the average Virginia gain, though not by a statistically signmargin.~n527 students.!

Overall

Structure ofknowledge

Concepts, Coh.

Nature ofleaning

Independence

Real-lifeapplicabilityReality link

Evolvingknowledge

Source ofability...

Pre 66.5 62.5 68.4 73.0 63.9 72.6Post 71.8 70.9 75.0 73.5 67.9 77.4Mean gainscore

5.3a 8.4a 6.6a 0.5 4.0 4.8

s.d. of gainscores

8.7 17.7 11.9 15.6 21.5 17.3

ap,0.02.

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IV. ELEMENTS OF AN EPISTEMOLOGY-FOCUSEDCURRICULUM

In this section, I present some elements of my curricuHigh school and college instructors, even ones teaching lalecture classes, could mold these elements to suit theirneeds, assuming students spend much of their time inand/or discussion sections. I also highlight the trade-offssociated with certain elements. My discussion does not foon elements that resemble other reform curricula. Howevewant to acknowledge that much of what I do is basedWorkshop Physics,11 RealTime Physics labs,16 the Univer-sity of Washington tutorials,9 and Mazur’s conceptuaquestions.17

I should clarify two points before diving into the detailFirst, I present these ideas as illustrations of epistemolofocused instruction, not as pre-packaged materials. Lgrading policies, and other elements must be adapted tolevel and motivation of the students, the class size, thestructor’s preferences, the flow of the class, and other factFor instance, I used different Newton’s law labs with mVirginia and California students, though I lack the space hto show both versions. Second, as discussed in more dbelow, shoehorning a couple of these elements intootherwise-unchanged class may accomplish little. Prelinary evidence suggests that a focus on epistemology neesuffuse the class in order to have a significant effect.

A. Epistemology lessons embedded into labs, problems,and class discussions

I used labs and other materials explicitly designed to ingrate conceptual development with epistemological devement. In the following, I describe two force labs designedhelp students understand that learning physical laws invorefining one’s intuitive ideas in order to reconcile them wthe physics. In other words, these materials try to pushdents toward Einstein’s view that science is ‘‘the refinemof everyday thinking.’’18 By contrast, many students initiallview common sense as a ‘‘separate’’ kind of thinking thcan’t be trusted in physics class; see Hammer.19

1. Newton’s second law lab

My first force lab begins in the style of some UniversityWashington tutorials,9 eliciting and confronting a commonstudent difficulty:

1. A car cruises steadily down the highway at 60mph. Wind resistance opposes the car’s motionwith a force of 5000 N. Intuitively is the forwardforce on the car less than 5000 N, equal to 5000N, or greater than 5000 N? Explain.

2. In this question, we’ll see if Newton’s secondlaw agrees with your intuitive guess.

~a! When the car cruises at constant speed 60mph, what is its acceleration,a? Explain youranswer in one sentence.

~b! Therefore, according toFnet5ma, when thecar moves at constant velocity, whatnet forcedoes it feel?

~c! So, is the forward force greater than, lessthan, or equal to the 5000-N backward force?Does this agree with your intuitive answer toquestion 1?

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The next question, however, asks students to reflect oncorresponding epistemological issue:

3. Most people have—or can at leastunderstand—the intuition that the forward forcemust ‘‘beat’’ the backward force, or else the carwouldn’t move. But as we just saw, when the carcruises at steady velocity, Newton’s second lawsays that the forward force merelyequals thebackward force;Fnet50. Which of the followingchoices best expresses your sense about what’sgoing on here?

~a! Fnet5ma doesn’t always apply, especiallywhen there’sno acceleration.

~b! Fnet5ma applies here. Although commonsense usually agrees with physics formulas,Fnet

5ma is kind of an exception.

~c! Fnet5ma applies here, and disagrees withcommon sense. But we shouldn’texpectformu-las to agree with common sense.

~d! Fnet5ma applies here, and appears to dis-agree with common sense. But there’s probably away to reconcile that equation with intuitivethinking, though we haven’t yet seen how.

~e! Fnet5ma applies here. It agrees with com-mon sense in some respects but not in other re-spects.

Explain your view in a few sentences.

In California, no single answer got a majority, and the mpopular were~b!, ~c!, and ~d!. In Virginia, most studentschose~d! or ~e!. The rest of the lab was designed not onlyhelp students understand Newton’s second law, but alshelp them realize that a large part of ‘‘understanding’’physical law is reconciling it, to the extent possible, wicommon sense. In California, students began by pullincart across the carpet with a rubber band. They were askefocus on the following issue:

4. Is there a difference between how hard youmust pull toget the cart moving, as compared tohow hard you must pull tokeepthe cart moving?You can answer this question by ‘‘feeling’’ howhard you’re pulling, and by observing how farthe rubber band is stretched.

Students could see and feel that more force was needeinitiate than to maintain the motion. In the tutorial-styfollow-up questions, students related their experimentalservations to Newton’s second law:

5. Let’s relate these conclusions to Newton’ssecond law.

~a! While you get the cart moving~i.e., while itspeeds up from rest!, does the cart have an ac-celeration? So, according to Newton’s secondlaw, does the forward forcebeat the backwardforce or merelyequal the backward force? Ex-plain.

~b! While you keep the cart moving~at steadyspeed!, does the cart have an acceleration ? So,according to Newton’s second law, does the for-ward forcebeat the backward force or merelyequal the backward force?

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~c! Look at your answers to parts~a! and ~b!.Using Newton’s second law, explain why experi-ment 4 came out the way it did. Check your an-swer with me.

Question 6 then asked students about the force needed tthe cart moving versus to keep it moving in the absencefriction. Finally, students were asked to summarize the mconceptual point of the lab:

7. OK, here’s the punch line. Most people havethe intuition that, if an object is moving forward,there must be a~net! forward force. Explain inwhat sense that intuition is helpful and correct,and in what sense that intuition might seem mis-leading.

As often happens in labs, some students needed help ‘‘sewhat they’re supposed to see’’~or in this case, ‘‘feeling whatthey’re supposed to feel’’! in the experiment. Except for thadifficulty, almost all students in both Virginia and Californworked through questions 1–6 with minimal help from tteacher. ~Before the lab, the California students workethrough a few examples designed to illustrate what‘‘net’’ force means.! About a third of the California studentsand a smaller fraction of the Virginia students, had troutying it all together in question 7, though most studentssponded that the ‘‘motion requires force’’ intuition appliesgetting an object moving but not to keeping it moving. Stespecially in California, a post-lab class discussion wneeded to help everyone get this point. The class discusalso aimed to help students tie together the mainepistemo-logical point of the lab, that learning physical laws is parta matter of refining rather than abandoning your intuitideas.

2. Newton’s third law lab

My Newton’s third law lab continues to push studentoward Einstein’s viewpoint. Once again, the beginningthe lab resembles a tutorial9 or a RealTime physics lab:16

1. A truck rams into a parked car@Fig. 2#.

~a! Intuitively, which is larger during the colli-sion: the force exerted by the truck on the car, orthe force exerted by the car on the truck?

~b! If you guessed that Newton’s third law doesnot apply to this collision, briefly explain whatmakes this situation different from when New-ton’s third lawdoesapply.

2. ~Experiment! To simulate this scenario, makethe ‘‘truck’’ ~a cart with extra weight! crash intothe ‘‘car’’ ~a regular cart!. The truck and car bothhave force sensors attached. Do whatever experi-ments you want, to see when Newton’s third lawapplies. Write your results here.

On question 1, most students wrote that the car must felarger force, since it reacts more. Therefore, the experimeconfirmation of the third law can reinforce students’ vie

Fig. 2. A moving truck rams into parked car, from the Newton’s third lalab. Which vehicle feels a bigger force from the other?

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that intuitions can’t be trusted in physics. To encouragerethinking of this conclusion, the following questions tryhelp students see that a certainversion of the ‘‘car reactsmore’’ intuition is correct and useful.

3. Most people have the intuition that the truckpushes harder on the car than vice versa, becausethe car ‘‘reacts’’ more strongly during the colli-sion. Let’s clarify this reaction intuition to see ifwe can reconcile it with Newton’s third law,which always applies.

~a! Suppose the truck has mass 1000 kg and thecar has mass 500 kg. During the collision, sup-pose the truck loses 5 m/s of speed. Keeping inmind that the car is half as heavy as the truck,how much speed does the car gain during thecollision? Visualize the situation, and trust yourinstincts.

Almost all students answer, correctly, that the car gains twas much speed as the truck loses. This intuitive ideaagreeswith Newton’s third law, as students find by workinthrough parts~b! through~e!:

~b! During the collision, the truck and car pushon each other for 0.20 s. Find the truck’s decel-eration during the collision.

~c! Assuming your part~a! intuition is correct,find the car’s acceleration during the collision.How does it compare to the truck’s acceleration?

~d! Find the net force felt by the truck during thecollision. Hint: Use your part~b! answer, andassume friction is negligible.

~e! Assuming your part~a! intuition is correct,find the net force felt by the car during the col-lision. How does this compare to the force felt bythe truck?

Although a small minority of students got lost in the logand needed some help from the teacher, most studentsrectly reached the conclusion that, if the car speeds uptwice as much as the truck slows down, then both vehicmust have felt the sameforce. The subsequent questions emphasize the epistemological importance of this conclusio

4. Here’s the point of question 3:Your own in-tuition predicts that the car and truck exert equalforces on each other during the collision. But inquestion 1, many of you said that the truck exertsa larger force on the car than vice versa. So, yourintuitions seem to conflict! This is common...

Here, why did your intuitions disagree~if theydid!? How can you reconcile your intuitions witheach other?

About half the students had no idea how to respond,many students asked, ‘‘What are you looking for here?’’ Tquestion probably needs to be rewritten. The next questthough very ‘‘forcing,’’ was clear to most students:

5. Here’s how I reconcile my conflicting intui-tions in this case:

‘‘My intuition says that the car reacts morestrongly than the truck reacts during the colli-sion. But by thinking through my intuitions care-

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fully in question 3, I found that my ‘‘reaction’’intuition is actually an intuition about ,not force.’’

Fill in the blank.

Almost all students said ‘‘velocity’’ or ‘‘acceleration.’’ Afollow-up discussion may have played a large role in helpstudents see the pedagogical flow of the lab. I got the sethat, with no follow up, many students would not ‘‘get’’ it

Questions 4 and 5 invite students to view their ‘‘conflicing’’ intuitions as two different versions of thesamebasicintuition, the idea that the car reacts more strongly thantruck during the collision. By discovering that one of thotwo versions is correct and helpful for understanding Neton’s third law at an intuitive level, students get a feel for tsense in which the refinement of everyday thinking is parlearning physics.

3. Class discussion: Refinement of raw intuition

The next day, I led a class discussion designed to unscore this epistemological point. I introduced the distinctbetween a vague,raw intuition, such as ‘‘the carreactstwiceas much during the collision,’’ and a more precise,refinedintuition, such as ‘‘the car feels twice as large aforceduringthe collision’’ or ‘‘the car has twice as muchaccelerationduring the collision.’’ In a whole-class discussion punctuaby several small-group discussions and problem-solvingterludes, students decided that they possessed the raw ‘‘tion’’ intuition long before entering physics class. I thepointed out that lab question 1 pushes students to refineintuition in terms of forces, while question 3 pushes studeto refine it in terms of acceleration. Students then tracedimplications of those two refinements more fully than thdid during the lab. The refinement in terms of acceleratagrees with the intuition that, during the collision, the cspeeds up by twice as much as the truck slows down. Trefinement not only agrees with, but also helps toexplainNewton’s third law intuitively: The car reacts more than t

Fig. 3. Whiteboard at the end of the ‘‘refinement’’ lesson. Students trathe consequences of refining theraw intuition ‘‘car reacts twice as much astruck’’ in two different ways. The point was that refining rather than abadoning the raw intuition can help us make sense of Newton’s third law.refinement in terms of acceleration highlights the insight that the car ‘acts’’ twice as much as the truck not because it feels more force, but rabecause it’s lighter and therefore reacts~accelerates! more in response to thesameforce.

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truck not because it feels a greater force, but because it’smassive and therefore ‘‘reacts’’ more to the same force.contrast, the refinement in terms of force disagrees withthird law, and also leads to the counterintuitive conclusthat the car acceleratesfour times as much as the truck duing the conclusion.~Students figured this out in smagroups.! Figure 3 shows the state of the whiteboard atend of this discussion. Again, the main point of this lesswasn’t to rehash the conceptual insights from the lab,rather, to highlight the epistemological insight that learniphysics involves refining rather than selectively ignoriyour everyday thinking.

Section IV A traced how I built a particular strand of mepistemological agenda into a connected series of labs, cdiscussions, and small-group discussions. As comparematerials designed to run themselves with minimal teacintervention, these materials require the instructor to interextensively with students during the labs and to lead substial class discussions afterwards, especially to help studtie together theepistemologicalpoints. Instructors shouldalso assign well-chosen homework problems that reinfothe main conceptual and epistemological points.

I now discuss some other elements of my epistemolofocused curricula.

B. ‘‘Epistemology’’ homework and in-class problems

I regularly assigned homework and in-class problemssigned to foster reflection about learning. To encourage hesty ~as opposed to ‘‘telling the teacher what he wantshear’’!, I based grading on the completeness, not the contof their responses. Sample assignments include:

1. Think about the material you learned for lastweek’s quiz.

~a! What role did memorization play in yourlearning of the material?

~b! What makes the material ‘‘hard’’?

~c! What advice about how to study would yougive to a student taking this course next year?

@In California, asked in October and again inJanuary.#

2. On last week’s circular motion lab, there wereexperiments, conceptual questions about thoseexperiments, and ‘‘textbook-like’’ summaries. Ineach case, the summary cameafter you at-tempted to answer some questions about the ma-terial covered in the summary. But on other labs,I’ve put the summariesbefore the related ques-tions.

~a! When it comes to helping you learn the ma-terial, what are the advantages of putting thetextbook-like summariesbefore the conceptualquestions about that same material? Please gointo as much detail as possible.

~b! When it comes to helping you learn the ma-terial, what are the advantages of putting thetextbook-like summariesafter the conceptualquestions about that same material? Please gointo as much detail as possible.

@California and Virgina#

3. In lab last week, most people seemed sur-prised to find an apparent contradiction between

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common sense and Newton’s second law (Fnet

5ma), for a car cruising at constant velocity.But the night before the lab, you read a textbooksection about Newton’s first and second laws.Why didn’t you notice the apparent contradictionwhile doing the reading?

I’m not ‘‘yelling’’ at you or blaming you; I knowyou’re careful, conscientious readers. That’s whyit’s interestingto think about why the apparentcontradiction went unnoticed. What could youand/or the textbook have done differently to helpyou discover—and possibly resolve—the appar-ent contradiction?

@Virginia#

Student’s responses helped me understand their evol~or nonevolving!! epistemological views throughout the yeaFor instance, in response to question 1~a!, a below-averagestudent answered as follows:

‘‘...In the beginning, I memorized certain typesof graphs, thinking they might show up on thetest. But this was a really bad idea. I didn’t un-derstand the actual concept! Later I realized thatI had to understand the concept if I wanted to dowell on the quiz... . Visualizing a situation or aproblem really helps. It really helped me!’’

Another average student’s response hinted that he wasviewing learning largely as memorization, though focusion concepts more than formulas:

‘‘While the class is centered around understand-ing the basic conceptual theories of physics,some memorization is required. Although formu-las will be provided, you must know what theformula can solve and why it works. Memorizingthe concepts of physics is more important thanthe formulas...’’

Question 1~c! elicited a full paragraph from most studentswill present results in a separate paper.

In response to question 3, many students blamed thebook, without seriously rethinking their reading strategiesmay have helped those students to hear a few of their clmates suggest that thinking of examples acounterexamples—an example of what teachers wouldan active learning strategy—might bring apparent contrations to the surface. In any case, this constant feedback astudents’ epistemological beliefs helped me plan subseqclasses, and also helped me ‘‘nudge’’ students individua

C. Effort-based homework grading, and solutionshanded out with the assignment

My high school and college teaching experiences indicthat many students initially view doing homework as a serate activity from learning and studying. Worried abohomework grades, students often copy each others’ answscour the textbook for a similar problem, and spend dispportionate time on correcting their algebra in order to getright answer. By contrast, I wanted students to view homwork as an opportunity to learn the material, where ‘‘leaing’’ involves thinking through a problem, getting feedbacand modifying your thinking accordingly. For this reasonimplemented two untraditional policies.

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First, I based students’ homework grades entirelywhether their answers showed a good-faith effort to wrewith the material. Thoughtful wrong answers got highscores than ‘‘rote’’ correct answers. Grading went justquickly ~or just as slowly!! as traditional grading, dependinon how carefully I commented upon students’ ideas. Tgrading system lowered students’ anxiety level and remomuch of the incentive to ‘‘just get through’’ the homeworrather than trying to learn.

Second, I handed out detailed solutions with each assment, covering some but not all of the assigned questionsthat students could get immediate feedback. You may wder, ‘‘Didn’t students just copy your answers?’’ At firsmany of them did. But I gave no credit for answers that weclearly based on mine. More important from an epistemlogical standpoint, I gave a graded mini-quiz carefully chsen to test conceptual understanding each week for thefive weeks of class. Students who simply copied my homwork answers did poorly, and class discussions aboutissue helped point them toward why. In addition, studespent much of their in-class time solving problems togetin small groups, an experience many of them found helpfor learning the material, as revealed by epistemology homwork questions and by class discussions. In brief, the fimonth of class was explicitly designed to push studentsward the epistemological realization that the best waylearn physics is to think through problems, alone andgroups, andthen to get feedback; and that acquiring a coceptual understanding is the only way to do well on mquizzes. By the third or fourth mini-quiz, in both Californiand Virginia, most students had stopped copying my homwork solutions. Some students became adept at essengrading their own homework, with notes to themselves inmargins about insights and mistakes. By the way, studehad the opportunity to wipe out their poor mini-quiz scorby demonstrating mastery of the material on a later test.

I don’t mean to present too rosy a picture. In Californabout 30% of the students often handed in homeworkwas dashed off with little thought, a ‘‘minimal pass,’’ odidn’t hand in homework at all. Interestingly, all but two othree of these students ended up whipping off their ownswers instead of copying mine. This didn’t indicate epismological progress. Instead, it reflected the realization tspewing out the first thing that comes to mind is quicker aeasier than reading my answer, digesting it, and reproduit in one’s own words~so that I can’t tell they copied!. Witha few exceptions, these students who put minimal effort ihomework did poorly on tests. So, my homework policyno panacea. If traditionally graded homework assignmewould have elicited more productive effort from this setstudents, then my policy harmed their learning. I hypoesize, however, that in a traditionally graded physics clathese same students would have copied each others’ ansor taken other shortcuts around learning.

Among students who were trying to learn the materieither for its own sake or for doing well on tests, the poligenerally had the desired effect of focusing students’ atttion more on learning the concepts and less on gettingright answer. The quality of students’ work varied widelsome students put in a lot more thought than others,many students found the concepts to be very difficult. Beven the lower-quality responses generally expressed thedents’ own ideas.

Trade-offs. Writing the detailed homework solutions take

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a lot of time, though you can save hours by handingpreviously published worked problems.20 Grading all themini-quizzes takes extra time. Also, especially in CalifornI had to go extra slowly during the first month, so that sdents who took a long time to discover productive stustrategies had time to catch up.

D. Homework and test questions emphasizing explanation

My homework and tests included many standard quantive problems. But to reward qualitative, conceptureasoning—a crucial part of my strategy to push studetoward the view that physics knowledge is more concepthan factual—I asked a high percentage of conceptual qtions on homework and tests. Here are some samplequestions~not all from the same test!!:

1. A rocket of weightmg51000 N takes offfrom its launch pad, gets faster for a few sec-onds, and then travels upward at constant speed.Neglect air resistance. While the rocket movesupward at constant speed, the upward force ex-erted by the engine on the rocket is...

~a! zero

~b! greater than zero, but less than 1000 N

~c! equal to 1000 N

~d! greater than 1000 N

Explain your answer in a few sentences.

@California#

2. A hockey puck@Fig. 4# slides rightward alongthe ice with negligible friction, heading toward aspring attached to the wall. After reaching pointB, the puck gradually compresses the spring untilthe puck momentarily comes to rest at pointC;then the spring gradually decompresses, shootingthe puck leftward from pointB back towardpoint A.

~a! At point C, is thenet force on the puck right-ward, leftward, or zero? Explain.

~b! Taking rightward as the positive direction,sketch rough graphs of the puck’s position, ve-locity, and acceleration versus time... .

@Virginia#

3. In lab, we sometimes projected onto a screenthe image produced by a concave mirror. Is itpossible to project onto a screen the image pro-duced by aconvexmirror? Explain why or whynot, using a diagram to help you present youranswer.~Simply telling me whatkind of image itis does notexplainanything.!

Fig. 4. Diagram for the puck-and-spring test question, #2. When the pmomentarily comes to rest at point C, is the net force on the puck rightwleftward, or zero?

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4. This circuit @Fig. 5# consists of a battery andfour identical light bulbs. The numbers 1 through4 in the diagram arenot resistances; they’re justlabels.Each bulb has the same resistance.

~a! Rank the four bulbs in order of brightness.Briefly explain your reasoning, qualitatively~with no calculations!.

~b! If bulb 3 burns out~in which case no currentflows through it!, what happens to the brightnessof the other three bulbs?

@Virginia#

In addition, my quizzes and tests never asked an easy‘n’ chug question. In the past, I included such questionshelp weaker students earn points and to help everyoneconfidence. But this well-intentioned policy may have ledan unintended side effect: the reinforcement of students’pectation that rote application of equations leads to succat least in some cases. Now, when I want to include an equestion, I ask a conceptual question closely and transently related to an issue students addressed in lab.

E. Reduced use of traditional textbook

The high school textbook I used in California, and talgebra-based college textbook I used in Virginia, covehuge range of topics, devoting little space to each oWithin a given chapter, the book typically begins by intrducing formal definitions and equations, followed by a feexamples and real-life applications. By contrast, I was tryto teach students that learning physics often involvesstartingwith real-life examples and commonsense intuitions, abuilding upon them to make careful definitions, to figure oequations, and so on. During this process, I wanted studto unearth and examine their own intuitive ideas, refinithem when needed, an activity the textbook supports onlthe most cursory way. So, the textbook and I broadcast cflicting messages about how to learn physics. Althoughsophisticated learner can learn from a traditional textbootraditional textbook does not successfully challenge na¨veepistemological beliefs or help students become better leers. For this reason, extensive reliance on the textbook mhave undermined my epistemological agenda. I rarelysigned textbook sections other than those introducing facinformation.

Since many high school classes make minimal use of tbooks ~except perhaps for homework assignments!, my ne-glect of the textbook evoked little response.

kd,

Fig. 5. Diagram for circuit problem, #4. Students rank the four identibulbs in order of brightness. Then they consider what happens to the brness of the remaining bulbs if bulb 3 burns out.

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F. Fluid lesson plans

Sometimes I deviated from my lesson plan in order to taadvantage of a teachable moment. For instance, during ation lesson in California, the class did an experimentwhich a heavy and light book with the same cover a‘‘kicked’’ across the floor with the same initial speed. Theslide the same distance. The ensuing class discussionintended to help students make sense of this result bothtuitively and mathematically. But one student wonderaloud why, when an equally fast car and truck slam thbrakes simultaneously, they slide different distances.cause this question leads to physicalandepistemological in-sight, I made a big deal of it, highlighting the fact that reonciling everyday experience and intuitions with each otand with physics principles is an essential part of learnphysics. To reinforce this point, I replaced my plannhomework assignment with the student’s question aboutcar versus truck.~It’s a hard question! We discussed itclass the next day.!

G. Radically reduced content coverage

I wanted students to understand the difference betweedeep understanding and a superficial, rote understandingunderstand this difference, students mustactually developadeep understanding of interconnected chunks of mateUnfortunately, Force Concept Inventory scores and otevidence suggest that, when material is covered at the trtional pace, few students achieve a deep understandinNewtonian mechanics.12 Because of this, and because dcussions of epistemological issues ate up some classhomework time, I slowed down. Especially in Californiwhen students’ homework and quizzes indicated a continlack of understanding, I spent extra time on the topic.

Trade-offs. In California, because students’ pace of leaing determined the pace of coverage, I covered muchmaterial than originally planned. Judging from their perfomance on tests containing challenging qualitative problein addition to standard quantitative problems, most studeacquired a basic conceptual understanding of force andtion in one dimension, energy, waves, optics, and aspecelectrostatics. But we skipped momentum, oscillatory mtion, electric potential, electric circuits, magnetism, and allmodern physics. Even the leanest reform curricula inclusomeof these topics. Furthermore, because I didn’t expstudents to interesting topics they couldn’t understadeeply, such as particle physics and quantum wave/parduality, the class was drier than it might have been; my etemological goals sometimes collided with motivationgoals. Specifically, although my California students’ averalevel of agreement with ‘‘I am very interested in sciencerose from 3.67 out of 5 in September to 4.11 in Junep,0.05), several students—including some high achieverremained comparatively uninterested. Some of them mhave been turned on by topics I skipped. In addition, myCalifornia students might have learned more breadth, wout sacrificing depth, in a faster-paced class.

In Virginia, where I was teaching a pre-established criculum, I treated many topics~such as oscillatory motion!qualitatively but not quantitatively, and I skipped numerosubtopics covered by the other physics teachers. Thosetopics included much of rotational dynamics, capacitanand electromagnetic induction. Within a given topic, I oftspent more time on the basic concepts at the expens

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problem-solving techniques, techniques to which studentother classes were exposed. As a result, my quickest studmight have benefitted from more coverage.

In the Virginia high school, the physics teachers giveshared midterm and final exam. Because I was skippingde-emphasizing numerous topics, I was concerned thatstudents would be ill-prepared. Partly for this reasothroughout the semester I talked with the other teacherget a detailed sense of the content and difficulty level ofquestions they would want to include on the exam. In tway, I tried to figure out the minimum content coveragecould get away with. Then, when it came time to write tmidterm and final exam, I took an active part, tweaking texam to be slightly more conceptual and more focusedthe core topics than it had been the previous year. As a remy students were prepared, and performed well.~The otherteachers reported being quite happy with the exam, too.! Butunless I had monitored the likely contents of the exam, aunless I had taken active part in its formation, my reductin content coverage could have hurt my students’ perfmance. A poor performance almost certainly would havedermined epistemological messages I was trying to conv

H. Instructor commitment to epistemologicaldevelopment

A paper such as this always invites the criticism thatgood results stem not from the explicit curriculum, but frothe extra effort, commitment, enthusiasm, or skill of tteacher. Until other instructors implement similar curricuelements, this issue cannot be resolved. In this section, hever, I argue that the key to success isn’t the curriculumorthe instructor alone, but rather, a wholehearted commitmto fostering epistemological development manifested incurriculum and in the instructor’s attitude and moment-bymoment actions. If this is correct, then other instructors cachieve the same results, even though teasing apart instreffects from curriculum effects becomes less meaningwhere does ‘‘curriculum’’ end and ‘‘instructor’s real-timdecision about what to do next’’ begin?

Here’s the argument. First, the fact that so many excelphysics courses fail to foster significant epistemologichange, even courses incorporating some of the curricelements discussed above, suggests that isolated piecepistemologically focused curriculum aren’t enough. Instethe epistemological focus must suffuse every aspect ofcourse. Therefore, the instructor’s commitment to an epimological agenda must go beyond a willingness to impment certain curricular elements. For instance, simply reping a couple of labs with the epistemologically focused latutorials from Sec. IV A may make little difference. I canstress this enough: We have no reason to think that paadoption of the curricular elements discussed above will lto epistemological change.

Second, the classroom atmosphere created by the instor, and the way he/she interacts with individual studenundoubtedly plays a large role in fostering reflection ablearning. I considered fostering epistemological developmto be my primary goal, co-equal with fostering conceptudevelopment about physics. For this reason, I always kepistemological considerations in the front of my mind whplanning lessons, writing materials, setting policies, andteracting with students. In the words of an anonymousviewer, my implementation of an epistemologically focuscurriculum was holistic and wholehearted. But just beca

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this wholeheartedness is an instructor effect doesn’t mother instructors can’t be equally wholehearted.

V. CONCLUSION

Students’ epistemological beliefs—their views aboutnature of knowledge and learning—affect their mindsmetacognitive practices, and study habits in a physics couEven the best reform curricula, however, have not been vsuccessful at helping students develop more sophisticepistemological beliefs. By contrast, two different epistemlogically focused high-school courses—one honors, ononhonors—led to significant, favorable changes in studebeliefs, as measured by MPEX and by a related assessmMost of the curricular elements are suitable for both hschool and college.

My students, like students in other reform curricula, spmost of their time working in small groups on activities aproblems, parts of which resemble tutorials9 and RealTimephysics labs.16 But epistemological considerations pervadevery aspect of the course, including homework- and tquestion selection, homework-grading policy, class discsions, and even labs. For these reasons, and becausedent cannot learn about ‘‘understanding’’ without having tpersonal experience of understanding chunks of intercnected material, my courses covered fewer conceptsproblem-solving techniques than they would have in thesence of an epistemological agenda. Instructors interestefostering epistemological development must decide if thtrade-offs are worth it. This paper aims to spark discussabout these issues, highlighting the possibility of helping sdents become better learners, while also highlighting therifices entailed by taking this goal seriously.

ACKNOWLEDGMENTS

I’d like to thank David Hammer and two anonymous reerees for their detailed comments on an earlier draft ofpaper. This work was supported by National Science Fodation Grant Nos. DGE-9714474 and REC-0087519.

a!Electronic mail: elby@physics.umd.edu1Edward F. Redish, Jeffery M. Saul, and Richard N. Steinberg, ‘‘Studexpectations in introductory physics,’’ Am. J. Phys.66 ~3!, 212–224~1998!.

2David M. Hammer, ‘‘Epistemological beliefs in introductory physicsCogn. Instruct.12 ~2!, 151–183~1994!; David M. Hammer, ‘‘Two ap-proaches to learning physics,’’ Phys. Teach.27 ~9!, 664–670~1989!.

3For instance, see Marlene Schommer, ‘‘The effects of beliefs aboutnature of knowledge in comprehension,’’ J. Ed. Psych.82 ~3!, 498–504~1990!; Marlene Schommer, Amy Crouse, and Nancy Rhodes, ‘‘Epistemlogical beliefs and mathematical text comprehension: Believing itsimple does not make it so,’’ibid. 84, 435–443~1992!; Nancy B. Songerand Marcia C. Linn, ‘‘How do students’ views of science influence knowedge integration?,’’ inStudents’ Models and Epistemologies of Scien,edited by M. C. Linn, N. B. Songer, and E. L. Lewis~1991!, Vol. 28, pp.761–784; Barbara Y. White, ‘‘Thinkertools—Causal models, concepchange, and science education,’’ Cogn. Instruct.10 ~1!, 1–100~1993!.

4Marlene Schommer, ‘‘Epistemological Development and Academic Pformance Among Secondary Students,’’ J. Ed. Psych.85, 406–411~1993!.

5Researchers disagree about where to draw the boundaries aroundepiste-mologyandmetacognition. My arguments don’t rely on a precise choiceboundary between the two concepts.

6At a bigger high school, many of my students might have opted for‘‘honors’’ physics class or a ‘‘conceptual’’~low-math! physics class.

7See http://www.physics.umd.edu/rgroups/ripe/perg/expects/mpex.htmthe full survey.

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8Barbara White, Andrew Elby, John Frederiksen, and Christina Schw‘‘The Epistemological Beliefs Assessment for Physical Science,’’ psented at the American Education Research Association, Montreal, 1~unpublished!.

9Lillian C. McDermott, Peter S. Shaffer, and the Physics Education GroTutorials in Introductory Physics, Preliminary ed.~Prentice–Hall, UpperSaddle River, NJ, 1998!. For discussion, see Lillian C. McDermott anPeter S. Shaffer, ‘‘Research as a guide for curriculum development:example from introductory electricity. I. Investigation of student undstanding,’’ Am. J. Phys.60 ~11!, 994–1003~1992!.

10Patricia Heller, Ron Keith, and S. Anderson, ‘‘Teaching problem solvthrough cooperative grouping. 1. Group vs individual problem solvingAm. J. Phys.60 ~7!, 627–636~1992!.

11Priscilla W. Laws, ‘‘Workshop physics: Replacing lectures with real eperience,’’ inComputers in Physics Instruction: Proceedings, edited by E.F. Redish and J. S. Risley~Addison–Wesley, Reading, MA, 1989!;‘‘Calculus-based physics without lectures,’’ Phys. Today44 ~12!, 24–31~1991!; ‘‘New approaches to science and mathematics teaching at libarts colleges,’’ Deadalus128 ~1!, 217–240~1999!.

12Richard R. Hake, ‘‘Interactive-engagement vs traditional methods: A sthousand-student survey of mechanics test data for introductory phycourses,’’ Am. J. Phys.66 ~1!, 64–74~1998!.

13To get a sense of the correspondence, we can calculate the correcoefficient between students’ scores on an EBAPS subscale andscores on the corresponding MPEX cluster. The correlation betwEBAPS Structure of Knowledgeand the sum of MPEXConceptsandCoherenceis 0.65. The correlation between EBAPSNature of Learningand MPEXIndependenceis 0.42. Those correlations are both statisticasignificant top,0.05. By contrast, the correlation between EBAPSReal-life applicability and MPEXReality linkis only 0.23, which is of marginalstatistical significance (p50.09). The low correlation reflects a substative difference between the two subscales. MPEXReality link focusespartly on students’ views about whetherthey will use physics conceptsoutside the classroom, whereas EBAPS focuses more on studentsabout whether, in principle, classroom physics concepts describe pheena in the real world.

14Marlene Schommer, Amy Crouse, and Nancy Rhodes, ‘‘Epistemologbeliefs and mathematical text comprehension: Believing it is simple dnot make it so,’’ J. Ed. Psych.84, 435–443~1992!.

15After we finished Newtonian mechanics, my students achieved an avescore of 84% on the Force Concept Inventory, comparable to the posscores of Harvard students; see Hake~Ref. 12!. I did not give my studentsthe FCI as a pre-test. An independent sample of 250 other 11th gphysics students at the same school took the FCI as a pre-test, achieviaverage score of 32%. My California students did not take the FCIgenerally performed well on FCI-like questions included on tests, incling those presented in Sec. IV D.

16David R. Sokoloff, Ronald K. Thornton, and Priscilla W. Laws,RealTimePhysics: Active Learning Laboratories~Wiley, New York, 1999!. For dis-cussion, see Ronald K. Thornton and David R. Sokoloff, ‘‘Learning mtion concepts using real-time microcomputer-based laboratory tools,’’ AJ. Phys.58 ~9!, 858–868~1990!.

17See Eric Mazur,Peer Instruction: A User’s Manual~Prentice–Hall, UpperSaddle River, NJ, 1997!.

18‘‘The whole of science is nothing more than a refinement of everydthinking. It is for this reason that the critical thinking of the physicicannot possibly be restricted to the examination of concepts from hisspecific field. He cannot proceed without considering critically a mumore difficult problem, the problem of analyzing the nature of everydthinking.’’—Albert Einstein, ‘‘Physics and Reality,’’ J. Franklin Inst.221,~1936!.

19David M. Hammer, ‘‘Students’ beliefs about conceptual knowledgeintroductory physics,’’ Int. J. Sci. Educ.16 ~4!, 385–403~1994!.

20Many textbooks come with an instructor’s solution manual or a stuguide with worked problems. Other sources of problems with detasolutions include Andrew Elby,The Portable T.A.: A Physics ProblemSolving Guide. Volume 2, 2nd ed.~Prentice–Hall, Upper Saddle River, NJ1998!; Research and Education Association and M. Fogiel,The PhysicsProblem Solver~REA, New York, 1976!.

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