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Conceptual Problem Solving in Physics 291The problem categorization test, equation instantiation test, and findingerrors tests did not show any significant differences between groups atthe three schools. However, there was a 12% difference in equationinstantiation favoring CPS at School A, and an 11% difference in problemcategorization at School B that show trends in the appropriate direction.The finding errors test was extremely difficult for these students and almostno one was able to correctly identify conceptual mistakes in a solution.In addition to the quantitative measures, statements from some of theteachers indicated observable differences in students’ performance.Teacher C commented that students were producing a higher quality ofsolutions and were engaging in richer discussions in their groups. Moreobjectively, the class (compared to his previous class) had higher performanceon an energy-momentum unit test and on a district-wide physicsassessment.4.5. Conclusions from the high school studyOverall, the high school teachers responded favorably to using the CPSapproach and their students showed a consistent 10–20% advantage on acommon set of assessments compared to classes that were taught usingtraditional problem solving instruction. Out of the five different assessmentsadministered, the approach was particularly influential on students’responses to conceptual questions and to their problem solving processes.Remember that this intervention required no change in the curriculumand no extra instruction time.The instructional materials were intentionally flexible, and each teacherchose to implement strategy writing and two column solutions in a slightlydifferent style. Teacher A had moderate success by using the approachsomewhat informally with a subset of his own problems, whereas TeacherB produced substantial differences with an implementation that includedthe worksheet templates designed by researchers (the fidelity with whichTeacher B implemented CPS was extremely close to what was originallyintended by the designers). Teacher C chose to give students a great deal ofpractice selecting appropriate principles for problems without solvingthem completely, yet this still resulted in improved problem solving performance.All of these teachers routinely have students work in groupsduring class, and this was also true of class periods that included CPS.The teachers also addressed several points to consider when implementingthe approach. For example, in response to students’ resistance towriting strategies they had to provide external motivation for followingthe framework such as points on homework or exams. Some teacherssuggested CPS works best for later topics in mechanics (i.e., conservationlaws) and for more complex problems that require planning, such asproblems that involve a combination of multiple principles. The teachers
292 Jose P. Mestre et al.acknowledge that identifying and justifying principles is a higher levelproblem solving skill that is difficult for students, and students needappropriate scaffolding to learn how to do this. A promising addition tothe approach includes using synthesizing concept diagrams to emphasizethe main ideas learned in a course (Bagno & Eylon, 1997).5. CONCLUDING REMARKSWe have reviewed different implementations of CPS with universityand high school students both in carefully controlled laboratory studies aswell as in the messy environment of real college and high school classrooms.The common feature across all of our implementations of CPSwas the emphasis on conceptual analyses of problems, in particularattempting to illustrate how conceptual knowledge is used to solve problemsand to make more explicit some of the tacit knowledge used byexperts in solving problems. For example, justifying why a particularprinciple could be applied to solve a problem by examining the problem’sstory line (question asked, context, objects in the problem and attributespresent such as friction) is something that experts do naturally but is a skillthat is not overtly taught in traditional instruction.In all three implementations reviewed, students who practiced CPSshowed advantages in conceptual measures as well as in problem solving.Also heartening is the fact that there is an element of robustness in CPS;despite the relatively short intervention in the three high schools (abouteight 50-min classes over a 4-month period), and the wide variation inteachers’ implementation, CPS students displayed benefits from the intervention.Additional good news is that CPS can be ‘‘blended’’ into a coursewithout major curricular changes, redesign, or disruptions. However,CPS is an approach that demands more work from students than is typicalin traditional physics classes (e.g., deep thinking about concepts; morewriting of prose about abstract concepts and how they apply to problemsolving—both uncommon in physics classes), which is likely to meet withmore resistance from students than traditional instructional approaches toproblem solving.An interesting final question to entertain is What next? This, webelieve, is a more meaningful question at the high school level than atthe college level. Our early work exploring ways to help students gainconceptual understanding as well as similar early work by Larkin, Reif andtheir collaborators led many others to apply results from physics educationresearch to the design of curricular reforms in introductory physics instruction.Another catalyst to this reform was the availability of concept inventories(Hestenes, Wells, & Swackhamer, 1992; Thornton & Sokoloff,1998) that measured students’ understanding of basic physics concepts
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Series EditorBRIAN H. ROSSBeckman I
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Academic Press is an imprint of Els
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viContents3. Science of Multimedia
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xContributorsHenry L. Roediger, III
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xiiPrefaceand there has been much e
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xivPrefaceInterventions for improvi
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2 Henry L. Roediger et al.delayed t
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22 Henry L. Roediger et al.9. BENEF
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24 Henry L. Roediger et al.subjects
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26 Henry L. Roediger et al.feedback
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30 Henry L. Roediger et al.of some
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32 Henry L. Roediger et al.Benefit
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34 Henry L. Roediger et al.Hasher,
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36 Henry L. Roediger et al.Son, L.
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38 John Sweller1. INTRODUCTIONCogni
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40 John Sweller‘‘baby-talk.’
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42 John Swellerof cognitive or meta
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44 John SwellerTable 1Natural Infor
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46 John Swellerconfigurations. A ch
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48 John Swellerreproduction results
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50 John Swellerto mutation, without
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52 John Swellerusing a complex or,
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54 John SwellerThe human cognitive
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56 John Swellerepigenetic system ha
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58 John SwellerWe can determine lev
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60 John Swellerthan memorizing the
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62 John SwellerTable 2EffectVariabi
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64 John Swelleroccurs when students
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66 John Sweller3.3.3. The Split-Att
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68 John Swellermerely restates the
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70 John SwellerThe expertise revers
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72 John Swellerobtained a reverse m
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74 John Swelleractivities that othe
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76 John SwellerRenkl, A. (2005). Th
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78 Richard E. Mayercognitive theory
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80 Richard E. Mayerpictures beginni
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82 Richard E. MayerThe dualchannelp
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84 Richard E. Mayerlearner selects
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86 Richard E. MayerRosenthal, Rosno
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88 Richard E. MayerGenerative proce
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90 Richard E. Mayer4.2. Evidence-ba
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92 Richard E. Mayersituation could
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94 Richard E. Mayer(Moreno & Mayer,
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96 Richard E. Mayer4.3.1. Segmentin
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98 Richard E. Mayerpresenting the w
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100 Richard E. MayerThe multimedia
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102 Richard E. Mayergame in industr
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104 Richard E. MayerClark, R. C., &
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106 Richard E. MayerMayer, R. E., &
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108 Richard E. MayerSweller, J. (19
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110 Timothy J. Nokes and Daniel M.
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Incorporating Motivation into a The
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CHAPTERFIVEOn the Interplay of Emot
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Implications for Enhancing Academic
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CHAPTERSIXThere Is Nothing So Pract
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There Is Nothing So Practical as a
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CHAPTERSEVENThe Power of Comparison
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The Power of Comparison in Learning
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CHAPTEREIGHTThe Ubiquitous Patterns
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The Ubiquitous Patterns of Incorrec
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Page 318 and 319: Index 303LLabor in vain, 28Language
Page 320 and 321: Index 305OOntological categories of
Page 322 and 323: Index 307WWeb-delivered multimedia
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Page 326 and 327: Contents of Recent Volumes 311Under
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