the psychology of learning and motivation - Percepts and Concepts ...

More documents

Recommendations

Info

The Power of Comparison in Learning and Instruction 215In Rittle-Johnson et al. (2009), described above, we also included acompare-problem-types condition. Recall that in this study, students hadlittle previous experience with equation solving. For students whoattempted to use algebra at pretest, the compare-problem-types conditionwas less effective than the compare methods condition and was not moreeffective than the sequential condition. However, for students who didnot use algebra at pretest, the compare-problem-types condition wasmore effective than the compare methods condition, although it wasnot more effective than the sequential condition.Overall, our comparing problems conditions have not been especiallyeffective in supporting learning relative to comparing methods or sequentialstudy of examples (see Table 2). These findings corroborate concernsraised by Reed (1989) that for complex multistep methods, comparingproblems may not effectively support transfer. Our findings also suggestthat comparing problems solved with complex methods does not supportprocedural flexibility or conceptual understanding as well as comparingmethods. However, we are not ready to abandon comparing problems forsupporting mathematics learning. Problem comparison seems particularlyuseful in helping people recognize the relevance of a method for solvingnew problems, so it may be more helpful for supporting learning in taskswhere this is particularly difficult.3.3. Summary of Our Mathematics Classroom StudiesDesigning classroom studies pushed our thinking about different types ofcomparisons, what learning outcomes each supports, and when learnersare prepared to learn from comparison. We have evaluated two types ofcomparisons in mathematics classrooms—correct method comparisonand problem comparison. Comparing correct methods consistently supportedprocedural flexibility across studies for students who knew one ofthe solution methods at pretest (see Table 2). For these students, comparingmethods sometimes supported greater procedural knowledge (Rittle-Johnson & Star, 2007; Rittle-Johnson et al., 2009) or greater conceptualknowledge (Rittle-Johnson & Star, 2009; Rittle-Johnson et al., 2009; Star& Rittle-Johnson, 2009). For novices, who did not know one of thesolution methods at pretest, comparing methods was helpful only after weslowed the pace of the lesson, aiding flexible use of the methods. Overall,comparing methods can help a variety of students learn, but its advantagesare more substantial if students have sufficient prior knowledge. How bestto develop this prior knowledge is an important topic for future research.We have evaluated comparing problems in only two studies, and it hasbeen generally less effective than comparing methods, especially for studentswith prior knowledge in the domain. It may be more effective forlearning other mathematical topics and merits additional research. Finally,
216 Bethany Rittle-Johnson and Jon R. Staralthough we did not isolate the impact of other types of comparisons, wehave prompted students in all conditions to occasionally make problemcategory comparisons. For example, a few reflection prompts included anew equation and asked students if a particular methods could be used tosolve it (typically, it could not). Perhaps as a result, we have seen fewinstances of students attempting to apply a particular method inappropriately(i.e., having difficulty distinguishing problem categories).4. OUR YEARLONG STUDY ON USING COMPARISON INALGEBRA ICLASSROOMSGiven the promise of comparison for supporting mathematics learning,we wanted to evaluate the effectiveness of teachers using comparisonthroughout the school year. In collaboration with Kristie Newton, we arecurrently conducting a randomized controlled trial, evaluating whetherusing comparison throughout the Algebra I curriculum will improvestudent learning. The need to design a yearlong, teacher led classroomintervention encouraged us to consider a wider range of comparisontypes, and two new types emerged. In this section, we discuss the materialswe developed, particularly the types of comparisons we supported, andthen overview our study design.4.1. Materials: Types of ComparisonsOn the basis of the promise of our worked example-based approach tosupporting comparison, we developed a set of supplementary materials ofworked example pairs (WEPs) that could be used in conjunction with anyAlgebra I curriculum. They were designed to maximize their potentialimpact based on previous research. A sample WEP is shown in Figure 2.As before, the two worked examples were presented side by side. Tofacilitate processing of the examples, we included thought bubbles, wheretwo students (Alex and Morgan) described their solution methods. Weused common language in these descriptions as much as possible to helpfacilitate alignment of the examples.All WEPs included explanation prompts. To help build consistencyacross examples and scaffold appropriate reflection, we included threetypes of explanation prompts for each WEP. Understand prompts, such as‘‘How did Alex solve the equation?,’’ were meant to ensure that studentsunderstood each worked example individually. Compare prompts, such as‘‘What are some similarities and differences between Alex’s and Morgan’sways,’’ were meant to encourage comparison of the two worked examples.Understand and compare prompts were similar across comparison
Page 3 and 4:
Series EditorBRIAN H. ROSSBeckman I
Page 5 and 6:
Academic Press is an imprint of Els
Page 7 and 8:
viContents3. Science of Multimedia
Page 9 and 10:
This Page Intentionally Left Blank
Page 11 and 12:
xContributorsHenry L. Roediger, III
Page 13 and 14:
xiiPrefaceand there has been much e
Page 15 and 16:
xivPrefaceInterventions for improvi
Page 17 and 18:
2 Henry L. Roediger et al.delayed t
Page 19 and 20:
4 Henry L. Roediger et al.an indire
Page 21 and 22:
6 Henry L. Roediger et al.[(Figure_
Page 23 and 24:
8 Henry L. Roediger et al.[(Figure_
Page 25 and 26:
10 Henry L. Roediger et al.seems so
Page 27 and 28:
12 Henry L. Roediger et al.interpre
Page 29 and 30:
14 Henry L. Roediger et al.Table 2
Page 31 and 32:
16 Henry L. Roediger et al.improved
Page 33 and 34:
18 Henry L. Roediger et al.this mat
Page 35 and 36:
20 Henry L. Roediger et al.length o
Page 37 and 38:
22 Henry L. Roediger et al.9. BENEF
Page 39 and 40:
24 Henry L. Roediger et al.subjects
Page 41 and 42:
26 Henry L. Roediger et al.feedback
Page 43 and 44:
28 Henry L. Roediger et al.supporti
Page 45 and 46:
30 Henry L. Roediger et al.of some
Page 47 and 48:
32 Henry L. Roediger et al.Benefit
Page 49 and 50:
34 Henry L. Roediger et al.Hasher,
Page 51 and 52:
36 Henry L. Roediger et al.Son, L.
Page 53 and 54:
38 John Sweller1. INTRODUCTIONCogni
Page 55 and 56:
40 John Sweller‘‘baby-talk.’
Page 57 and 58:
42 John Swellerof cognitive or meta
Page 59 and 60:
44 John SwellerTable 1Natural Infor
Page 61 and 62:
46 John Swellerconfigurations. A ch
Page 63 and 64:
48 John Swellerreproduction results
Page 65 and 66:
50 John Swellerto mutation, without
Page 67 and 68:
52 John Swellerusing a complex or,
Page 69 and 70:
54 John SwellerThe human cognitive
Page 71 and 72:
56 John Swellerepigenetic system ha
Page 73 and 74:
58 John SwellerWe can determine lev
Page 75 and 76:
60 John Swellerthan memorizing the
Page 77 and 78:
62 John SwellerTable 2EffectVariabi
Page 79 and 80:
64 John Swelleroccurs when students
Page 81 and 82:
66 John Sweller3.3.3. The Split-Att
Page 83 and 84:
68 John Swellermerely restates the
Page 85 and 86:
70 John SwellerThe expertise revers
Page 87 and 88:
72 John Swellerobtained a reverse m
Page 89 and 90:
74 John Swelleractivities that othe
Page 91 and 92:
76 John SwellerRenkl, A. (2005). Th
Page 93 and 94:
78 Richard E. Mayercognitive theory
Page 95 and 96:
80 Richard E. Mayerpictures beginni
Page 97 and 98:
82 Richard E. MayerThe dualchannelp
Page 99 and 100:
84 Richard E. Mayerlearner selects
Page 101 and 102:
86 Richard E. MayerRosenthal, Rosno
Page 103 and 104:
88 Richard E. MayerGenerative proce
Page 105 and 106:
90 Richard E. Mayer4.2. Evidence-ba
Page 107 and 108:
92 Richard E. Mayersituation could
Page 109 and 110:
94 Richard E. Mayer(Moreno & Mayer,
Page 111 and 112:
96 Richard E. Mayer4.3.1. Segmentin
Page 113 and 114:
98 Richard E. Mayerpresenting the w
Page 115 and 116:
100 Richard E. MayerThe multimedia
Page 117 and 118:
102 Richard E. Mayergame in industr
Page 119 and 120:
104 Richard E. MayerClark, R. C., &
Page 121 and 122:
106 Richard E. MayerMayer, R. E., &
Page 123 and 124:
108 Richard E. MayerSweller, J. (19
Page 125:
110 Timothy J. Nokes and Daniel M.
Page 128 and 129:
Incorporating Motivation into a The
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
CHAPTERFIVEOn the Interplay of Emot
Page 154 and 155:
Implications for Enhancing Academic
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181: Implications for Enhancing Academic
Page 186 and 187: CHAPTERSIXThere Is Nothing So Pract
Page 188 and 189: There Is Nothing So Practical as a
Page 214 and 215: CHAPTERSEVENThe Power of Comparison
Page 216 and 217: The Power of Comparison in Learning
Page 242 and 243: CHAPTEREIGHTThe Ubiquitous Patterns
Page 244 and 245: The Ubiquitous Patterns of Incorrec
Page 280 and 281:
The Ubiquitous Patterns of Incorrec
Page 282 and 283:
The Ubiquitous Patterns of Incorrec
Page 284 and 285:
CHAPTERNINEConceptual Problem Solvi
Page 286 and 287:
Conceptual Problem Solving in Physi
Page 288 and 289:
Page 290 and 291:
Page 292 and 293:
Page 294 and 295:
Page 296 and 297:
Page 298 and 299:
Page 300 and 301:
Page 302 and 303:
Page 304 and 305:
Page 306 and 307:
Page 308 and 309:
Page 310 and 311:
Page 312 and 313:
Page 314 and 315:
IndexAAcademic performancedrive the
Page 316 and 317:
Index 301Correct method comparison,
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
Page 324 and 325:
CONTENTS OF RECENT VOLUMESVolume 40
Page 326 and 327:
Contents of Recent Volumes 311Under
Page 328 and 329:
Contents of Recent Volumes 313Volum
show all

the psychology of learning and motivation - Percepts and Concepts ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?