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

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Implications for Enhancing Academic Achievement 151to elicit a negative emotional response (Ashcraft & Kirk, 2001; Chipman,Krantz, & Silver, 1992; Lyons & Beilock, 2010; Suinn, 1972) that includesincreased heartbeat and cortisol (Faust, 1992; Mattarella-Micke, Mateo,Kozak, Foster, & Beilock, 2011), worrisome thoughts (Richardson &Woolfolk, 1980), and an avoidance of situations that involve numericalprocessing (Krinzinger, Kaufmann, & Willmes, 2009). There are twogeneral interpretations for why higher math anxiety is associated with poormath achievement. The first suggests that highly math anxious students aresimply less competent in math to begin with, which leads them to experiencea higher degree of stress in this domain (Fennema, 1989). From thisaccount, math anxiety is the result of poor proficiency in math and not thecause of performance failure. This interpretation is rooted in some truth,since math anxious individuals are typically less motivated in math-relatedsituations than non-math-anxious individuals (Ashcraft & Kirk, 2001) andmath anxiety is associated with lower math competence as well as with anavoidance of math classes in general (Hembree, 1990).However, researchers like Ashcraft and Kirk (2001) contend that mathanxiety itself can cause deficits in math problem solving, which caneventually lead to poor math outcomes (Hopko, Ashcraft, Gute,Ruggiero, & Lewis, 1998). Support for this view comes from previouswork (Hembree, 1990; see also Kamann & Wong, 1993) showing thatcounseling interventions designed to treat math anxiety itself (but do notprovide math instruction or practice in mathematics) actually increase theposttreatment math achievement scores of math anxious individuals. Ifmath anxiety were simply the by-product of poor math competence, thenwe would not expect math anxious students receiving anxiety-specificcounseling to perform at the level of their low math anxious peers.Also, other work by Faust, Ashcraft, and Fleck (1996) has shown thatwhile math anxiety can impact how students perform on a timed test withdifficult math problems (high-load testing condition), the negative consequencesof math anxiety disappear when students are tested in anuntimed paper and pencil test (a low-load testing condition). Since paperand pencil tests allow students to reduce the cognitive load associated withmath problem solving, this work would suggest that math anxiety mayhave an online cognitive consequence, which supplements a reducedmath competency interpretation of math anxiety.4.1. A working memory interpretationBy online, we mean that math anxiety has an impact on the execution ofmath problem solving. Specifically, math problem solving situations arethought to encourage an anxiety response among math anxious individualsthat disrupts the cognitive processes responsible for math problem solving—namely, WM. Some of the earliest work supporting an online account
152 Sian L. Beilock and Gerardo Ramirezfound that students with high math anxiety took much longer to respond toarithmetic problems with a carry versus no-carry operations than those withlow math anxiety (Ashcraft & Faust, 1994; Faust et al., 1996). This issignificant because performing a carry operation highly depends on WM(Geary & Widaman, 1992), which led researchers to speculate that mathanxiety may be disrupting processes responsible for maintaining superiorperformance during cognitively demanding math problems.In a more direct test of this claim, Ashcraft and Kirk (2001) asked agroup of college students to solve a series of fairly easy arithmeticproblems that varied based on whether they required a carry operation(e.g., 25 + 17) or not (e.g., 23 + 11). Ashcraft and Kirk reasoned that ifmath anxiety impacts WM processing, then this should be particularlytrue of problems that require additional mental workload (e.g., arithmeticwith a carry operation). However, to really implicate WM as thesource of math anxiety failure, they asked students to concurrently solvea secondary task that taxes WM. This secondary task required studentsto memorize either two (low load) or six (high load) letters as theysolved math problems. Their results showed that among studentsassigned to the two-letter load condition, those with high versus lowmath anxiety did not differ in amount of errors committed when tryingto solve the math problems. This was true in both problems thatrequired carry operation and those that did not. However, amongstudents in the six-letter load condition, those with high math anxietycommitted significantly more errors than those with low math anxiety,but these effects were limited to problems with a carry operation.These results provided strong evidence that while math anxiety may berelated to math avoidance in general, it also seems to influence the onlineexecution of math problem solving. Furthermore, math anxiety does notseem to prevent efficient problem solving in all forms of math but isinstead particularly detrimental to problems that rely heavily on WMresources (Ashcraft & Kirk, 2001; Faust et al., 1996).4.2. Math anxiety developmentWhile most studies have concentrated on examining math anxiety in latehigh school and college populations, there is some work demonstratingthat math anxiety is present among both middle (Meece, Wigfield, &Eccles, 1990; Wigfield & Meece, 1988) and primary school students(Krinzinger et al., 2009). For example, Wigfield and Meece asked studentsas young as sixth grade to fill out a math anxiety questionnaire andan attitude questionnaire that assess students’ expectations for success andperceived ability in math. They found that higher math anxiety wasassociated with reduced perceptions of ability and future expectationsof success in mathematics. A similar pattern of results was found in a
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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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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
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
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Page 128 and 129: Incorporating Motivation into a The
Page 152 and 153: CHAPTERFIVEOn the Interplay of Emot
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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
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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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CHAPTERNINEConceptual Problem Solvi
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Conceptual Problem Solving in Physi
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IndexAAcademic performancedrive the
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Index 301Correct method comparison,
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Index 303LLabor in vain, 28Language
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Index 305OOntological categories of
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Index 307WWeb-delivered multimedia
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CONTENTS OF RECENT VOLUMESVolume 40
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Contents of Recent Volumes 311Under
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Contents of Recent Volumes 313Volum
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