Abstract
The ability to identify schematic knowledge is an important goal for both assessment and instruction. In the current paper, schematic knowledge of statistical probability theory is explored from the declarative-procedural framework using multiple methods of assessment. A sample of 90 undergraduate introductory statistics students was required to classify 10 pairs of probability problems as similar or different; to identify whether 15 problems contained sufficient, irrelevant, or missing information (text-edit); and to solve 10 additional problems. The complexity of the schema on which the problems were based was also manipulated. Detailed analyses compared text-editing and solution accuracy as a function of text-editing category and schema complexity. Results showed that text-editing tends to be easier than solution and differentially sensitive to schema complexity. While text-editing and classification were correlated with solution, only text-editing problems with missing information uniquely predicted success. In light of previous research these results suggest that text-editing is suitable for supplementing the assessment of schematic knowledge in development.
Article PDF
Similar content being viewed by others
References
J.R. Anderson (1982) ArticleTitleAcquisition of cognitive skill Psychological Review 89 IssueID4 369–406 Occurrence Handle10.1037//0033-295X.89.4.369
J.R. Anderson (1990) The Adaptive Character of Thought (Vol.1) Erlbaum NJ: Hillsdale
J.R. Anderson R. Milson (1989) ArticleTitleHuman memory: An adaptive perspective Psychological Review 96 IssueID4 703–719 Occurrence Handle10.1037//0033-295X.96.4.703
J.R. Anderson D.M. Neves (1981) Knowledge compilation: Mechanisms for the automatization of cognitive skills J.R. Anderson (Eds) Cognitive Skills and their Acquisition Lawrence Erlbaum Associates Hillsdale, NJ 57–84
J.R. Anderson C.D. Schunn (2000) Implications of the ACT-R learning theory: No magic bullets R. Glaser (Eds) Advances in Instructional Psychology (Vol. 5) Erlbaum Mahwah, NJ 1–33
M. Benaroch (2001) ArticleTitleDeclarative representation of strategic control knowledge International Journal of Human–Computer Studies 55 881–917 Occurrence Handle10.1006/ijhc.2001.0511
D.P. Birney G.S. Halford (2002) ArticleTitleCognitive complexity of suppositional reasoning: An application of the relational complexity metric to the knight-knave task Thinking and Reasoning 8 IssueID2 109–134 Occurrence Handle10.1080/13546780143000161
M.D.S. Braine (1990) The “Natural Logic” approach to reasoning W.F. Overton (Eds) Reasoning, Necessity, and Logic: Developmental Perspectives Lawrence Erlbaum Hillsdale, NJ 133–157
R.M.J. Byrne S.J. Handley (1997) ArticleTitleReasoning strategies for suppositional deductions Cognition 62 1–49 Occurrence Handle10.1016/S0010-0277(96)00720-2 Occurrence Handle1:STN:280:ByiC2M%2Flsl0%3D Occurrence Handle8997169
T.N. Carraher D. Carraher A.D. Schliemann (1985) ArticleTitleMathematics in the streets and in schools British Journal of Developmental Psychology 3 21–29
P. Chandler J. Sweller (1991) ArticleTitleCognitive load theory and the format of instruction Cognition and Instruction 8 293–332
Z. Chen (1999) ArticleTitleSchema induction in children’s analogical problem solving Journal of Educational Psychology 91 IssueID4 703–715 Occurrence Handle10.1037//0022-0663.91.4.703
P.W. Cheng K.J Holyoak (1985) ArticleTitlePragmatic reasoning schemas Cognitive Psychology 17 391–416 Occurrence Handle10.1016/0010-0285(85)90014-3 Occurrence Handle1:STN:280:BimD2MvmvFE%3D Occurrence Handle4064622
M.T. Chi P.J.H. Fletovich R. Glaser (1981) ArticleTitleCategorization and representation of physics problems by experts and novices Cognitive Sciences 5 121–152
M.T. Chi R. Glaser E. Rees (1982) Expertise in problem solving R.J. Sternberg (Eds) Advances in the Psychology of Human Intelligence (Vol. 1) Lawrence Erlbaum Associates Hillsdale, New Jersey 7–75
N.J. Cohen R.A. Poldrack H. Eichenbaum (1997) ArticleTitleMemory for items and memory for relations in the procedural/declarative memory framework Memory 5 131–178 Occurrence Handle1:STN:280:ByiA3c7gslM%3D Occurrence Handle9156097
M Cook (2001) Mathematics: The thinking arena for problem solving A.L. Costa (Eds) Minds. A Resource Book for Teaching Thinking ASCD VA
G. Cooper J. Sweller (1987) ArticleTitleEffects of schema acquisition and rule automation on mathematical problem-solving transfer Journal of Educational Psychology 79 IssueID4 347–362 Occurrence Handle10.1037//0022-0663.79.4.347
T. Jong Particlede M. Ferguson-Hessler (1986) ArticleTitleCognitive structures of good and poor novice problem solvers in physics Journal of Educational Psychology 78 IssueID4 279–288 Occurrence Handle10.1037//0022-0663.78.4.279
T. Jong Particlede M. Ferguson-Hessler (1996) ArticleTitleTypes and qualities of knowledge Educational Psychologist 31 IssueID2 105–113
Garfield, J. (1994). Beyond testing and grading: Using assessment to improve student learning. Journal of Statistics Education, 2(1), Available online at http://www. amstat.org/publications/jse/v2n1/garfield.html
M.L. Gick (1986) ArticleTitleProblem-solving strategies Educational Psychologist 21 IssueID1 & 2 99–120
M.L. Gick K.J. Holyoak (1983) ArticleTitleSchema induction and analogical transfer Cognitive Psychology 15 1–38 Occurrence Handle10.1016/0010-0285(83)90002-6
G.S. Halford (1993) Children’s Understanding: The Development of Mental Models Lawrence Erlbaum Associates Hillsdale, NJ
M. Hegarty M. Koshevnikov (1999) ArticleTitleTypes of visual-spatial representations and mathematical problem solving Journal of Educational Psychology 91 IssueID4 684–689 Occurrence Handle10.1037//0022-0663.91.4.690
P.N. Johnson-Laird R.M. Byrne (1991) Deduction Lawrence Erlbaum Associates Hove
K.C. Kirasic G.L. Allen S.H. Dobson K.S. Binder (1996) ArticleTitleAging, cognitive resources, and declarative learning Psychology and Aging 11 IssueID4 658–670 Occurrence Handle10.1037//0882-7974.11.4.658 Occurrence Handle1:STN:280:ByiC2M3nvFI%3D Occurrence Handle9000297
Konold, C. (1995). Issues in assessing conceptual understanding in probability and statistics. Journal of Statitics Education, 3(1), Available online at http://www. amstat.org/publications/jse/v3n1/konold.html
J. Littlefield J.J. Rieser (1993) ArticleTitleSemantic features of similarity and children’s strategies for identifying relevant information in mathematical story problems Cognition and Instruction 11 IssueID2 133–188
R. Low R. Over (1989) ArticleTitleDetection of missing and irrelevant information within algebraic story problems British Journal of Educational Psychology 59 296–305
R. Low R. Over (1990) ArticleTitleText editing of algebraic word problems Australian Journal of Psychology 42 IssueID1 63–73
R. Low R. Over (1992) ArticleTitleHierarchical ordering of schematic knowledge relating to area-of-rectangle problems Journal of Educational Psychology 84 IssueID1 62–69 Occurrence Handle10.1037//0022-0663.84.1.62
R. Low R. Over (1993) ArticleTitleGender differences in solution of algebraic word problems containing irrelevant information Journal of Educational Psychology 85 IssueID2 331–339 Occurrence Handle10.1037//0022-0663.85.2.331
R. Low R. Over L. Doolan S. Michell (1994) ArticleTitleSolution of algebraic word problems following training in identifying necessary and sufficient information within problems American Journal of Psychology 107 IssueID3 423–439
R.E. Mayer (1982) ArticleTitleMemory for algebra story problems Journal of Educational Psychology 74 IssueID2 199–216 Occurrence Handle10.1037//0022-0663.74.2.199
B.H. Ngu R. Low J. Sweller (2002) ArticleTitleText editing in chemistry instruction Instructional Science 30 379–402 Occurrence Handle10.1023/A:1019833014623
L.R. Novick S.M. Hurley M. Francis (1999) ArticleTitleEvidence for abstract, schematic knowledge of three spatial diagram representations Memory and Cognition 27 IssueID2 288–308 Occurrence Handle1:STN:280:DyaK1M3ktlShtA%3D%3D
T. Nuñes (1994) Street intelligence R.J. Sternberg (Eds) Encyclopedia of Human Intelligence (Vol. 2) Macmillan New York 1045–1049
Piaget, J. (1950). The Psychology of Intelligence (M. Piercy & Berlyne., Trans.): Routledge & Kegan Paul
J.L. Quilici R.E. Mayer (1996) ArticleTitleRole of examples in how students learn to categorise statistics word problems Journal of Educational Psychology 88 IssueID1 144–161 Occurrence Handle10.1037//0022-0663.88.1.144
J.L. Quilici R.E. Mayer (2002) ArticleTitleTeaching students to recognize structural similarities between statistics word problems Applied Cognitive Psychology 16 IssueID3 325–342 Occurrence Handle10.1002/acp.796
L. Rips (1983) ArticleTitleCognitive processes in propositional reasoning Psychological Review 90 IssueID1 38–71 Occurrence Handle10.1037//0033-295X.90.1.38
L. Rips (1989) ArticleTitleThe psychology of knights and knaves Cognition 31 85–116 Occurrence Handle10.1016/0010-0277(89)90019-X Occurrence Handle1:STN:280:BiaB2M%2FisFY%3D Occurrence Handle2486296
L. Rips (1994) The Psychology of Proof: Deductive Reasoning in Human Thinking MIT Press Cambridge, Mass
B. Rittle-Johnson R.S. Siegler M.W. Alibali (2001) ArticleTitleDeveloping conceptual understanding and procedural skill in mathematics: An iterative process Journal of Educational Psychology 93 346–362 Occurrence Handle10.1037//0022-0663.93.2.346
D.E. Rumelhart D.A. Norman (1981) Analogical processes in learning J.R. Anderson (Eds) Cognitive Skills and their Acquisition. Lawrence Erlbaurm Associates Hillsdale, NJ 335–359
E.R. Savelsbergh T. Jong Particlede M. Ferguson-Hessler (2002) ArticleTitleSituational knowledge in physics: The case of electrodynamics Journal of Research in Science Teaching 39 IssueID10 928–951 Occurrence Handle10.1002/tea.10057
A.H. Schoenfeld D.J. Herrmann (1982) ArticleTitleProblem perception and knowledge structure in expert and novice mathematical problem solvers Journal of Experimental Psychology: Learning, Memory, and Cognition 8 IssueID5 484–494
J. Sweller (1988) ArticleTitleCognitive load during problem solving: Effects on learning Cognitive Science 12 257–285 Occurrence Handle10.1016/0364-0213(88)90023-7
J. Sweller (1989) ArticleTitleCognitive technology: Some procedures for facilitating learning and problem solving in mathematics and science Journal of Educational Psychology 81 IssueID4 457–466 Occurrence Handle10.1037//0022-0663.81.4.457
J. Sweller (1993) ArticleTitleSome cognitive processes and their consequences for the organisation and presentation of information Australian Journal of Psychology 45 IssueID1 1–8
J. Sweller P. Chandler P. Tierney M. Cooper (1990) ArticleTitleCognitive load and selective attention as factors in the structuring of technical material Journal of Experimental Psychology: General 119 176–192 Occurrence Handle10.1037//0096-3445.119.2.176
J. Sweller M. Levine (1982) ArticleTitleEffects of goal specificity on means-ends analysis and learning Journal of Experimental Psychology: Learning, Memory, and Cognition 8 IssueID5 463–474
J. Sweller R. Mawer W. Howe (1982) ArticleTitleConsequences of history-cued and means-ends strategies in problem solving American Journal of Psychology 95 455–483
J. Sweller J. Van Merriënboer F. Paas (1998) ArticleTitleCognitive architecture and instructional design Educational Psychology Review 10 IssueID3 251–296 Occurrence Handle10.1023/A:1022193728205
InstitutionalAuthorNameUniversity of Southern Queensland (1993) Unit 75002 Data Analysis Study Book Distance Education Centre Toowoomba, USQ
T. Van Gog F. Paas J. Van Merriënboer (2004) ArticleTitleProcess-oriented worked examples: Improving transfer performance through enhanced understanding Instructional Science 32 83–98 Occurrence Handle10.1023/B:TRUC.0000021810.70784.b0
M. Ward J. Sweller (1990) ArticleTitleStructuring effective worked examples Cognition and Instruction 7 IssueID1 1–30
D.J. Woltz (1988) ArticleTitleAn investigation of the role of working memory in procedural skill acquisition Journal of Experimental Psychology. General 117 IssueID3 319–331 Occurrence Handle10.1037//0096-3445.117.3.319
D.J. Woltz M.K. Gardner S.P. Gyll (2000) ArticleTitleThe role of attention processes in near transfer of cognitive skills Learning and Individual Differences 12 209–251 Occurrence Handle10.1016/S1041-6080(01)00038-3
X. Zhu H.A. Simon (1987) ArticleTitleLearning mathematics from examples and by doing Cognition and Instruction 4 IssueID3 137–166
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Birney, D.P., Fogarty, G.J. & Plank, A. Assessing schematic knowledge of introductory probability theory. Instr Sci 33, 341–366 (2005). https://doi.org/10.1007/s11251-005-3198-7
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11251-005-3198-7