The consistency effect depends on markedness in less successful but not successful problem solvers : An eye movement study in primary school children

This study examined the effects of consistency (relational term consistent vs. inconsistent with required arithmetic operation) and markedness (relational term unmarked [‘more than’] vs. marked [‘less than’]) on word problem solving in 10–12 years old children differing in problem-solving skill. The results showed that for unmarked word problems, less successful problem solvers showed an effect of consistency on regressive eye movements (longer and more regressions to solution-relevant problem information for inconsistent than consistent word problems) but not on error rate. For marked word problems, they showed the opposite pattern (effects of consistency on error rate, not on regressive eye movements). The conclusion was drawn that, like more successful problem solvers, less successful problem solvers can appeal to a problem-model strategy, but that they do so only when the relational term is unmarked. The results were discussed mainly with respect to the linguistic–semantic aspects of word problem solving.

[1]  K. Rayner Eye movements in reading and information processing: 20 years of research. , 1998, Psychological bulletin.

[2]  Cesare Cornoldi,et al.  Working memory and intrusions of irrelevant information in a group of specific poor problem solvers , 1999, Memory & cognition.

[3]  Lieven Verschaffel,et al.  Influence of the semantic structure of word problems on second graders' eye movements. , 1990 .

[4]  Manfred Bierwisch,et al.  Somewhat Longer — Much Deeper — Further and Further: Epilogue to the Dimensional Adjective Project , 1989 .

[5]  H. Lee Swanson,et al.  The Influence of Working Memory and Classification Ability on Children′s Word Problem Solution , 1993 .

[6]  M J Pickering,et al.  The processing of metonymy: evidence from eye movements. , 1999, Journal of experimental psychology. Learning, memory, and cognition.

[7]  Sheila J. Jones Visual and verbal processes in problem-solving , 1970 .

[8]  M. Hegarty,et al.  Comprehension of Arithmetic Word Problems: Evidence from Students' Eye Fixations. , 1992 .

[9]  Diane J. Briars,et al.  An integrated model of skill in solving elementary word problems cognition and instruction , 1984 .

[10]  W Kintsch,et al.  Understanding and solving word arithmetic problems. , 1985, Psychological review.

[11]  Mike Rinck,et al.  Chapter 16 – Eye Movement Measures to Study Global Text Processing , 2003 .

[12]  R. Mayer,et al.  Students' miscomprehension of relational statements in arithmetic word problems. , 1987 .

[13]  M. Bierwisch,et al.  Dimensional Adjectives: Grammatical Structure and Conceptual Interpretation , 1989 .

[14]  Peter A. Frensch,et al.  The Role of Information Reduction in Skill Acquisition , 1996, Cognitive Psychology.

[15]  Gary R. Morrison,et al.  The Role of Rewording and Context Personalization in the Solving of Mathematical Word Problems. , 1991 .

[16]  Francesca Pazzaglia,et al.  A comparison of updating processes in children good or poor in arithmetic word problem-solving , 2005 .

[17]  E. Stern,et al.  What makes certain arithmetic word problems involving the comparison of sets so difficult for children , 1993 .

[18]  H. Schriefers Lexical and conceptual factors in the naming of relations , 1990, Cognitive Psychology.

[19]  J. Stevens Applied Multivariate Statistics for the Social Sciences , 1986 .

[20]  M. Schoot,et al.  Lexical ambiguity resolution in good and poor comprehenders: An eye fixation and self-paced reading study in primary school children , 2009 .

[21]  Stephen J. Pape,et al.  Compare word problems: Consistency hypothesis revisited , 2003 .

[22]  P. French Linguistic marking, strategy, and affect in syllogistic reasoning , 1979, Journal of Psycholinguistic Research.

[23]  M A Just,et al.  A theory of reading: from eye fixations to comprehension. , 1980, Psychological review.

[24]  K. Denise Muth,et al.  Solving Arithmetic Word Problems: Role of Reading and Computational Skills , 1984 .

[25]  Stuart K. Card,et al.  Role of semantics in remembering comparative sentences , 1969 .

[26]  G. McConkie,et al.  What guides a reader's eye movements? , 1976, Vision Research.

[27]  E. Corte,et al.  Influence of rewording verbal problems on children's problem representations and solutions , 1985 .

[28]  E. D. Bruyne,et al.  WISC-R: Nederlandstalige uitgave , 1986 .

[29]  P N Johnson-Laird,et al.  Reasoning about relations. , 2005, Psychological review.

[30]  Jamie I. D. Campbell,et al.  Identical elements model of arithmetic memory: Extension to addition and subtraction , 2006, Memory & cognition.

[31]  W. Kintsch The role of knowledge in discourse comprehension: a construction-integration model. , 1988, Psychological review.

[32]  Kerry Lee,et al.  Working memory and literacy as predictors of performance on algebraic word problems. , 2004, Journal of experimental child psychology.

[33]  R. Kail,et al.  Sources of developmental change in children's word-problem performance. , 1999 .

[34]  James G. Greeno,et al.  Developmental analysis of understanding language about quantities and of solving problems. , 1988 .

[35]  Lieven Verschaffel,et al.  Solving compare problems: An eye movement test of Lewis and Mayer's consistency hypothesis. , 1992 .

[36]  Richard E. Mayer,et al.  Frequency norms and structural analysis of algebra story problems into families, categories, and templates , 1981 .

[37]  L. Siegel,et al.  Short-term memory, working memory, and inhibitory control in children with difficulties in arithmetic problem solving. , 2001, Journal of experimental child psychology.

[38]  H. Haider,et al.  Eye movement during skill acquisition: More evidence for the information-reduction hypothesis , 1999 .

[39]  M. Sommer,et al.  Psychometric Approaches Help Resolve Competing Cognitive Models: When Less Is More Than It Seems , 2005 .

[40]  E. Corte,et al.  The Effect of Semantic Structure on First Graders' Strategies for Solving Addition and Subtraction Word Problems. , 1987 .

[41]  Heiner Deubel,et al.  The mind's eye : cognitive and applied aspects of eye movement research , 2003 .

[42]  John H. Mueller,et al.  Solving Difference Problems: Wording Primes Coordination. , 1994 .

[43]  John D. Bransford,et al.  Teaching thinking and problem solving: Research foundations. , 1986 .

[44]  H. H. Clark,et al.  Psychology and language : an introduction to psycholinguistics , 1979 .

[45]  W. Kintsch,et al.  The role of understanding in solving word problems , 1988, Cognitive Psychology.

[46]  Lieven Verschaffel,et al.  Using Retelling Data to Study Elementary School Children's Representations and Solutions of Compare Problems. , 1994 .

[47]  Menno van der Schoot,et al.  The Role of Two Reading Strategies in Text Comprehension: An Eye Fixation Study in Primary School Children. , 2008 .

[48]  Herbert H. Clark,et al.  Linguistic processes in deductive reasoning. , 1969 .

[49]  M. Hegarty,et al.  Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. , 1995 .

[50]  U. Andersson The contribution of working memory to children's mathematical word problem solving , 2007 .