Telling stories: the perils and promise of using verbal reports to study math strategies.

The problem size effect in adult arithmetic performance is generally attributed to direct retrieval processes operating on a network representation in long-term memory. J. LeFevre and her colleagues (J. LeFevre, J. Bisanz, et al., 1996; J. LeFevre, G. S. Sadesky, & J. Bisanz, 1996) challenged this explanation using verbal report evidence that adults also use time consuming nonretrieval strategies to solve simple addition and multiplication. The authors replicated J. LeFevre and colleagues' methods, but added instructional biasing and silent control conditions to test these methods. Both reaction time and report results suggest that LeFevre and colleagues' conclusions about nonretrieval frequency may have been influenced by instructions that revealed the experimental hypothesis and affected participants' strategy reports. Obtaining evidence about adult strategy use in simple arithmetic will require understanding instructional demand and appropriate report methodology.

[1]  J. Payne Thinking Aloud: Insights Into Information Processing , 1994 .

[2]  R. Siegler,et al.  Strategy choice procedures and the development of multiplication skill. , 1988, Journal of experimental psychology. General.

[3]  M. Ashcraft Cognitive arithmetic: A review of data and theory , 1992, Cognition.

[4]  Mark H. Ashcraft,et al.  Mental addition in third, fourth, and sixth graders , 1982 .

[5]  G. Groen,et al.  A chronometric analysis of simple addition. , 1972 .

[6]  B. Fischhoff,et al.  Journal of Experimental Psychology: Human Learning and Memory , 1980 .

[7]  R. Siegler The perils of averaging data over strategies: An example from children's addition. , 1987 .

[8]  Jamie I. D. Campbell,et al.  Mental multiplication skill: Structure, process, and acquisition. , 1985 .

[9]  M. Ashcraft,et al.  The relationships among working memory, math anxiety, and performance. , 2001, Journal of experimental psychology. General.

[10]  Jeffrey Bisanz,et al.  Selection of Procedures in Mental Addition: Reassessing the Problem Size Effect in Adults , 1996 .

[11]  D. Geary,et al.  Simple and complex mental subtraction: strategy choice and speed-of-processing differences in younger and older adults. , 1993, Psychology and aging.

[12]  Thomas D. Cook,et al.  Subject effects in laboratory research: An examination of subject roles, demand characteristics, and valid inference. , 1972 .

[13]  David R. Paredes,et al.  Starting to add worse: Effects of learning to multiply on children's addition , 1990, Cognition.

[14]  K. A. Ericsson,et al.  Protocol analysis: Verbal reports as data, Rev. ed. , 1993 .

[15]  J. LeFevre,et al.  More on the relation between division and multiplication in simple arithmetic: Evidence for mediation of division solutions via multiplication , 1999, Memory & cognition.

[16]  W. J. Dixon,et al.  Processing Data for Outliers , 1953 .

[17]  M. Orne On the social psychology of the psychological experiment: With particular reference to demand characteristics and their implications. , 1962 .

[18]  G. Hitch,et al.  Separate roles for executive and phonological components of working memory in mental arithmetic , 2000, Memory & cognition.

[19]  M. McCloskey Cognitive mechanisms in numerical processing: Evidence from acquired dyscalculia , 1992, Cognition.

[20]  Robert J Crutcher,et al.  Telling What We Know: The Use of Verbal Report Methodologies in Psychological Research , 1994 .

[21]  Michael W. Faust Mathematics Anxiety Effects in Simple and Complex Addition , 1996 .

[22]  G D Logan,et al.  The transition from algorithm to retrieval in memory-based theories of automaticity , 1991, Memory & cognition.

[23]  A. Baroody Children's mathematical thinking , 1987 .

[24]  O. Svenson Memory retrieval of answers of simple additions as reflected in response latencies , 1985 .

[25]  Eric J. Johnson,et al.  The validity of verbal protocols , 1989, Memory & cognition.

[26]  S. Hecht,et al.  Individual solution processes while solving addition and multiplication math facts in adults , 1999, Memory & cognition.

[27]  M. Masson,et al.  Using confidence intervals in within-subject designs , 1994, Psychonomic bulletin & review.

[28]  Eric A. Jenkins,et al.  How Children Discover New Strategies , 1989 .

[29]  K. A. Ericsson,et al.  Protocol Analysis: Verbal Reports as Data , 1984 .

[30]  M. Perlmutter,et al.  Cognitive arithmetic: comparison of operations. , 1984, Journal of experimental psychology. Learning, memory, and cognition.

[31]  Ruth B. Ekstrom,et al.  MANUAL FOR KIT OF REFERENCE TESTS FOR COGNITIVE FACTORS (REVISED 1963) , 1963 .

[32]  Jamie I. D. Campbell Network interference and mental multiplication. , 1987 .

[33]  D. Geary,et al.  Individual differences in cognitive arithmetic. , 1987, Journal of experimental psychology. General.

[34]  C. Lebiere,et al.  The Atomic Components of Thought , 1998 .

[35]  Jeffrey Bisanz,et al.  Multiple routes to solution of single-digit multiplication problems. , 1996 .

[36]  Jamie I. D. Campbell Architectures for numerical cognition , 1994, Cognition.

[37]  D. Geary,et al.  Cognitive addition: strategy choice and speed-of-processing differences in young and elderly adults. , 1991, Psychology and aging.

[38]  Mark H. Ashcraft,et al.  The development of mental arithmetic: A chronometric approach☆ , 1982 .

[39]  Timothy D. Wilson,et al.  The Proper Protocol: Validity and Completeness of Verbal Reports , 1994 .

[40]  M. Page,et al.  Manipulations of a Verbal Conditioning Situation Based upon Demand Characteristics Theory. , 1973 .

[41]  Mark H. Ashcraft,et al.  Cognitive Psychology and Simple Arithmetic: A Review and Summary of New Directions. , 1995 .

[42]  Livingston Alexander,et al.  The Development of an Abbreviated Version of the Mathematics Anxiety Rating Scale , 1989 .

[43]  Mark H. Ashcraft,et al.  Evidence for retrieval and decision processes in mental addition , 1978 .