Compare word problems: Consistency hypothesis revisited

Abstract Compare problems involve relationships between quantities. In inconsistent language (IL) formats, relational terms conflict with solution operations. Lewis and Mayer’s (1987) consistency hypothesis, which explains likely translations of IL problems to match problem solvers’ schemas, is examined Using think-aloud and recall data. Supporting hypotheses, students committed more errors overall and reversal errors specifically (i.e., used opposite operation) on IL than their consistent language (CL) counterparts and recalled IL problems as CL problems especially following reversal errors. Counter to expectations, language consistency did not result in differences in behaviors, reading or response times, or quality of recall. Additional analyses indicate a strong impact of fraction-of-a-number relational terms and provide evidence of difficulties forming representations and solving problems involving fraction-of-a-number construction.

[1]  C. Hirsch.  Curriculum and Evaluation Standards for School Mathematics , 1988 .

[2]  Peter Smagorinsky,et al.  The Reliability and Validity of Protocol Analysis , 1989 .

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

[4]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[5]  J. Hiebert.  Conceptual and procedural knowledge : the case of mathematics , 1987 .

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

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

[8]  Peter Afflerbach,et al.  Verbal Protocols of Reading: The Nature of Constructively Responsive Reading , 1996 .

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

[10]  A. Schoenfeld.  Cognitive Science and Mathematics Education , 1987 .

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

[12]  Louise M. Rosenblatt,et al.  The Transactional Theory of Reading and Writing , 2018, Theoretical Models and Processes of Literacy.

[13]  Thomas P. Carpenter,et al.  Problem Structure and First-Grade Children's Initial Solution Processes for Simple Addition and Subtraction Problems , 1981 .

[14]  B. Greer.  Multiplication and division as models of situations. , 1992 .

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

[16]  E. Corte,et al.  Making sense of word problems , 2000 .

[17]  E. Fischbein,et al.  THE ROLE OF IMPLICIT MODELS IN SOLVING VERBAL PROBLEMS IN MULTIPLICATION AND DIVISION , 1985 .

[18]  Jacob Cohen,et al.  A power primer. , 1992, Psychological bulletin.

[19]  Harry Singer,et al.  Theoretical models and processes of reading , 1976 .

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

[21]  E. Corte,et al.  An empirical test of the impact of primitive intuitive models of operations on solving word problems with a multiplicative structure , 1996 .

[22]  Richard E. Mayer,et al.  Memory for algebra story problems. , 1982 .

[23]  Alan H. Schoenfeld,et al.  Episodes and Executive Decisions in Mathematical Problem Solving. , 1981 .

[24]  G. Roland,et al.  Council of Teachers of Mathematics , 1999 .

[25]  W. Kintsch,et al.  Strategies of discourse comprehension , 1983 .

[26]  Peter P. Afflerbach,et al.  On the Use of Verbal Reports in Reading Research , 1984 .

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

[28]  Jacob Cohen.  Statistical Power Analysis for the Behavioral Sciences , 1969, The SAGE Encyclopedia of Research Design.

[29]  Carolyn N. Hedley,et al.  Thinking and literacy : the mind at work , 1995 .

[30]  Alan H. Schoenfeld,et al.  Mathematical Problem Solving , 1985 .

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

[32]  R. Lesh,et al.  Acquisition of mathematics concepts and processes , 1983 .

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

[34]  R. Sternberg.  Human Abilities: An Information Processing Approach , 1985 .

[35]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

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