Tara Chiatovich, Cognitive Development Quad Chart De Bock, D., Van Dooren, W., Janssens, D., Verschaffel, L. (2002). Improper use of linear reasoning: An in-depth study of the nature and the irresistibility of secondary school students

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Tara Chiatovich, Cognitive Development Quad
ChartDe Bock, D., Van Dooren, W., Janssens, D.,
Verschaffel, L. (2002). Improper use of linear
reasoning An in-depth study of the nature and
the irresistibility of secondary school students
errors. Educational Studies in Mathematics, 50,
311-334.
Research Questions What aspects of childrens knowledge base are responsible for the occurrence and strength of the phenomenon of improperly using the linear model in word problems? How do these aspects relate to other more general misconceptions? Method Researchers conducted in-depth interviews with 20 7th- and 20 10th-graders consisting of 5 phases (1) a non-linear word problem that children had to solve and a question about their confidence that they had found the correct solution and (2-5) various forms of help (all based on creating cognitive conflict) with the problem. The word problem used two sizes of an irregular figure (e.g., Santa Clause) and indirectly asked how much larger the big figure was than the small figure (e.g., by asking how much more paint would be needed for the big figure).
Results Many students were slow to abandon their incorrect answers, and some were not convinced by the correct solution. Wrong answers were primarily due to (a) intuitive nature of linearity, (b) explicit (mis)application of linearity, (c) lack of geometrical understanding (e.g., not knowing that the width increases at the same rate as the height), and (d) incorrect word problem beliefs/strategies. students improper use of linear reasoning can also be seen as a symptom of an immature and even distorted disposition towards mathematical modelling (p. 330). Strengths Good use of pilot to avoid problems (e.g., different versions of a similar word problem so that students would not get inside information from past participants, computations involved just hard enough) right method for the research questions. Weaknesses Rather small homogenous sample (Flemish students at a boarding school) lack of generalizability.