Example of task analysis of math problem-solving

The following article, although quite technical and quantoid in nature, includes an interesting task-analysis flow chart of mathematical problem solving that might serve as a conceptual model for analyzing cognitive and achievement tasks....the figure caught my attention.

[Double click image to enlarge]

Daniel, R. C., & Embretson, S. E. (2010). Designing Cognitive Complexity in Mathematical Problem-Solving Items. Applied Psychological Measurement, 34(5), 348-364.

Cognitive complexity level is important for measuring both aptitude  and achievement in large-scale testing. Tests for standards-based  assessment of mathematics, for example, often include cognitive  complexity level in the test blueprint. However, little research  exists on how mathematics items can be designed to vary in cognitive complexity level. In fact, determining the cognitive complexity level of items is usually based on correspondence to definitions rather than on empirically and theoretically justifiable variables that can predict item difficulty. In the current study, mathematical problem-solving items were designed for varying cognitive complexity levels based on a cognitive model of item processing. Structural variants of item models were designed to vary on two aspects of the cognitive model, the equation source and the number of subgoals. Participants were randomly assigned to test forms that contained different structural variants of the item models. Results from the linear logistic test model, the two-parameter-logistic—constrained model, and a corresponding linear mixed modeling procedure indicated that the item design variables affected both item difficulty and response time. Implications of the results for using structural variants in item generation and for the plausibility of the hypothesized cognitive model are discussed.

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