The "k"-means clustering method, while widely embraced in college student typology research, is often misunderstood and misapplied. Many researchers regard "k"-means as a near-universal solution for uncovering homogeneous student groups, believing its success hinges primarily on the selection of an appropriate "k."…

The current study examined the incremental validity of the clinical clusters from the Woodcock-Johnson III Tests of Cognitive Abilities (WJ-III COG) for predicting scores on the Woodcock-Johnson III Tests of Achievement (WJ-III ACH). All participants were children and adolescents (N = 4,722) drawn from the nationally representative WJ-III…

Proof is a central concept in mathematics education, yet mathematics educators have failed to reach a consensus on how proof should be conceptualized. I advocate defining proof as a clustered concept, in the sense of Lakoff (1987). I contend that this offers a better account of mathematicians' practice with respect to proof than previous accounts…

Due to the rapid advances in computing and sensing technologies, enormous amounts of data are being generated everyday in various applications. The integration of data mining and data visualization has been widely used to analyze these massive and complex data sets to discover hidden patterns. For both data mining and visualization to be…

This study examines the organization and development of 5 domains of reasoning (categorical, quantitative, spatial, causal, and propositional) and the construct validity of a test designed to measure development from early adolescence to early adulthood. The theory underlying the test is first summarized and the conceptual design of the test is…