To achieve adaptive learning, a dynamic assessment system equipped with a cognitive diagnosis was developed for this study, which adopts a three-stage model of diagnosis-intervention-assessment. To examine how this system influenced spatial geometry learning, the study used a quasi-experimental method to investigate student learning outcomes…

Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions…

When directed to ignore evidence of a witness's previous bad character because of a violation of the rules of evidence, are jurors' beliefs still affected? The intuition is that they will be because in everyday argumentation, fallacies, like the ad hominem, are effective argumentative strategies. An ad hominem argument (against the person)…

Errors in detecting randomness are often explained in terms of biases and misconceptions. We propose and provide evidence for an account that characterizes the contribution of the inherent statistical difficulty of the task. Our account is based on a Bayesian statistical analysis, focusing on the fact that a random process is a special case of…

Diagnosis of misconceptions or "bugs" in procedural skills is difficult because of their unstable nature. This study addresses this problem by proposing and evaluating a probability-based approach to the diagnosis of bugs in children's multicolumn subtraction performance using Bayesian networks. This approach assumes a causal network relating…

P. R. Killeen's (2005a) probability of replication ("p[subscript rep]") of an experimental result is the fiducial Bayesian predictive probability of finding a same-sign effect in a replication of an experiment. "p[subscript rep]" is now routinely reported in "Psychological Science" and has also begun to appear in…

What people mean by randomness should be taken into account when teaching statistical inference. This experiment explored subjective beliefs about randomness and probability through two successive tasks. Subjects were asked to categorize 16 familiar items: 8 real items from everyday life experiences, and 8 stochastic items involving a repeatable…