This article examines the problem of specification error in 2 models for categorical latent variables; the latent class model and the latent Markov model. Specification error in the latent class model focuses on the impact of incorrectly specifying the number of latent classes of the categorical latent variable on measures of model adequacy as…

The purpose of this study was to extend the literature on decoding by bringing together two lines of research, namely person and word factors that affect decoding, using a crossed random-effects model. The sample was composed of 196 English-speaking Grade 1 students. A researcher-developed pseudoword list was used as the primary outcome measure.…

This article describes an investigation of Buffon's coin problem and related problems with the aid of an applet. The problems are accessible at a variety of grade levels and facilitate making connections between geometry and probability.

In 2006, Marcus du Sautoy delivered the Royal Institution Christmas Lectures on the subject of mathematics. From this, a workshop was created using ideas illustrated in the programme. A group of mathematical students from the University of Oxford, known as Marcus' Marvellous Mathemagicians, were trained in this workshop and now travel to schools…

This article contrasts 2 approaches to analyzing transitivity of preference and other behavioral properties in choice data. The approach of Regenwetter, Dana, and Davis-Stober (2011) assumes that on each choice, a decision maker samples randomly from a mixture of preference orders to determine whether "A" is preferred to "B." In contrast, Birnbaum…

Dual Process Theories (DPT) of reasoning posit that judgments are mediated by both fast, automatic processes and more deliberate, analytic ones. A critical, but unanswered question concerns the issue of monitoring and control: When do reasoners rely on the first, intuitive output and when do they engage more effortful thinking? We hypothesised…

Building on previous arguments for why educational researchers should not provide effect-size estimates in the face of statistically nonsignificant outcomes (Robinson & Levin, 1997), Onwuegbuzie and Levin (2005) proposed a 3-step statistical approach for assessing group differences when multiple outcome measures are individually analyzed…

The very early appearance of abstract knowledge is often taken as evidence for innateness. We explore the relative learning speeds of abstract and specific knowledge within a Bayesian framework and the role for innate structure. We focus on knowledge about causality, seen as a domain-general intuitive theory, and ask whether this knowledge can be…

In providing a continued focus on tasks and activities that help to illustrate key ideas embedded in the new Australian Curriculum, this issue the authors focus, on Geometry in the Measurement and Geometry strand with strong links for an integrated focus on the Statistics and Probability strand. The small unit of work on the sorting and…

Optimizing learning over multiple retrieval opportunities requires a joint consideration of both the probability and the mnemonic value of a successful retrieval. Previous research has addressed this trade-off by manipulating the schedule of practice trials, suggesting that a pattern of increasingly long lags--"expanding retrieval practice"--may…

This article presents the mathematical approach of the optimal strategy to win the "Release the prisoners" game and the integration of this analysis in a math class. Outline lesson plans at three different levels are given, where simulations are suggested as well as theoretical findings about the probability distribution function and its mean…

For over a century, chemists have investigated the rates of chemical reactions using experimental conditions involving huge numbers of molecules. As a consequence, the description of the kinetics of the reaction in terms of average values was good enough for all practical purposes. From the pedagogical point of view, such a description misses the…

Cognitive scientists have studied internal cognitive structures, processes, and systems for decades in order to understand how they function in human learning. Nevertheless, questions concerning the diagnosis of changes in these cognitive structures while solving inductive reasoning tasks are still being scrutinized. This paper reports findings…

The authors of this article review the development and discuss potential uses for a new instrument that evolved from follow-up research conducted after completion of a five-year study of innovative curricular and instructional practices. The instrument is A Stakeholder's Perceptions of Innovative Reform Efforts (ASPIRE). The primary purpose of…

Using data from a longitudinal study of Mexican-origin girls (ages 11-17 at Time 1), we examined sociocultural (i.e., family structure, nativity, and acculturation), interpersonal (i.e., supportive parenting and conflict), and developmental (i.e., menarche timing and autonomy expectations) predictors of sexual initiation. Using Cox proportional…