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…

This article proposes that sampling design effects have potentially huge unrecognized impacts on the results reported by large-scale district and state assessments in the United States. When design effects are unrecognized and unaccounted for they lead to underestimating the sampling error in item and test statistics. Underestimating the sampling…

This article contributes to the empirical literature on remediation in community colleges by using policy variation across North Carolina's community colleges to examine how remediation affects various outcomes for traditional-age college students. We find that being required to take a remedial course (as we define it in this article) either in…

This study aims to investigate about the existence of a graphical facilitation effect on probabilistic reasoning. Measures of undergraduates' performances on problems presented in both verbal-numerical and graphical-pictorial formats have been related to visuo-spatial and numerical prerequisites, to statistical anxiety, to attitudes towards…

Using a conjoint survey of 161 students at South Dakota State University (SDSU), we mapped a probability-of-enrolment curve for SDSU students, consistent with demand theory. A quasi-demand curve was created from the conditional-logit model. This study shows that along with the price of tuition fees, distance from home, availability of majors, and…

The grades K-2 Florida Center for Reading Research (FCRR) Reading Assessment (FRA) consists of computer-adaptive alphabetic and oral language screening tasks that provide a Probability of Literacy Success (PLS) linked to grade-level performance (i.e., the 40th percentile) on the word reading (in kindergarten) or reading comprehension (in grades…