Griffiths and Tenenbaum (2006) asked individuals to make predictions about the duration or extent of everyday events (e.g., cake baking times), and reported that predictions were optimal, employing Bayesian inference based on veridical prior distributions. Although the predictions conformed strikingly to statistics of the world, they reflect…

This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are…

This study investigates Chinese and U.S. teachers' cultural beliefs concerning effective mathematics teaching from the teachers' perspectives. Although sharing some common beliefs, the two groups of teachers think differently about both mathematics understanding and the features of effective teaching. The sample of U.S. teachers put more emphasis…

One factor in the debate surrounding the underrepresentation of women in science technology, engineering and mathematics (STEM) involves male-female mathematical ability differences in the extreme right tail (top 1% in ability). The present study provides male-female ability ratios from over 1.6 million 7th grade students in the right tail (top 5%…

General sign theory (GST) deals with how distinct sign systems are grounded, developed with increasing abstractness over time, and differentiated in efficacies in experience and discourse. GST has 3 components: The theory of true narrative representations (TNR theory) shows that TNRs are unique in being relatively well determined with respect to…

The emergence of modern humans with their extraordinary cognitive capacities is ascribed to a novel type of cognitive computational process (sustained non-routine multi-level operations) required for abstract projectuality, held to be the common denominator of the cognitive capacities specific to modern humans. A brain operation (latching) that…

This study examined the status of critical thinking (CT) and reasoning skills in information communication and technology (ICT) for 190 college students in a higher education system. It analyzed how the students performed in CT, reasoning, and internet copyright and ethical issues. A CT assessment was designed to analyze the CT and reasoning…

This paper discusses variation in reasoning strategies among expert mathematicians, with a particular focus on the degree to which they use examples to reason about general conjectures. We first discuss literature on the use of examples in understanding and reasoning about abstract mathematics, relating this to a conceptualisation of syntactic and…

The purpose of this study was to examine the policy implications allowing administrators to exempt a student from required arts instruction if the student obtained unsatisfactory scores on the high-stake state mandated tests in English and mathematics. This study examined English language arts and math test scores for 37,222 eighth grade students…

The purpose of this study was to examine the policy implications allowing administrators to exempt a student from required arts instruction if the student obtained unsatisfactory scores on the high-stake state mandated tests in English and mathematics. This study examined English language arts and math test scores for 37,222 eighth grade students…

In November 2008 at Purdue University, the 2nd Workshop on Human Problem Solving was held. This workshop, which was a natural continuation of the first workshop devoted almost exclusively to optimization problems, addressed a wider range of topics that reflect the scope of the "Journal of Problem Solving." The workshop was attended by 35…

Alignment between content standards and standardized tests is a significant issue to society, science pedagogy, and test validation. To better understand the issues related to alignment, this study compares the alignment in physics among three education systems: Jiangsu (China), New York State (United States), and Singapore. The same coding…

The aim of the present study is to provide further evidence that the errors that arise from improper application of the linear model are not random and not easy to overcome. Using three different types of test, we attempt to show that the errors referred to in the literature as "pseudo-analogous" are the result of an epistemological…

Categorization in well-known natural concepts is studied using a special version of the Varying Abstraction Framework (Vanpaemel, W., & Storms, G. (2006). A varying abstraction framework for categorization. Manuscript submitted for publication; Vanpaemel, W., Storms, G., & Ons, B. (2005). A varying abstraction model for categorization. In B. Bara,…

This essay discusses Alain LeRoy Locke (1885-1954), Professor of Philosophy (Howard University) and examines his experiences, reasoning, and rhetoric as they challenge the accepted notions of race, education, and democracy. As an African American practicing philosophy in a racist nation, Locke also examined value communities and value differences…