One goal of inquiry-oriented instruction is student engagement with others' mathematical ideas. This paper analyzes a relatively short episode in which students engaged with others' ideas; the instructor facilitated engagement in order to support students in making mathematical progress. Students expressed some bafflement pertaining to the…

The formal acceptance of a mathematical proof is based on its logical correctness but, from a cognitive point of view, this form of acceptance is not always naturally associated with the feeling that the proof has necessarily proved the statement. This is the case, in particular, for proof by contradiction in geometry, which can be linked to a…

The present study aimed to examine the effect of proficiency on the pragmatic comprehension of speech acts, implicatures, and routines, as well as the way learners of different proficiency levels employ strategies when comprehending a pragmatic task. Thirty-three high-proficiency and forty-one low-proficiency Chinese learners of English completed…

This article explores how conceptualizing "the moment" in entrepreneurship contributes to understanding entrepreneurial processes of learning and creativity. The significance of "the aha moment" in entrepreneurial behaviour is widely used at a popular level but has not been well explored in relation to knowledge of human…

Learning physics often requires overcoming common misconceptions based on naïve interpretations of observations in the everyday world. One proposed way to help learners build appropriate physics intuitions is to expose them to computer simulations in which motion is based on Newtonian principles. In addition, playing video games that require…

The Dodgson winner seems very intuitive and reasonable: when a Condorcet winner doesn't exist, pick the candidate that is closest, under some measure, to being a Condorcet winner. However, Dodgson's method is computationally intensive. Approximate methods are more tractable. By placing these methods in a geometric framework, we can understand how…

A possible contributing factor to students' difficulty in learning advanced mathematics is the conflict between students' "natural" learning styles and the formal structure of mathematics, which is based on definitions, theorems, and proofs. Students' natural learning styles may be a function of their intuition and language skills. The purpose of…

The need for some form of explicit grammar instruction is recognised in most current approaches to second language teaching. Since the usefulness of explicit instruction is at least to some extent dependent on the difficulty of the rules that are taught, an important question for teachers is whether their judgements of rule difficulty are…

Teaching style preferences of 157 teachers of gifted students were correlated with percent of time spent in teaching gifted children, years of teaching experience, and teaching level. Of the styles identified (Sensing-Thinking, Sensing-Feeling, Intuitive-Thinking, and Intuitive-Feeling), more experienced teachers revealed a preference for the…