Invention and Productive Failure activities ask students to generate methods that capture the important properties of some given data (e.g., uncertainty) before being taught the expert solution. Invention and Productive Failure activities are a class of scientific inquiry activities in that students create, implement, and evaluate mathematical…

Many drugs of abuse produce changes in impulsive choice, that is, choice for a smaller-sooner reinforcer over a larger-later reinforcer. Because the alternatives differ in both delay and amount, it is not clear whether these drug effects are due to the differences in reinforcer delay or amount. To isolate the effects of delay, we used a titrating…

The Malaysian Quality of Life Index (MQLI) released by the Economic Planning Unit (EPU), has led authors to search for alternative method of expressing this index. One of the limitations in MQLI computations is the failure to recognise unequal weights for each accounted component. This paper offers a new way of expressing the quality of life index…

In this article we consider, via a specific modelling example, the educational benefits to be gained from running mathematical activities with our sixth-form and undergraduate students that, in modern parlance, might be termed "rich tasks". The idea for this modelling activity arose while the author was reading a popular-science book on cosmology…

The present study examined the long-term usefulness of estimated parameters used to adjust the scores from a performance assessment to account for differences in rater stringency. Ratings from four components of the USMLE[R] Step 2 Clinical Skills Examination data were analyzed. A generalizability-theory framework was used to examine the extent to…

Humans and animals can perform much more complex tasks than they can acquire using pure trial and error learning. This gap is filled by teaching. One important method of instruction is shaping, in which a teacher decomposes a complete task into sub-components, thereby providing an easier path to learning. Despite its importance, shaping has not…

Previous research has shown that when confronted with missing-value word problems, primary school students strongly tend to use proportional solution approaches, even if these approaches are inappropriate. The authors investigated whether (besides the missing-value formulation of word problems) the numbers appearing in word problems are part of…

We unpack the notion of mathematics teacher educators modeling teaching in mathematics teacher education courses. Specifically, we investigated what practicing teachers gained from mathematics teacher educators' modeling by examining: (1) What do mathematics teacher educators believe they model about effective instructional practice? (2) What do…

Cohen Kadosh, Tzelgov, and Henik [Cohen Kadosh, R., Tzelgov, J., & Henik, A. (2008). A synesthetic walk on the number line: The size effect. "Cognition", 106, 548-557] present a new paradigm to probe properties of the mental number line. They describe two experiments which they argue to be inconsistent with the exact small number model proposed by…

This dissertation develops analytical tools which enable rigorous evaluation of competing syllabic parses on the basis of temporal patterns in speech production data. The data come from the articulographic tracking of fleshpoints on target speech organs, e.g., tongue, lips, jaw, in experiments with native speakers of American English and Moroccan…

This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…

This study uses simulation techniques to examine the statistical power of the group- randomized design and the matched-pair (MP) randomized block design under various parameter combinations. Both nearest neighbor matching and random matching are used for the MP design. The power of each design for any parameter combination was calculated from…

As Duncomb and Yinger (2001) have stated, "School consolidation represents the most dramatic change in education governance and management in the United States in the twentieth century. Over 100,000 school districts have been eliminated through consolidation since 1938, a drop of almost 90 percent (NCES 1999, Table 90). This longstanding…

Over the past several years, we have been exploring and researching a phenomenon that occurs among undergraduate students that we called extension of linear models to non-linear contexts or overgeneralization of linear models. This phenomenon appears when some students use linear representations in situations that are non-linear. In a first phase,…

This theoretical paper explores the decision-making process involved in modelling and mathematizing situations during problem solving. Specifically, it focuses on the authority behind these choices (i.e., what or who determines the chosen mathematical models). We show that different types of situations involve different sources of authority,…