Modelling roles of mathematics in physics has proved to be a difficult task, with previous models of the interplay between the two disciplines mainly focusing on mathematical modelling and problem solving. However, to convey a realistic view of physics as a field of science to our students, we need to do more than train them to become fluent in…

Non-mathematics specialists' competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students…

Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and…

The reconciliation of theories of concepts based on prototypes, exemplars, and theory-like structures is a longstanding problem in cognitive science. In response to this problem, researchers have recently tended to adopt either hybrid theories that combine various kinds of representational structure, or eliminative theories that replace concepts…

This theoretical analysis addresses "the unreasonable effectiveness of mathematics in the natural sciences" (Wigner, 1960). For example, how is it that ellipses--constructed by Greek geometers nearly two millennia before Kepler used them--provide such precise models for describing planetary motion? Historical models of gravity and…

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

In an effort to assess models of inductive reasoning and deductive reasoning, the authors, in 3 experiments, examined the effects of argument length and logical validity on evaluation of arguments. In Experiments 1a and 1b, participants were given either induction or deduction instructions for a common set of stimuli. Two distinct effects were…

Many educators believe that mathematical investigation involves both problem posing and problem solving, but some teachers have taught their students to investigate during problem solving. The confusion about the relationship between investigation and problem solving may affect how teachers teach their students and how researchers conduct their…

In the present study, I examine a modelling strategy as employed by a teacher in the context of an algebra lesson. The actions of this teacher suggest that a modelling approach will have a greater impact on enriching student learning if we do not lose sight of the need to manage associated cognitive loads that could either aid or hinder the…

Chronometric studies of language and memory processing typically emphasize changes in mean response time (RT) performance across conditions. However, changes in mean performance (or the lack thereof) may reflect distinct patterns at the level of underlying RT distributions. In seven experiments, RT distributional analyses were used to better…

Comments on the article by E. Brandstatter, G. Gigerenzer, and R. Hertwig (2006). The authors discuss the priority heuristic, a recent model for decisions under risk. They reanalyze the experimental validity of this approach and discuss how these results compare with cumulative prospect theory, the currently most established model in behavioral…

It is argued that the reduction of cognitive dissonance can be viewed as a constraint satisfaction problem, and a computational model of the process of consonance seeking is proposed. Simulations from this model matched psychological findings from the insufficient justification and free-choice paradigms of cognitive dissonance theory. (SLD)

A model of interference and forgetting based on the search of associative memory (SAM) theory is presented. The SAM theory describes retrieval processes in long-term memory. A model of contextual fluctuation processes is incorporated to provide a time-dependent variable to handle time-based interference phenomena. (SLD)

Capacity limitations in absolute judgment tasks are discussed in relation to information theory. Information theory can provide a quantitative way of resolving questions about limitations on the amount of information we can receive and the process of recoding. (SLD)

A decision field theory is proposed and used to explain motivational and cognitive mechanisms that guide the deliberation process involved in decisions made under uncertainty. Decision theories are extended into the stochastic-dynamic category. The proposed theory is compared with four other theories of decision making under uncertainty. (SLD)