To span the great distance from the solar system to the farthest clusters of galaxies in the universe, astronomers break down the distance indicators into steps. The nearest ones are measured geometrically, with what is known as parallax. Among the objects whose distances are thus directly measured are a rare type of star known as a Cepheid…

This paper presents issues related to the use of technology by secondary school pre-service mathematics teachers engaged in open mathematical modelling projects. Pre-service teachers developed these projects within a regular mathematics education course during the teacher education program at the university concerned. This environment, called a…

Here we examine a new task to assess working memory for visual arrays in which the participant must judge how many items changed from a studied array to a test array. As a clue to processing, on some trials in the first 2 experiments, participants carried out a metamemory judgment in which they were to decide how many items were in working memory.…

The phenomenon of outbreaks of dangerous diseases is both intriguing to students and of mathematical significance, which is exactly why the authors engaged eighth graders in an introductory activity on the growth that occurs as an epidemic spreads. Various contexts can set the stage for such an exploration. Reading adolescent literature like…

In an effort to assess the relations between reasoning and memory, in 8 experiments, the authors examined how well responses on an inductive reasoning task are predicted from responses on a recognition memory task for the same picture stimuli. Across several experimental manipulations, such as varying study time, presentation frequency, and the…

Radical behaviorism considers private events to be a part of ongoing observable behavior and to share the properties of public events. Although private events cannot be measured directly, their roles in overt action can be inferred from mathematical models that relate private responses to external stimuli and reinforcers according to the same…

This article examines how visual representations may mediate the teaching and learning of mathematics over time in Japanese elementary classrooms. Using the Zone of Proximal Development Mathematical Learning Model (Murata & Fuson, 2006; Fuson & Murata, 2007), the process of mediation is explicated. The tape diagram, a central visual…

Color coding is used to guide attention in computer displays for such critical tasks as baggage screening or air traffic control. It has been shown that a display object attracts more attention if its color is more similar to the color for which one is searching. However, what does "similar" precisely mean? Can we predict the amount of attention…

The goal of this study was to determine how the fear relevancy of outcomes during probabilistic classification learning affects behavior and strategy use. Novel variants of the "weather prediction" task were created, in which cue cards predicted either looming fearful or neutral outcomes in a between-groups design. Strategy use was…

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

The coincidence hypothesis predicts that dissimilarity between objects that differ on two separable dimensions is larger than predicted from their unidimensional differences on the basis of triangle inequality and segmental additivity. The coincidence hypothesis was supported in two-dimensional stimuli studies. (Author/CM)

Subjects decided whether sentences as "The treaty passed" were "true" or "false," given number of votes cast for the bill and criterion that determined its status. An additive-stages model was applied to verification times from the present and prior studies, and was used to describe certain markedness and congruity…

The applicability of the identical elements (IE) model of arithmetic fact retrieval (T. C. Rickard, A. F. Healy, & L. E. Bourne, 1994) to cued recall from episodic (image and sentence) memory was explored in 3 transfer experiments. In agreement with results from arithmetic, speedup following even minimal practice recalling a missing word from an…

A novel attentional capture effect is reported in which visual-verbal serial recall was disrupted if a single deviation in the interstimulus interval occurred within otherwise regularly presented task-irrelevant spoken items. The degree of disruption was the same whether the temporal deviant was embedded in a sequence made up of a repeating item…

Two experiments tested a neo-Piagetian model of verbal short-term memory, comparing it with the articulatory loop model. Findings indicated that the proposed model accounted for effects of M capacity, word length, and presentation modality on short-term memory. The model's fit to the data was acceptable, and parameter estimates were consistent…