The effectiveness of different concrete and pictorial models on students' understanding of the part-whole construct for fractions was investigated. Using interview data from fourth and fifth grade students from three different districts that adopted the "Mathematics Trailblazers" series, authors identified strengths and limitations of models used.…

This paper presents an investigation by pre-service secondary school teachers in a geometry class of the relationship between the perpendicular distance from the eyeball to the wall (x) and the viewable vertical distance on the wall (y) using a view tube of constant length and diameter. In undertaking the investigation, students used tabular and…

Applying three mathematical modeling techniques, this study proposes and tests the fit of an academic performance model, and then estimates the relative importance of four performance predictors: academic ability, performance goal orientation, educational technology use, and social network density. Drawing on social network theory, findings from…

With teachers and students in Government and Catholic schools in three geographical clusters in Victoria, the Task Type and Mathematics Learning (TTML) project is investigating the best ways to use different types of mathematics tasks, particularly in Grades 5 to 8. This article describes Type 1 tasks and discusses how they contribute to…

This paper reports a part of a study on the construction of mathematical meanings in terms of development of semiotic systems (gestures, speech in oral and written form, drawings) in a Vygotskian framework, where artefacts are used as tools of semiotic mediation. It describes a teaching experiment on perspective drawing at primary school (fourth…

The article presents a mathematical model of short-term recognition based on dual-process models and the three-component theory of working memory [Oberauer, K. (2002). Access to information in working memory: Exploring the focus of attention. "Journal of Experimental Psychology: Learning, Memory, and Cognition, 28", 411-421]. Familiarity arises…

Comments on articles by Botvinick et al. and Jacob et al. M. M. Botvinick, T. S. Braver, D. M. Barch, C. S. Carter, and J. D. Cohen (2001) implemented their conflict-monitoring hypothesis of cognitive control in a series of computational models. The authors of the current article first demonstrate that M. M. Botvinick et al.'s (2001)…

The online deployment of Technology Engineered online Student Ratings of Instruction (SRIs) by colleges and universities in the United States has dynamically changed the deployment of course evaluation. This research investigation is the fourth part of a post hoc study that analytically and psychometrically examines the design, reliability, and…

This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…

Time course estimates from eye tracking during spoken language processing (the "visual world paradigm", or VWP) have enabled progress on debates regarding fine-grained details of activation and competition over time. There are, however, three gaps in current analyses of VWP data: consideration of time in a statistically rigorous manner,…

The restoration of wolves to Yellowstone National park after a 7-year absence created a natural experiment on the ecological effects of top predators. In this activity, students use mathematical models to explore how carrion from wolf kills can reduce negative effects of climate change on scavengers in the park.

One challenge that middle school teachers commonly face is finding insightful, hands-on applications when teaching basic mathematical concepts. One concept that is a foundation of middle school mathematics is the notion of "linear functions." Although a variety of models can be used for linear equations, such as temperature conversions,…

Schizophrenia may be associated with a fundamental disturbance in the temporal coordination of information processing in the brain, leading to classic symptoms of schizophrenia such as thought disorder and disorganized and contextually inappropriate behavior. Although a variety of behavioral studies have provided strong evidence for perceptual…

Several decades ago, V. A. Krutetskii conducted a multiyear study to investigate the various types of thinking that academically advanced, or as he called them, gifted mathematicians used. Following an in-depth look at Krutetskii's nine ways of thinking, a model is proposed that will provide direction for teachers in selecting problems. The model…

A component-functions model of choice behavior is proposed for performance on interdependent concurrent variable-interval (VI) variable-interval schedules based on the product of two component functions, one that enhances behavior and one that reduces behavior. The model is the solution to the symmetrical pair of differential equations describing…