The increased Simon effect with increasing the ratio of congruent trials may be interpreted by both attention modulation and irrelevant stimulus-response (S-R) associations learning accounts, although the reversed Simon effect with increasing the ratio of incongruent trials provides evidence supporting the latter account. To investigate if…

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

Modeling using mathematics and making inferences about mathematical situations are becoming more prevalent in most fields of study. Descriptive statistics cannot be used to generalize about a population or make predictions of what can occur. Instead, inference must be used. Simulation and sampling are essential in building a foundation for…

Immersive 3D worlds can be designed to effectively engage students in peer-to-peer collaborative learning activities, supported by scientific visualization, to help with understanding complex concepts associated with learning science, technology, engineering, and mathematics (STEM). Previous research studies have shown STEM learning benefits…

In this article we present an exploratory tool for extracting systematic patterns from multivariate data. The technique, hierarchical segmentation (HS), can be used to group multivariate time series into segments with similar discrete-state recurrence patterns and it is not restricted by the stationarity assumption. We use a simulation study to…

We developed an introductory statistics course for pre-service elementary teachers. In this paper, we describe the goals and structure of the course, as well as the assessments we implemented. Additionally, we use example course work to demonstrate pre-service teachers' progress both in learning statistics and as novice teachers. Overall, the…

This dissertation answers three research questions: (1) What are the characteristics of a combinatoric measure, based on the Average Search Length (ASL), that performs the same as a probabilistic version of the ASL?; (2) Does the combinatoric ASL measure produce the same performance result as the one that is obtained by ranking a collection of…

This paper describes the procedures of reconstructing ancient architecture using solid modeling with geometric analysis, especially the Golden Ratio analysis. In the past the recovery and reconstruction of ruins required bringing together fragments of evidence and vast amount of measurements from archaeological site. Although researchers and…

The exponential function model of radioactive decay and the concept of a half-life are used in nuclear experiments that appear in introductory and intermediate laboratories. In our interactions with students, we have found that students at all levels have significant confusion about both the term exponential and what is meant by a half-life as…

Does speed provide a "model for" rate of change in other contexts? Does JavaMathWorlds (JMW), animated simulation software, assist in the development of the "model for" rate of change? This project investigates the transference of understandings of rate gained in a motion context to a non-motion context. Students were 27 14-15 year old students at…

Argues that conventional dynamic modeling techniques divert attention from the importance of model structure and discusses various methods of system representation that are suitable for the analysis and improvement of model structure. (Available from IPC (America) Inc., 205 East 42 Street, New York, NY 10017; $46.80 annually.) (Author/JG)

Meaningful educational activities and cognitive tools might improve students' active involvements in the teaching-learning process and encourage their reflections on the concepts and relations to be investigated. It is claimed that usage of manipulatives not only increase students' conceptual understanding and problem solving skills but also…

Presents a numerical simulation of a simple food chain together with a set of mathematical rules generalizing the model to a food web of any complexity. Discusses some of the model's interesting features and its use by students. (Author/JRH)

Provided are three program listings which may be used to illustrate this fractal figure. Extensions of these algorithms and their use in the study of chaos and fractals are suggested. (CW)

Investigates the construction of understanding of the motion of an object down an inclined plane which takes place through the process of model building in an integrated algebra, trigonometry, and physics class. Discusses four major themes related to student learning through modeling that emerged from the results. Discusses implications for…