This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a…

Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

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…

In this article, the authors identify and anecdotally describe three tutor archetypes: the pragmatist, the architect, and the surveyor. These descriptions, based on observations of remedial mathematics tutors at a land-grant university, shed light on a variety of philosophical beliefs regarding and pedagogical approaches to tutoring. An analysis…

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…

This submission contains the Proceedings of the 2013 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Brock University in St. Catharines, Ontario. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

P. J. Kellman, P. Garrigan, and T. F. Shipley's theory of 3-dimensional object interpolation asserts that existing data, as well as logical considerations, support the view that an identical contour interpolation process underlies the interpolation of partially camouflaged and partially occluded objects (modal completion and amodal completion,…

Papini and Pellegrini (Papini, M. R., & Pellegrini, S. "Scaling relative incentive value in consummatory behavior." "Learning and Motivation", in press) observed that, within limits, the level of consummatory responding of rats exposed to incentive downshifts in the concentration of sucrose solutions was similar when the ratio of test/training…

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…

This article details the results of a written test designed to reveal how education majors construct and evaluate histograms and frequency polygons. Included is a description of the mistakes made by the students which shows how they tend to confuse histograms with bar diagrams, incorrectly assign data along the Cartesian axes and experience…

This paper explores the use of spreadsheets to develop an exploratory environment where mathematics students can develop their own understanding of the parameters of commonly encountered families of functions: linear, logarithmic, exponential and power. The key to this understanding involves opening up the definition of rate of change from the…

Three widely used sixth-grade textbooks were studied to see how fraction concepts were represented. The textbooks selected were "Connected Mathematics," "Middle Grades MathThematics," and Glencoe's "Mathematics: Applications and Concepts Course 1." Three specific areas were examined: representation mode, model, and problem context. Results of…

We present a case study of the physical principles necessary to model the high altitude parachute jump made by Colonel Joseph Kittinger, USAF, in 1960, in order to determine the maximum speed attained and to calculate whether this speed was sufficient to exceed the speed of sound at that altitude. There is considerable discrepancy in the value of…

The authors explored the effects of teaching conceptual model-based problem-solving instruction on students' ability to solve problems in various situations. Participants were 3 4th-and 5th-grade students with or at risk for mathematics disabilities. The authors used an adapted multiple-probe across-participants design to assess the functional…

In this article, the authors share an episode from an after-school program and focus on eight of the twenty-four urban, sixth-grade students who volunteered to work on mathematical problem solving. When students are given a supportive environment, open-ended tasks, and thoughtful teacher questioning, their reasoning can develop naturally. By…