Solving real-life problems through mathematical modeling is one of the aims of modern mathematics curricula. For this reason, prospective mathematics teachers need to acquire modeling skills and use these skills in learning environments in terms of creating rich learning environments. With this study, it is aimed to examine the reflections of…

We analyzed 5th grade students' interactions with one computer-based modeling simulation to examine how they defined and prioritized variables in a dynamically simulated environment. Results revealed that exposure to the simulation environment helped students visualize continuous motions, interpret the different quantities present in the model,…

This paper reports on a case study of two elementary school students with mathematical learning disabilities (MLD) (ages 10 and 11) using augmented reality (AR), digital and physical modelling in mathematics class. MLD students worked on modelling geometric shapes (cubes, cuboids, squared pyramids, and octahedrons) and forms (polygons) by…

US high school (HS) students are lagging behind their foreign peers in math performance. It is thus necessary to design teaching modules that motivate US HS students to learn more math and to improve their math skills. Our study set out to test two different software programs designed for the development of such skills. MATLAB Simulink provides a…

This article describes a unit in which students investigate total solar eclipses, such as the one coming August 21, from several perspectives. It incorporates mathematical thinking and aligns with the "Next Generation Science Standard." This article refers to physical, virtual, and mathematical modeling. Various models and perspectives…

In this article we discuss the possible uses of NetLogo as an educational tool for High School and early-years undergraduate students. The paper is geared towards teachers from all disciplines who require students to problem solve, be quantitative and logical but want a project orientated platform to build or reinforce knowledge. The tools and…

In this study, we follow students' modeling and covariational reasoning in the context of learning about big data. A three-week unit was designed to allow 12th grade students in a mathematics course to explore big and mid-size data using concepts such as trend and scatter to describe the relationships between variables in multivariate settings.…

In this article, the authors present a lesson whose goal is to utilise a scientific environment to immerse a trigonometry student in the process of mathematical modelling. The scientific environment utilised during this activity is a physics simulation called "Wave on a String" created by the PhET Interactive Simulations Project at…

Mathematical software packages such as Polymath, MATLAB, and Mathcad are currently widely used for engineering problem solving. Applications of several of these packages to typical chemical engineering problems have been demonstrated by Cutlip, et al. The main characteristic of these packages is that they provide a "problem-solving environment…

Describes a study of the effectiveness of computer-simulation programs in enhancing biology students' familiarity with ecological modeling and concepts. Finds that computer simulations improved student comprehension of ecological processes expressed in mathematical form, but did not allow a full understanding of ecological concepts. Contains 28…

Analyzes the mathematics of rotational and translational motion and how one can influence the other in the context of cams and cranks. Describes how the individual components can be brought together to simulate a four-stroke engine and how the engine animates again using the same simple macro. (Author/ASK)

Describes a computer simulation called "Supercontinent Aggregation and Dispersal" designed to model the interplay between the movement of the continents and the flow patterns of rock in the mantle. Discusses the strengths and weaknesses of the program in relation to the effects of continents on the mantle. (CW)

Some aspects of biology, for example the Hardy-Weinberg simulation of population genetics or modelling heat flow in lizards, have an undeniable mathematical basis. Students can find the level of mathematical skill required to deal with such concepts to be an insurmountable hurdle to understanding. If not used effectively, spreadsheet models…

Many multidimensional item response theory (IRT) models have been proposed. A comparison is made between the so-called full information models and the models that use only pairwise information. Three multidimensional models described are: (1) the compensatory model of R. D. Bock and M. Aitken (1981) using the computer program TESTFACT; (2) a model…

Explores what kinds of calculus-related insights seem to typify calculus-related reasoning. Introduces "qualitative calculus" in which learning is focused on synthesis. Discusses the resemblance and difference between traditional calculus and qualitative calculus, advantages of learning qualitative calculus, and how understanding qualitative…