The subject of mathematics is important for many other subjects, including physics. The questions we ask in physics often need a mathematical translation to be graphically interpreted and transformed. Students learn physics when interacting with physical questions; questions from physics also give insights and discoveries in mathematical problems.…

This article proposes a framework for classroom teachers to use in making pedagogical decisions regarding which mathematical materials (concrete and digital) to use, when they might be most appropriately used, and why. Two iPad apps ("Area of Shapes (Parallelogram)" and "Area of Parallelogram") are also evaluated to demonstrate…

Identifies difficulties of using microcomputer-based systems as surrogate teachers and some benefits from their appropriate use in partnership with the teacher. Uses considered include application program, simulation program, drill and practice, tutorial program, computer modeling, and administration program. (JEG)

The paper contains a model of a technique for increasing the quality of educational and instructional opportunity for all students. This model is developed around the flexible or modularly scheduled secondary school. Also included is a procedure containing a computer program, with which the administrator can develop the master schedule of the…

To help mathematics educators realise the power of computer-based applications and modelling, this paper deals with four questions: (a) What implications does technology have for the range of applications and modelling problems that can be introduced? (b) In what cases does technology facilitate the learning of applications and modelling? (c) When…

Describes a four-phase method of helping students who are mathematically unsophisticated and have difficulty relating their common sense, English-language understanding of a system to an abstract, mathematical description. The approach uses interactive simulation models. (Author/IRT)

The so-called discrete approach in calculus instruction involves introducing topics from the calculus of finite differences and finite sums, both for motivation and as useful tools for applications of the calculus. In particular, it provides an ideal setting in which to incorporate computers into calculus courses. This approach has been…

Describes a two-quarter sequence of graduate courses in numerical methods and modeling for chemical engineers. Rationale, course content, methodology, topic development, and such course requirements as homework and design projects are considered. Emphasis is placed on the treatment of numerical methods implemented in commercial software. (JM)

An approach to teaching the exponential function using discrete methods, rather than continuous analysis, is presented. A model for simple geometric growth is explored, with a computer program given. (MNS)

The problem of structuring sequences of instructional stimuli such that learning is optimized is modelled as a sequential decision problem with an imbedded mathematical model of learning providing a criterion function. Three types of optimization methods for such a representation are investigated for the specific case of paired-associate learning…

A rationale for the use of gaming and simulation for instructional purposes is developed in the introduction to this paper. The major portion of the text is comprised of several models of computer programs for economics instruction. (SHM)

As presented in this report the basic purpose of CAIR (Computer-Aided International Relations Teaching) is to introduce university students and policy analysts in government agencies to substantive data analysis in the field of international studies. The student will be exposed to quantitative political science, learn the role and limitations of…