Background/purpose: In modern mathematical education, it is important to develop students' ability to understand the fundamental properties of geometric objects deeply. This makes it relevant to study the additivity of the area of triangles as a property inherent in various kinds of quantities and ways of representing it methodologically in the…

The main objective of this paper is to propose a didactic framework for teaching Applied Mathematics in higher education. After describing the structure of the framework, several applications of inquiry-based learning in teaching numerical analysis and optimization are provided to illustrate the potential of the proposed framework. The framework…

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner. First, using geometrical software, we investigate four theorems that represent interesting geometrical properties,…

Automated theorem proving (ATP) for Propositional Classical Logic is an algorithm to check the validity of a formula. It is a very well-known problem which is decidable but co-NP-complete. There are many algorithms for this problem. In this paper, an educationally oriented implementation of Semantic Tableaux method is described. The program has…

In two experiments, participants judged the average numerosity between two sequentially presented dot patterns to perform an approximate arithmetic task. In Experiment 1, the response was given on a 0-20 numerical scale (categorical scaling), and in Experiment 2, the response was given by the production of a dot pattern of the desired numerosity…

The availability of sophisticated computer programs such as "Wolfram Alpha" has made many problems found in the secondary mathematics curriculum somewhat obsolete for they can be easily solved by the software. Against this background, an interplay between the power of a modern tool of technology and educational constraints it presents is…

We explore how curvature and torsion determine the shape of a curve via the Frenet-Serret formulas. The connection is made explicit using the existence of solutions to ordinary differential equations. We use a paperclip as a concrete, visual example and generate its graph in 3-space using a CAS. We also show how certain physical deformations to…

Investigates how animation is used to improve students' comprehension of the limit concept in an experimental course in which the main topics are approximation and interpolation by Taylor polynomials. Uses Mathematica software to generate the dynamic graphics, visualize the process of convergence, and give meaning to the definitions. Analyzes…

Illustrates how muMATH can be used for manipulating abstract differentiation rules, optimization, implicit differentiation, related rules, and verifying the chain rule. (MVL)

Illustrated is the problem of solving equations and some different strategies students might employ when using available technology. Gives illustrations for: exact solutions, approximate solutions, and approximate solutions which are graphically generated. (RT)

Provides a program listing in True BASIC which constructs several kinds of matrices: (1) matrices with integral entries that have inverses that have integral entries; (2) matrices with integral entries that have inverses that are rational numbers with reasonable denominators; and (3) matrices with integral entries and prescribed integer…

Describes two chemistry computer programs: (1) "Eureka: A Chemistry Problem Solver" (problem files may be written by the instructor, MS-DOS 2.0, IBM with 384K); and (2) "PC-File+" (database management, IBM with 416K and two floppy drives). (MVL)

Explains graphing functions when using LOTUS 1-2-3. Provides examples and explains keystroke entries needed to make the graphs. Notes up to six functions can be displayed on the same set of axes. (MVL)

Describes two software programs for the Apple II series and TRS-80 Models III and IV: (1) "Personal Energy Inventory" (grades 9-12, records and manages data, not considered user friendly); (2) "Energy Conservation" (grades 7-12, aids in converting and problem solving, uses drill and practice). (MVL)

This document contains the second volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 43 research reports by presenters with last names beginning between Adl…