The article introduces a software application (MATH) supporting an education of Applied Mathematics, with focus on Numerical Mathematics. The MATH is an easy to use tool supporting various numerical methods calculations with graphical user interface and integrated plotting tool for graphical representation written in Qt with extensive use of Qwt…

This paper proposes modelling based learning as a tool for learning and teaching mathematics. The example of modelling real world problems leading to the exponential function as the solution of differential equations is described, as well as the observations about students' activities during the process. The students were acquainted with the…

Many epistemic activities, such as spatial reasoning, sense-making, problem solving, and learning, are information-based. In the context of epistemic activities involving mathematical information, learners often use interactive 3D mathematical visualizations (MVs). However, performing such activities is not always easy. Although it is generally…

This paper shows the basic concept of Functional Modelling in mathematics education which has become more and more important in recent years. Hence it is necessary to think about suitable graphical methods to explain the fundamental idea of a function and its influence on values and other functions. PROGRAPH diagrams are a potentially good way to…

This article examines three important facets of the incorporation of new technologies into educational practice, focusing on emergent usages of the mathematical tools of computer algebra and dynamic geometry. First, it illustrates the interpretative flexibility of these tools, highlighting important differences in ways of conceptualizing and…

This paper analyses technology-based instruction on data-analysis with box plots. Examples of instruction taken from the research literature inform a study of two classes of 17 year-old students (upper secondary) in which the mathematical relationships that their teachers targeted are distinguished as being, or not being, relevant to statistical…

In this paper, I review both mathematics education and CSCL literature and discuss how we can better take advantage of CSCL tools for developing mathematical proof skills. I introduce a model of proof in school mathematics that incorporates both empirical and deductive ways of knowing. I argue that two major forces have given rise to this…

This article traces the historical development of fractal geometry from early in the twentieth century and offers an explanation of the mathematics behind the recursion formulas and their representations within computer graphics. Also included are the fundamentals behind programing for fractal graphics in the C Language with appropriate…

There is much research that documents what many teachers know, that students struggle with many concepts in probability and statistics. This article presents two sample activities the authors use to help preservice teachers develop ideas about how they can use technology to promote their students' ability to understand mathematics and connect…

The LOGO programing of 30 ninth graders was analyzed from 3 theoretical perspectives: the van Hiele levels, the Structure of Observed Learning Outcomes taxonomy, and Skemp's model of mathematical understanding. Results indicate that success in LOGO programing appears necessary but insufficient for success with the geometric aspects of the analyzed…

Describes the derivation of the parameters incorporated into computer programs that are utilized to draw hypocycloids, which are the loci of points traced out by a point on a disk as it rolls against a circle and its interior. Includes information to obtain copies of the programs described. (JJK)

A program has been written for the interactive computer graphics facility at Rensselaer Polytechnic Institute that is designed to assist the user in learning the mathematical technique of convolving two functions. Because convolution can be represented graphically by a sequence of steps involving folding, shifting, multiplying, and integration, it…

This is the first of a two-part series on the general concept of vector space. Provides tool procedures to allow investigation of vector properties, vector addition and subtraction, and X and Y components. Lists several sources of additional vector ideas. (JM)

Investigates the mathematical behavior of 30 college students in a problem situation that requires them to find the inverse of a given compound element in an environment of LOGO turtle graphics. Results from interviews indicate that, in searching for the inverse, students tend to invert the elements but not the order. (MDH)

Presents the geometric, software-ergonomic, and educative standards for interactive graphics systems envisioned for planimetric constructions and calculations in secondary mathematics instruction. Describes the geometric-didactic potentials of the MS DOS-Version 1.6 of CABRI-Gomtre which is an Intelligent Tutoring System with the possibilities for…