This article discusses the advanced characteristics of a mathematical and geometrical system explained and published in the course of several preceding journal articles (Teia, 2015, 2016, 2018a and 2018b). The reading of the preceding articles is encouraged for a clearer understanding of the discussion that follows.

The purpose of this research study was to understand how linear algebra students in a university in the United States make sense of subspaces of vector spaces in a series of in-depth qualitative interviews in a technology-assisted learning environment. Fourteen mathematics majors came up with a diversity of innovative and creative ways in which…

Despite few limitations, GeoGebra as a dynamic geometry software stood as a powerful instrument in helping university math majors understand, explore, and gain experiences in visualizing the limits of functions and the ?-d formalism. During the process of visualizing a theorem, the order mattered in the sequence of constituents. Students made use…

This study describes the mathematical construction of a real-life model by means of parametric equations, as well as the two- and three-dimensional visualization of the model using the software GeoGebra. The model was initially considered as "determining the parametric equation of the curve formed on a plane by the point of a pen, positioned…

This study investigates prospective secondary mathematics teachers' visual representations of polynomial and rational inequalities, and graphs of exponential and logarithmic functions with GeoGebra Dynamic Software. Five prospective teachers in a university in the United States participated in this research study, which was situated within a…

I report on the findings from research and literature on (a) use of symbols in mathematics, (b) algebraic/trigonometric expressions, (c) solving equations, and (d) functions and calculus. From these, some insights and implications for teaching and learning are derived.

The purpose of this study was to assess algebra and geometric prerequisites skills as incorporated into the Applied Calculus Optimization Problem (ACOP) solution. The difficulties that students encounter in applying algebraic and geometric prerequisites at the early stages of the ACOP solution were identified. The study analyzes errors related to…

This CD-ROM consists of software that allows both teachers and students to create and experiment with mathematical models by linking shapes, graphs, numbers, and equations. It is usable for demonstrations, home learning, reinforcing concepts, illustrating concepts that are difficult to visualize, further pupil investigations, and project work.…

The Proceedings of PME-XVI has been published in three volumes because of the large number of papers presented at the conference. Volume 1 contains: (1) brief reports from each of the 11 standing Working Groups on their respective roles in organizing PME-XVI; (2) brief reports from 6 Discussion Groups; and (3) 35 research reports covering authors…

This document contains the fourth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Kun and…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…