GeoGebra is the most well-known Dynamic Geometry Application (DGA) in the world. Many researchers are interested in GeoGebra as a tool to make interactive mathematics resources. Here we focus on a snapping function in GeoGebra, which is a kind of general feature of DGA: the mouse cursor is attracted to a specific position or a specific object and…

Vietnam today is having solid innovations in the fields of science, technology, economics, and education. In particular, the Mathematical General Education program launched in 2018 has emphasized the exploitation of information technology in teaching. GeoGebra software is taught right from the 6th grade. GeoGebra software has many advantages in…

This design case describes the development of the Invention Coach, an intelligent exploratory learning environment (ELE) for the constructivist activity of Invention. The Invention Coach scaffolds students as they invent mathematical formulas to describe contrasting cases. In this paper, we detail our process and rationale for three key design…

In a 9-month training experiment, 64 first graders with a risk factor were randomly assigned to computer-assisted structured discovery of the add-1 rule (e.g., the sum of 7 + 1 is the number after "seven" when we count), unstructured discovery learning of this regularity, or an active-control group. Planned contrasts revealed that the…

We describe exercises in which students use PascGaloisJE to formulate conjectures about certain binomial identities which hold when the binomial coefficients are interpreted as elements in the cyclic group Z[subscript p] of integers modulo a prime integer "p". In addition to having an appealing visual component, these exercises are open-ended and…

The progression from simple interest to compound interest leads naturally and quickly to the number e, involving mathematical discovery learning through writing programs. Several programs are given, with suggestions for a teaching sequence. (MNS)

Explores a particular method of searching for roots that lends itself well to discovery learning through writing a computer program. The teacher-student interaction is given, and two computer program listings are included. (MNS)

The use of trial-and-error strategies to solve problems is endorsed. Types of problems with which trial and error is effective are discussed, with examples of how it is used, and teaching considerations are briefly considered. A computer program for one problem is included. (MNS)

Uses of Dynamic Geometry Software (DGS) are often limited purely to a verifying role. Presents a case study that emerged from a project in which DGS formed an integral part of the pedagogical arrangement. The study demonstrates how the contrasting power of DGS might be utilized in a guided discovery setting. (Contains 17 references.) (Author/ASK)

The analysis and simulation of spiral growth in plants integrates algebra and trigonometry in a botanical setting. When the ideas presented here are used in a mathematics classroom/computer lab, students can better understand how basic assumptions about plant growth lead to the golden ratio and how the use of circular functions leads to accurate…

Presents an analysis of the question in the title which involves a discussion of fractions, number theory, and probability through modeling, exploring, and other mathematical connections. (MKR)

Suggested are investigations of rational numbers and their decimal representations where a computer generates the data for explorations. Conjectures and two program listings are included. (MNS)

Three examples are given in which students create their own Logo software to explore the topics of number patterns and operations, fractions, and decimal parts in measurement. (MNS)

Activities to extend the core curriculum through the study of the periodicity of rational numbers to help students develop calculator and research skills are presented. Four worksheets are included, to be used as discovery activities. A computer program is listed, as well as examples of periodic pictures. (MNS)

Presents activities which use graphing calculators to explore parametric equations of spirals, circles, and polygons. (MKR)