Problem Solving and Problem Posing in a Dynamic Geometry Environment

In this study, we considered dynamic geometry software (DGS) as the tool that mediates students’ strategies in solving and posing problems. The purpose of the present study was twofold. First, to understand the way in which students can solve problems in the setting of a dynamic geometry environment, and second, to investigate how DGS provides opportunities for posing new problems. Two mathematical problems were presented to six pre-service teachers with prior experience in dynamic geometry. Each student participated in two interview sessions which were video recorded. The results of the study showed that DGS, as a mediation tool, encouraged students to use in problem solving and posing the processes of modeling, conjecturing, experimenting and generalizing. Furthermore, we found that DGS can play a significant role in engendering problem solving and posing by bringing about surprise and cognitive conflict as students use the dragging and measuring facilities of the software

Developing student spatial ability with 3D software applications

This paper reports on the design of a library of software applications for the teaching and learning of spatial geometry and visual thinking. The core objective of these applications is the development of a set of dynamic microworlds, which enables (i) students to construct, observe and manipulate configurations in space, (ii) students to study different solids and relates them to their corresponding nets, and (iii) students to promote their visualization skills through the process of constructing dynamic visual images. During the developmental process of software applications the key elements of spatial ability and visualization (mental images, external representations, processes, and abilities of visualization) are carefully taken into consideration

Stereometry activities with DALEST

This book reports on a project to devise and test a teaching programme in 3D geometry for middle school students based on the needs, knowledge and experiences of a range of countries within the European Union. The main objective of the project was the development (and testing) of a dynamic three-dimensional geometry microworld that enabled the students to construct, observe and manipulate geometrical figures in space and which their teachers used to help their students construct an understanding of stereometr

Developing the 3DMath dynamic geometry software: theoretical perspectives on design

Designing successful learning environments entails drawing on theoretical perspectives on learning while, at the same time, being cognisant of the affordances and constraints of the technology. This paper reports on the development of a software environment called 3DMath, a dynamic three-dimensional geometry microworld aimed at enabling learners to construct, observe and manipulate geometrical figures in a 3D-like space. During the development of 3DMath, the key elements of visualisation, including theoretical ideas of mental images, external representations, and the processes and abilities of visualisation, were taken into consideration. The aim of this paper is to illustrate how the design of this particular software was informed by these elements of visualisation, as well as by theories related to the philosophical basis of mathematical knowledge and by semiotics. The paper illustrates how the features of software can be designed to take account of relevant theoretical notions and to satisfy the characteristics of instructional techniques that are appropriate to theoretical perspectives on learning

Developing 3D dynamic geometry software: theoretical perspectives on design

This paper reports on the theoretical perspectives underpinning the design of a 3D geometry software environment called 3DMath. The idea of 3DMath is to develop a dynamic three dimensional geometry microworld, which enables (i) students to construct, observe and manipulate geometrical figures in 3D space, (ii) students to focus on modeling geometric situations, and (iii) teachers to help students construct their understanding of stereometry. During the developmental of 3DMath, the key elements of visualization (mental images, external representations, and the processes and abilities of visualization) are being carefully taken into consideration. The aim of this paper is to illustrate how the design of the 3DMath software is informed by these key elements of visualization, as well as by theories related to the philosophical basis of mathematical knowledge and to semiotics. Thus, the paper describes how the features of the software are designed to enhance the elements of visualization, and to satisfy the characteristics of instructional techniques that are appropriate to these theoretical perspectives

Unpacking 9th grade students’ algebraic thinking

International audienceThe purpose of the present study was to propose and empirically validate a model describing secondary school students’ algebraic thinking. Based on a synthesis of the literature, a model for Grade 9 students’ algebraic thinking was formulated. The major constructs incorporated in this model were “generalized arithmetic”, “transformational ability” and “meta-algebra”. The study involved one hundred fourteen students. Data analysis validated the hypothesized model and suggested a sequential effect between the three factors. Transformational ability had a direct effect on generalized arithmetic and the latter had a direct effect on meta-algebra

Developing an active learning environment for the learning of stereometry

This paper reports on the design of a dynamic environment for the learning of stereometry (DALEST) and the teaching of spatial geometry and visual thinking. The development of the software was in the framework of DALEST project which aimed at developing a dynamic three-dimensional geometry microworld that enables students to construct, observe and manipulate geometrical figures in space, and to focus on modelling geometric situations. The environment will also, support teachers in helping their students to construct a suitable understanding of stereometry. During the developmental process of software applications the key elements of spatial ability and visualization were carefully taken into consideration with emphasis on enhancing dynamic visualization as an act of construction of transformations between external media and student’s mind