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

Interdisciplinary Mathematics Education

Mathematics Education; Learning; Teachin

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

Interdisciplinary mathematics education: a state of the art

This book provides an essential introduction to the state-of the-art in interdisciplinary Mathematics Education. First, it begins with an outline of the field’s relevant historical, conceptual and theoretical backgrounds, what “discipline” means and how inter-, trans-, and meta-disciplinary activities can be understood. Relevant theoretical perspectives from Marx, Foucault and Vygotsky are explained, along with key ideas in theory, e.g. boundaries, discourses, identity, and the division of labour in practice. Second, the book reviews research findings of mainly empirical studies on interdisciplinary work involving mathematics in education, in all stages of education that have become disciplined. For example, it reports that a common theme in studies in middle and high schools is assessing the motivational benefits for the learner of subsuming disciplinary motives and even practices to extra-academic problem-solving activities; this is counter-balanced by the effort needed to overcome the disciplinary boundaries in academic institutions, and in professional identities. These disciplinary boundaries are less obviously limitations in middle and primary schools, and in some vocational courses. Third and finally, it explores selected case studies that illustrate these concepts and findings, both in terms of the motivational benefits for learners and the institutional and other boundaries involved

Kindergarten students' understanding of probability concepts

This study explored kindergarten students’ intuitive strategies and understandings in probabilities. The paper aims to provide an in depth insight into the levels of probability understanding across four constructs, as proposed by Jones (1997), for kindergarten students. Qualitative evidence from two students revealed that even before instruction pupils have a good capacity of predicting most and least likely events, of distinguishing fair probability situations from unfair ones, of comparing the probability of an event in two sample spaces, and of recognizing conditional probability events. These results contribute to the growing evidence on kindergarten students’ intuitive probabilistic reasoning. The potential of this study for improving the learning of probability, as well as suggestions for further research, are discussed

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

Mathematical modelling as a prototype for interdisciplinary mathematics education?-Theoretical reflections

International audienceIn the last years the discussion for promoting Science, Technology, Engineering, and Mathematics (STEM) education became a central goal of educational policy in many countries worldwide, in an attempt to prepare students for a scientific and technological society. However, interdisciplinary mathematics teaching and learning is not limited to the "STE" and should include other disciplines across the curriculum. Mathematical modelling, as a mathematical practice and key competence within mathematics education standards could be interpreted as an excellent example for promoting not only modelling competencies, but also interdisciplinary mathematics education (IdME) in school. In this paper we focus theoretically on the question, 'Which core similarities and differences can be stated between the two fields along three perspectives?', by presenting a piece of theory describing the interplay between IdME and mathematical modelling

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