GeoGebra: towards realizing 21st century learning in mathematics education

Purpose – This study examines the effect using GeoGebra dynamic geometry software on students’ ability to confront geometry problem solving, their achievement in spatial visualization skills, and their usage of cognitive skills in applying, analyzing, evaluating, creating and constructing ideas for geometry problem solving on the topic of Shape and Space towards supporting 21st century learning of Mathematics Education.Methodology – Quantitative and qualitative data were collected for this study. A total of 102 Form Two students participated in the study, which had employed the pre-test and post-test quasi-experimental research design. The research participants were divided into three groups, namely Experimental Group 1 (n=33), Experimental Group 2 (n=35) and Control Group (n=34). A guideline book on using GeoGebra dynamic geometry software in learning of Shape and Space, developed by the researchers and validated by a panel of experts, was used by the teachers and students in the experimental groups. The quantitative data, obtained via the Topical Test (TT) and Spatial Visualization Ability Test (SVAT), were analysed using MANOVA. The reliability coefficients of TT and SVAT were 0.972 and 0.953 respectively. The qualitative data, collected via interviews, teaching observations, video recordings and students’ works, was thematically analysed. Findings – The experimental groups’ TT and the SVAT post-test mean scores for both the experimental groups were significantly higher than the control group’s TT and the SVAT post-test mean scores. The learning of Shape and Space using GeoGebra dynamic geometry software had enabled students to produce works with evidence of critical, creative and innovative elements in their solutions. The experimental groups’ students agreed that using the dynamic software something new to them and was indeed as an attractive way to learn mathematics because they had the opportunity to experience hands-on learning of mathematics using ICT. They voiced their dessire to also use the GeoGebra dynamic geometry software when learning other mathematics topics. Significance – The use of GeoGebra dynamic geometry software to support the notion of integration of technology in the teaching and learning of mathematics in schools has the potential to promote active students involvement in mathematics learning. The active learning could provide students with meaningful learning experiences and opportunities to produce quality, creative and innovative works.The dynamic software has the capacity to support students’ logical and systematic approaches in solving geometry problems and also triggers multiple ways of interactions and collaborations in the mathematics classrooms. The stimulation of students’ creative and innovative thinking provide evidence for the potential support of the dynamic software towards realizing 21st century learning within Mathematics Education

Dynamic Euclidean Geometry: pseudo-Toulmin modeling transformations and instrumental learning trajectories

The present paper attempts to bridge the world of DGS technology with the world Euclid bequeathed to us in his "Elements". Competence in the DGS environment depends on the competence of the cognitive analysis as students seek to decode their ideas using the tools provided by the software. The dynamic notions (e.g., dynamic point, dynamic segment, instrumental decoding, hybrid-dynamic objects, active/ “alive” representations etc.), are taken as given and form the specific /particular theoretical basis for the constructive processes. Dynamic Euclidean constructions will be considered using pseudo-Toulmin’ diagrams. These considerations provide a theoretical basis for the idea that, in order to solve a mathematical construction problem in Dynamic Euclidean Geometry, we have to build up the interdependencies of tools in various sequential steps (based on theorems and definitions and the competence in using tools) which can be linked to the level of our conceptualization. The central idea is the following: Do the tools of Dynamic Euclidean Geometry determine a new kind of Geometry? Is Dynamic Euclidean Geometry a new kind of geometry? Does it have its own axiomatic system or its own undefined terms? In the paper, the notion of an instrumental learning path/trajectory is introduced as the interdependence/intra-dependence between dynamic tools, diagrams and mathematical objects during an instrumental decoding process. Keywords: Dynamic geometry, Euclid “Elements”, instrumental learning trajectories, Dynamic Euclidean Geometry DOI: 10.7176/JEP/12-9-09 Publication date:March 31st 202

Traditional Teaching About Angles Compared To An Active Learning Approach That Focuses On Students Skills In Seeing, Measuring And Reasoning, Including The Use Of Dynamic Geometry Software: Differences In Achievement

This research was about an intervention developed for students at the junior high school level, in which the researcher was teaching the concept of angles through paper exercises as well as dynamic geometry software (DGS), using an active learning approach. This research was to find out the impacts of the use of such an approach on students in their learning activities. The researcher compared two parallel classes at the same level, which were the first level of junior high school (age 13-14 years old). The experimental class was taught by the researcher according to the designed intervention. Meanwhile, the control class was taught by the collaborative teacher according to her regular teaching method without using DGS. The data were collected by means of tests (pretest and the posttest), questionnaires, and interviews. Analysis of the pretest scores shows that the experimental class did better than the control class did, but there was initially no significant difference. After the intervention, analysis shows that the experimental class did better than the control class in the end, and the difference was significant. Key words: Active learning, DGS, Student’s achievement, Traditional teachin

Designing digital technologies and learning activities for different geometries

This chapter focuses on digital technologies and geometry education, a combination of topics that provides a suitable avenue for analysing closely the issues and challenges involved in designing and utilizing digital technologies for learning mathematics. In revealing these issues and challenges, the chapter examines the design of digital technologies and related forms of learning activities for a range of geometries, including Euclidean and co-ordinate geometries in two and three dimensions, and non-Euclidean geometries such as spherical, hyperbolic and fractal geometry. This analysis reveals the decisions that designers take when designing for different geometries on the flat computer screen. Such decisions are not only about the geometry but also about the learner in terms of supporting their perceptions of what are the key features of geometry

About a constructivist approach for stimulating students' thinking to produce conjectures and their proving in active learning of geometry

The paper describes processes that might lead secondary school students to produce conjectures in a plane geometry. It highlights relationship between conjecturing and proving. The author attempts to construct a teaching-learning environment proposing activities of observation and exploration of key concepts in geometry favouring the production of conjectures and providing motivation for the successive phase of validation, through refutations and proofs. Supporting didactic materials are built up in a way to introduce production of conjectures as a meaningful activity to students

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

On development of students' abilities in problem posing: a case of plan geometry

The paper reports on results of the training, which was aimed at the formation of skills and habits of posing problems of different complexity levels in the course of plane geometry using the drawing as the primary source for students’ activities in problem posing process. The paper describes and analyses some tasks, which were developed to enable the researchers to look into the thinking processes used by students when they are involved in problem posing activities. The author stresses role of students’ skills to inquiry work and important features of the use of technology in the different stages of the training

Using materials from the history of mathematics in discovery-based learning

This paper reports on attempt to integrate history of mathematics in discovery-based learning using technology. Theoretical grounding of the idea is discussed. An exploratory environment on triangle geometry is described. It is designed to support and motivate students' activities in learning through inquiry. Conjectures about properties of Lemoine point and Simson line are produced and proved by students using e-learning textbook