Home » Vol. 27 no. 1 (2020)

# Vol. 27 no. 1 (2020)

## Content of Vol. 27 No. 1 (2020)

### Integrating STEM-related Technologies into Mathematics Education at a Large Scale

By  Zsolt Lavicza; Theodosia Prodromou; Kristof Fenyvesi; Markus Hohenwarter; Istvan Juhos; Balazs Koren; Jose Manuel Diego-Mantecon

This paper outlines the growing phenomenon and need to integrate technologies into mathematics and science teaching and learning. There are a number of successful projects for valuable integration of technologies around the world, however, these successes are often limited reaching a relatively small number of teachers and students. In this paper, we aim to offer examples of large-scale technology projects that could create a critical mass of users that could further drive innovation and sustainability for educational technology integration. We outline how GeoGebra became one of the most widely used dynamic mathematics software with a user base of more than 100 million; highlight directions of research for technology development and integration; and describe the Geomatech project that aimed to train 2500 teachers in 950 schools in Hungary. We hope that such examples, the developed technology, resources and pedagogies could contribute to further valuable integrations of technologies in mathematics and science education.

### On Materials Which Allow Students to Find Out Mathematical Propositions Using Snapping on GeoGebra

By Hara, Tomoki; Ahara, Kazushi

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 it looks like magnetic attraction. Snapping to a lattice point is originally implemented in GeoGebra. Some examples of extended snapping function are introduced in GeoGebra Material platform. The goal of this paper is to argue the effectiveness of snapping function in GeoGebra from the viewpoint of making educational materials. We propose some positive examples of resources with snapping functions. We also use GeoGebra resources both with and without snapping functions, and report the results of questionnaires about these materials in a class of a simulated lesson.

### Dynamic Geometry Systems in Proving 3D Geometry Properties

By Ferrarello, Daniela; Mammana, Maria Flavia; Taranto, Eugenia

A classroom activity for high-school students, aiming at introducing space geometry from plane geometry has been introduced back in 2009 by Mammana, Margarone, Micale, Pennisi and Pluchino (2009a). The activity was based on the use of a Dynamic Geometry System and of the analogy between figures. Several aspects of the activity have been studied in different research studies. What we focus on, in this paper, is the power of the Dynamic Geometry System and of the analogy in the proof phase when working in a three dimensional environment, highlighting the cognitive process evolving in some 3D geometry proofs, by using videos recorded during the activities in the classroom.

### Stories & Technology: Gateways to Mathematics for All

By Terrell, Karen; DeBay, Dennis

This article suggests the use of presentation technologies and electronic books as ways in which to employ Universal Design for Learning (UDL) principles in the mathematics classroom. In particular, the focus is on using easily accessible technologies to assist students with print and language difficulties in comprehending and reasoning with mathematical word problems. Two examples of these implementations will be presented and examined.

### Learning How to Solve Linear Equation with Equation Buster

By Gandra, Ana Paula; Aires, Ana Paula; Catarino, Paula

This paper reports a study developed with twenty-six students from a 7th-grade class and was carried in the context of teaching experience in the school year of 2016/2017, using an applet, Equation Buster, on the learning of solving single-variable linear equations. The research objectives are to assess how this applet can help students to see the value of isolating the unknown when solving an equation, to visualize the addition and multiplication properties of equality, to discover these relationships from themselves, and to contribute the development of their algebraic thinking. The methodological approach is qualitative with the characteristics of case study research. The results show that using Equation Buster together with the teacher’s mediation helps students to learn how to solve equations by applying the properties of equality or/and the rules of solving equations. It was concluded that there was a significant evolution in the students’ performance in the area of generalization.

### Peer Review Methodology in a Blended Course for Mathematics Teacher Education

By Dello Iacono, Umberto; Pierri, Anna; Taranto, Eugenia

In the last years, the interest of mathematics educators in digital tools has progressively increased, having as consequence a great impact on how teachers plan their teaching activities. In this paper we investigate, by using the Meta-Didactical Transposition, if the peer review methodology, carried out in a blended course, can facilitate the teachers as instructional designers. The aim of the meta-didactical praxeologies put in action by the trainers was focused on the sharing and reflection with the teachers on a specific topic relative to the argumentative competence. A qualitative analysis of the educational activities produced by the teachers has shown that the peer review methodology enables the teachers to improve their role of the instructional designer.

### Visual Mental Images’ Connected Paper-and-Pencil Iconic and Non-Iconic Representations

By Vagova, Renata; Kmetova, Maria; Lavicza, Zsolt

Although we move and live in three-dimensional space, many prefer “two-dimensional” thinking in mathematics lessons. As a result, the transition between physical objects and their graphical representations can be considered one of the most common difficulties in learning and teaching solid geometry. This paper describes results of our quantitative-qualitative research focused on solving a non-standard spatial visualisation problem. Demanding mathematical operations are not required in its solution, but creating the right mental images of 3D objects and the ability of their mental manipulation are key to the correct solution. Students’ paper-and-pencil solutions were the main source of research data and the principal aim of the study was to examine the relation between the number of correct external representations (iconic or non-iconic) and the numerical scores in student solutions. In this article, we focus on the qualitative findings and supplement them with quantitative results.

### Visualizing and Understanding Optimization Problems Using Dynamic Software

By Gordon, Sheldon P.

The article uses dynamic visualizations in Excel to examine a variety of ways in which students can attain a much greater depth of understanding of optimization problems in introductory calculus. The topics discussed include a variety of common optimization problems that appear in virtually every calculus textbook that can all be enhanced dramatically using dynamic software that provides both graphical and numerical support to increase student understanding.