Applications of Tulip Motif in Turkish Art with Geometer’s Sketchpad Program

In the 21st century we live in, technology is developing rapidly. Inevitably, the technologies used in almost every area of daily life will also reflect in the field of education. Educational technologies, which enable students to grasp abstract concepts more easily and facilitate the teaching process for teachers, have increased their impact in schools. The effects of dynamic geometry software on course success, attractiveness, and concretization in mind have been the subject of different studies. Dynamic geometry software that can visualize algebraic expressions with graphics creates an interdisciplinary working environment with its drawing features. Thanks to Geometer’s Sketchpad (GSP), one of this software, students can dynamically create very different patterns and shapes. Students can realize higher-level cognitive learning thanks to the relationships and inferences they make on these shapes. These and similar patterns that emerged thanks to GSP can increase students’ awareness in different fields by combining different disciplines such as history, mathematics and art. In this study, the drawing stages of the tulip motif, which we come across in important architectural works in the Ottoman and Anatolian Seljuk history, which have been the subject of ornament art, are shown via GSP using both the transformation geometry and functions.

Prospective teachers constructing dynamic geometry activities for gifted pupils: Connections between the frameworks of Krutetskii and van Hiele

The Swedish educational system has, so far, accorded little attention to the development of gifted pupils. Moreover, up to date, no Swedish studies have investigated teacher education from the perspective of mathematically gifted pupils. Our study is based on an instructional intervention, aimed to introduce the notion of giftedness in mathematics and to prepare prospective teachers (PTs) for the needs of the gifted. The data consists of 10 dynamic geometry software activities, constructed by 24 PTs. We investigated the constructed activities for their qualitative aspects, according to two frameworks: Krutetskii’s framework for mathematical giftedness and van Hiele’s model of geometrical thinking. The results indicate that nine of the 10 activities have the potential to address pivotal abilities of mathematically gifted pupils. In another aspect, the analysis suggests that Krutetskii’s holistic description of mathematical giftedness does not strictly correspond with the discrete levels of geometrical thinking proposed by van Hiele.

Dealing with Degeneracies in Automated Theorem Proving in Geometry

We report, through different examples, the current development in GeoGebra, a widespread Dynamic Geometry software, of geometric automated reasoning tools by means of computational algebraic geometry algorithms. Then we introduce and analyze the case of the degeneracy conditions that so often arise in the automated deduction in geometry context, proposing two different ways for dealing with them. One is working with the saturation of the hypotheses ideal with respect to the ring of geometrically independent variables, as a way to globally handle the statement over all non-degenerate components. The second is considering the reformulation of the given hypotheses ideal—considering the independent variables as invertible parameters—and developing and exploiting the specific properties of this zero-dimensional case to analyze individually the truth of the statement over the different non-degenerate components.

Research trends in dynamic geometry software: A content analysis from 2005 to 2021

Dynamic geometry software (DGS), especially GeoGebra, have been used in mathematics lessons around the world since it enables a dynamic learning environment. To date, there exist so many published researches about DGS, which leads to the need for meaningful organisation. This study aims to give a broad picture about researches related to DGS. For this reason, 210 articles accessed from the Web of Science database were analysed in terms of their purpose, research design, sample level, sample size, data collection tools and data analysing methods by using the content analysis method. According to the findings, for each section the most frequently used ones were as follows: ‘the effect of DGS on something’ as a purpose, qualitative method as a research design, high school students as a sample level, 101–300 intervals as a sample size, documents and achievement tests as instruments and descriptive analysis for quantitative and qualitative studies. These results can help researchers to see the past trends in DGS and conduct new studies. Keywords: Dynamic geometry software, DGS, GeoGebra, content analysis, mathematics education

A critical analysis of how the potential of Dynamic Geometry Software as a visualisation tool may enhance the teaching of Mathematics

Visualisation in the mathematics classroom has its own pedagogical value and plays a significant role in developing mathematical intuition, thought and ideas. Dynamic visualisation possibilities of current digital technologies afford new ways of teaching and learning mathematics. The freely available GeoGebra software package is highly interactive and makes use of powerful features to create objects that are dynamic, and which can be moved around on the computer screen for mathematical exploration. This research study was conceptualised within the GeoGebra Literacy Initiative Project (GLIP) – an ICT teacher development project in Mthatha in the Eastern Cape, South Africa. The focus of this study was on how GeoGebra could be used as a teaching tool by harnessing its powerful visualisation capacity. In the study, selected GLIP teachers collaboratively developed GeoGebra applets, then implemented and evaluated them. The research methodology took the form of action research cycles in which the design, implementation and evaluation of successive applets determined the data gathering and analysis process. My data consisted mainly of recorded observations and reflective interviews. The underlying theoretical foundation of this study lies in constructivism, which aligned well with the conceptual and analytical framework of Kilpatrick et al.’s (2001) description of teaching proficiency. An in-depth analysis of my classroom observations resulted in multiple narratives that illuminated how teachers harnessed the visualisation capabilities inherent in the software. My findings showed that dynamic visualisation and interactivity afforded by the use of technology are key enabling factors for teachers to enhance the visualisation of mathematical concepts. My analysis across participants also showed that technical difficulties often compromised the use of technology in the teaching of mathematics. The significance of this research is its contribution to the ongoing deliberations of visualisation and utilisation of technological resources, particularly through the empowerment of a community of teachers. The findings recognised that the integration of technology required appropriate training, proper planning and continuous support and resources for the teaching of mathematics. This action research provided insightful information on integrating Dynamic Geometry Software (DGS) tools in mathematics classrooms that could be useful to teachers and curriculum planners.

That Was Then…This is Now: Utilizing the History of Mathematics and Dynamic Geometry Software

Pre-service mathematics teacher (PST) education often addresses within Geometry Classes how to utilize Dynamic Geometric Software (DGS). Other classes may also incorporate teaching pre-service teachers about the history of mathematics. Although research has documented the use of Dynamic Geometric Software (DGS) in teaching the history of mathematics (HoM) (Zengin, 2018), the focus of this research specifically targets the development of proof for pre-service teachers by utilizing DGS to revisit historical proofs with a modern lens. The findings concur with Fujita et.al. (2010), Zengin (2018), and Conners (2007) work on proof. The novelty of this article was the combination of incorporating the history of mathematics (HoM), dynamic geometry software (DGS), and Toulmin’s model of argumentation. A pedagogical approach appeared to emerge: DGS’s dynamic nature allowed PSTs to see several examples of a method to provide them with an illustration that may be used in proofs.

The Effectiveness of Dynamic Geometry Software Applications in Learning Mathematics: A Meta-Analysis Study

The purpose of this study was to (1) assess the impact of using Dynamic Geometry Software (DGS) on students’ mathematical abilities, (2) determine the differences in effectiveness based on study characteristics in order to help educators decide under what conditions the use of DGS would be suitable in improving students' mathematical abilities. This meta-analysis study investigates 57 effect sizes from 50 articles that have been published in journals, international and domestic proceedings from 2010 to 2020 using the Comprehensive Meta-Analysis (CMA) tool as a calculation tool. Meanwhile, the Hedges coefficient is applied to the calculation of the effect size at the 95% confidence level. Based on a random effect model with a standard error of 0.09, the analysis results have found an overall effect size of 1.07. This means that learning using DGS has a high positive effect on students' mathematical abilities. The effect size of 1.07 explains the average student who uses DGS exceeds 84% math ability of those in conventional classes that are initially equivalent. Analysis of the study characteristics found significant differences in terms of sample size, student to computer ratio, and education level. This research showed the DGS used was more effective under certain conditions. First, it is very effective in sample conditions less than or equal to 30. Second, it provides classrooms with a sufficient number of computers, allowing students to use them individually, which is required to achieve higher effectiveness levels. Third, DGS is effective in high schools and colleges than in junior high schools. These facts can help educators in deciding on the appropriate sample sizes, student to computer ratios, and future levels of education in using DGS.

Visual argumentations in teaching trigonometry

In this paper, we study the possibility of building a learning path that allows students to develop trigonometric knowledge and skills by the end of Grade 10 of secondary science-based schools. In particular, we describe an action research experiment, in part done through distance learning, aimed at incorporating all trigonometry topics within the framework of the study of Euclidean geometry. The inquiry-based learning methodology and the support of dynamic geometry software with a laboratory teaching approach were used. The learning path is based on several “visual/dynamic proof” and is explained by an example lesson on the Cosines Law. The experiment could be extended by teachers into physical/virtual classrooms and could offer practical strategies and tools for teaching trigonometry.