Research bibliography: dynamic geometry software

This bibliography lists research that has investigated the use of dynamic geometry software (DGS) in the teaching and learning of mathematics. The bibliography is not intended to be exhaustive; rather it includes the major studies across the range of research that has been published

Proof in dynamic geometry environments

This article suggests that there is a range of evidence that working with dynamic geometry software affords students possibilities of access to theoretical mathematics, something that can be particularly elusive with other pedagogical tools. Yet the paper concludes that further research into the use dynamic geometry software to support the development of students’ mathematical thinking could usefully focus on the nature of the tasks students tackle, the form of teacher input, and the role of the classroom environment and culture

Geometry learning: The role of tasks, working models, and dynamic geometry software

We present several learning experiences that illustrate how three aspects of the geometric competence, constructing and analyzing properties of figures, identifying patterns and investigating and geometric problem solving, were developed by pupils that participated in the implementation of an innovative geometry teaching unit in grade 8. The topics addressed were dealing with properties of two dimensional figures, Pythagoras theorem, loci, translations and similarity of triangles. The development of the geometric competence was clearly supported by the dynamic geometry environment but unfolded in different ways, depending on the way how pupils reacted to the different types of tasks.Apresentamos várias experiências de aprendizagem que ilustram como três aspectos da competência geométrica, construir e analisar propriedades de figuras, identificar regularidades e investigar e resolver foram desenvolvidos por alunos que participaram de uma experiência de ensino inovadora no campo da Geometria no 8.º ano de escolaridade. Os temas tratados incluem o trabalho com figuras bidimensionais, teorema de Pitágoras, lugares geométricos, translações e semelhança de triângulos. O desenvolvimento da competência geométrica foi claramente apoiado pelo ambiente de geometria dinâmica mas processou-se de formas diferentes, em resultado do modo como os alunos reagiram aos diferentes tipos de tarefa

Discovering New Tessellations Using Dynamic Geometry Software

In this paper we use dynamic geometry software to investigate a class of tilings called k-uniform tilings or tessellations. A tiling consisting of regular polygons whose vertices belong to k-transitivity classes under the action of its symmetry group (vertex-k-transitive) is said to be k-uniform. We also present constructions of tilings consisting of irregular polygons that are vertex-k-transitive

Tools and technologies in mathematical didactics

This short paper provides an overview of recent European research about the use and impact of tools and technologies in mathematical didactics. Such research is categorised as focusing on theoretical ideas, on algebraic knowledge when using spreadsheet and computer algebra (CAS), and on dynamic geometry software (DGS). The paper reveals the variety of software technologies, education levels, and methodologies utitised in European research

Instrumented activity and semiotic mediation: two frames to describe the conjecture construction process as curricular organizer

We document part of the process through which conjectures produced by students, with the aid of the dynamic geometry software Cabri, when they solve proposed geometric problems, become a curriculum organizer in the classroom. We first focus on characterizing students’ instrumented activity recurring to utilization schema (Rabardel, 1995, in Bartolini Bussi and Mariotti, 2008), and then describe the teacher’s content management through which the ideas produced by the students become key elements of knowledge construction

Teachers\u27 Conceptions of Mathematics and Intelligent Tutoring System Use

The purpose of this mixed-methods study was to investigate the relationship between teachers’ conceptions of mathematics and their use of intelligent tutoring systems for mathematics instruction. Intelligent tutoring systems are adaptive computer programs which administer mathematics instruction to students based on their cognitive state. A conception is a mixture of beliefs and knowledge. The participants in this study were 93 junior high school mathematics teachers from three school districts in the Midwest. Data were gathered using a two-part online survey. The first part of the survey contained questions about their use of intelligent tutoring systems, graphing calculators, Desmos and dynamic geometry software. The second part of the survey contained Likert questions from the teachers’ version of the Conceptions of Mathematics Inventory. Desmos is a website providing interactive classroom activities and a user-friendly graphing calculator. Dynamic geometry software is a class of interactive geometry programs. The quantitative analysis revealed no statistically significant interactions between teachers’ conception scores and intelligent tutoring system use, or between teachers’ conception scores and how intelligent tutoring systems were used. There were statistically significant interactions between teachers’ conception scores and their use of graphing calculators, Desmos, and dynamic geometry software. The qualitative analysis revealed that teachers used intelligent tutoring systems for differentiation. Teachers used graphing calculators, Desmos, and dynamic geometry software for visual, computational, and exploratory purposes. Teachers exclusively using intelligent tutoring systems to incorporate technology should also incorporate technology which promotes student exploration

PENGARUH PEMBELAJARAN MATEMATIKA BERBANTUAN DYNAMIC GEOMETRY SOFTWARE (DGS) TERHADAP KEMAMPUAN SPASIAL: STUDI REVIU SISTEMATIS DAN META-ANALISIS

Beberapa studi meta-analisis terkait pengaruh pembelajaran matematika berbantuan Dynamic Geometry Software terhadap kemampuan matematis sudah dilakukan oleh beberapa peneliti. Namun, mereka belum mengkaji secara khusus penggunaan Dynamic Geometry Software dalam pembelajaran matematika untuk kemampuan spasial siswa. Studi ini bertujuan untuk mengestimasi, menguji dan membandingkan pengaruh dari pembelajaran matematika berbantuan Dynamic Geometry Software terhadap kemampuan spasial siswa, serta menginvestigasi dan menguji beberapa faktor potensial yang diprediksi sebagai faktor penyebab heterogennya kemampuan spasial siswa dengan menggunakan studi reviu sistematis dan meta-analisis. Dari 56 studi primer yang disintesis, implementasi pembelajaran matematika berbantuan Dynamic Geometry Software mempunyai ukuran efek g=0,848 dengan pengaruh yang sedang terhadap kemampuan spasial siswa. Selanjutnya, konten geometri adalah faktor yang signifikan menyebabkan heterogenitas kemampuan spasial siswa. Namun, heterogenitas kemampuan spasial siswa secara signifikan tidak disebabkan oleh jenjang pendidikan, durasi perlakuan, kapasitas kelas, software yang digunakan, dan tempat penelitian pembelajaran matematika berbantuan Dynamic Geometry Software. Studi ini memberikan masukan pada guru dan dosen matematika bahwa mereka sebaiknya menggunakan Dynamic Geometry Software sebagai salah satu variasi dalam pembelajaran matematika untuk menumbuh kembangkan kemampuan spasial siswa. Juga, dalam menumbuh kembangkan kemampuan spasial siswa melalui implementasi pembelajaran matematika berbantuan Dynamic Geometry Software, mereka sebaiknya memperhatikan konten geometri yang diajarkan. Researchers have conducted several meta-analysis studies on the effect of Dynamic Geometry Software assisted mathematics learning on mathematical ability. However, they have yet to study specifically the use of Dynamic Geometry Software in mathematics learning for students' mathematical spatial abilities. This study aims to estimate, test, and compare the effect of Dynamic Geometry Software-assisted mathematics learning on students' spatial abilities. In addition, this study investigates and examines several potential factors that are predicted to be the causal factors for the heterogeneity of students' spatial abilities using systematic review studies and meta-analysis. Of the 56 primary studies synthesized, the implementation of Dynamic Geometry Software assisted mathematics learning has an effect size of g=0.848 with a moderate effect on students' mathematical spatial abilities. Furthermore, geometry content is a significant factor causing the heterogeneity of students' mathematical spatial abilities. However, the heterogeneity of students' mathematical spatial abilities was not significantly caused by educational level, duration of treatment, class capacity, software used, and place of research on mathematics learning assisted by Dynamic Geometry Software. This study provides input to mathematics teachers and lecturers that they should use Dynamic Geometry Software as a variation in mathematics learning to develop students' mathematical spatial abilities. Also, in developing students' mathematical spatial abilities through implementing Dynamic Geometry Software-assisted mathematics learning, they should pay attention to the geometry content being taught

Proof in dynamic geometry contexts

Proof lies at the heart of mathematics yet we know from research in mathematics education that proof is an elusive concept for many mathematics students. The question that this paper raises is whether the introduction of dynamic geometry software will improve the situation – or whether it make the transition from informal to formal proof in mathematics even harder. Through discussion of research into innovative teaching approaches with computers the paper examines whether such approaches can assist pupils in developing a conceptual framework for proof, and in appropriating proof as a means to illuminate geometrical ideas