scholarly journals A practice for using Geogebra of pre-service mathematics teachers’ mathematical thinking process

2020 ◽  
Vol 7 (1) ◽  
pp. 102-116
Author(s):  
Tuğba Hangül ◽  
Ozlem Cezikturk
Keyword(s):  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Classroom Environment ◽  
Mathematical Thinking ◽  
Mathematical Problem ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Instructional Technologies ◽  
Geometric Concepts ◽  
Academic Year

We aim to examine the pre-service mathematics teachers' mathematical problem-solving processes by using dynamic geometry software and to determine their evaluations based on experiences in this process. The design is document analysis, one of the qualitative research approaches. In the fall semester of the 2019–2020 academic year, a three-problem task was carried out in a classroom environment where everyone could use geogebra individually. A total of 65 pre-service mathematics teachers enrolled in the course of educational technology. This task includes questions that they would use, their knowledge of basic geometric concepts to construct geometrical relations and evaluations related to this process. Besides the activity papers of the prospective teachers, geogebra files were also examined. The result is pre-service mathematics teachers who are thought to have a certain level of mathematical background are found to have incorrect/incomplete information even in the most basic geometric concepts and difficulties with regard to generalisation. Keywords: Dynamic geometry, geogebra, instructional technologies, mathematical thinking, teacher education.

scholarly journals A dynamic approach to quadrilateral definitions

Pythagoras ◽  
2004 ◽  
Vol 0 (59) ◽  
Author(s):  
Rajendran Govender ◽  
Michael De Villiers
Keyword(s):  
Mathematics Teachers ◽  
Sufficient Conditions ◽  
Dynamic Geometry ◽  
Secondary Mathematics ◽  
Necessary And Sufficient Conditions ◽  
Dynamic Geometry Software ◽  
Dynamic Approach ◽  
Secondary Mathematics Teachers ◽  
Geometric Concepts ◽  
Necessary And Sufficient

This study examined 18 prospective secondary mathematics teachers' understanding of the nature of definitions, and their use of the dynamic geometry software Sketchpad to improve not only their understanding of definitions but also their ability to define geometric concepts themselves. Results indicated that the evaluation of definitions by accurate construction and measurement enabled students to achieve a better understanding of necessary and sufficient conditions, as well as the ability to more readily find counter-examples, and to recognise and improve on uneconomical definitions.

scholarly journals Investigation of pre-service elementary mathematics teachers’ problem posing situations in dynamic geometry environment

2018 ◽  
Vol 9 (1) ◽  
pp. 125-148
Author(s):  
Birnaz Kanbur Tekerek ◽  
Ziya Argün
Keyword(s):  
Mathematics Teachers ◽  
Elementary Mathematics ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Problem Posing ◽  
Dynamic Geometry Environment ◽  
Spring Semester ◽  
Geometric Concepts ◽  
Multiple Case

This study examined problem posing situations of pre-service elementary mathematics teachers in dynamic geometry environment by using problem posing strategies. The qualitative method of multiple case study was applied and geometric concepts that participants used for each type of problem posing are examined. Eight participants from 3rd grade pre-service mathematics teachers voluntarily participated in the study in 2015-2016 fall semester had previously received Computer Aided Mathematics course in the 2014-2015 spring semester. During six weeks’ data collection period, participants tried to pose new problems via dynamic geometry software by using given problem posing situations and their studies were recorded by screen saving program. The relationship between the problems that given to them and the concepts in the new problems were examined through screen recordings. Findings show new problems are established in parallel with the shape or problem statement in the problem posing situations given to them. Compared with other types of problem posing situations, it is seen the concepts are more diversified in the free problem posing. Participants develop their problem posing skills during the process so it is suggested these topics should be included in mathematics education undergraduate program in order for future students to gain these skills.

scholarly journals Comparison of prospective mathematics teachers’ problem posing abilities in paper-pencil test and on dynamic geometry environment in terms of creativity

2020 ◽  
Vol 9 (3) ◽  
pp. 243
Author(s):  
MEHMET FATIH ÖÇAL ◽  
TUĞRUL KAR ◽  
GÜRSEL GÜLER ◽  
ALI SABRI İPEK
Keyword(s):  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Creative Thinking ◽  
Dynamic Geometry ◽  
Thinking Skills ◽  
Problem Posing ◽  
Dynamic Geometry Environment ◽  
Mathematical Concepts ◽  
Prospective Mathematics Teachers

This study aims to investigate the similarities and differences between prospective mathematics teachers’ creative thinking skills in paper-pencil test and on a Geogebra-supported environment in terms of problem-posing. This case study used purposive sampling method for determining the participants. Findings revealed that the activities carried out in the GeoGebra-supported environment were insufficient to produce creative problems, and GeoGebra’s main utility to prospective teachers was in identifying their mistakes related to mathematical concepts and discrepancies among numerical values of the problems posed. The reasons for the low achievement in posing problem were discussed: These were; (i) lack of problem-posing experience, (ii) the structure of problem-posing activity, and (iii) prospective teachers’ mathematical content knowledge.

Using Dynamic Geometry Software to Engage Students in the Standards for Mathematical Practice

2015 ◽  
pp. 227-256
Author(s):  
Milan Sherman ◽  
Carolyn McCaffrey James ◽  
Amy Hillen ◽  
Charity Cayton
Keyword(s):  
Mathematics Classroom ◽  
Dynamic Geometry ◽  
Mathematical Practice ◽  
Dynamic Geometry Software ◽  
Teaching Mathematics ◽  
Instructional Technologies ◽  
Mathematical Relationships ◽  
Case Based

This case provides readers with an opportunity to consider issues pertaining to the use of instructional technologies in the mathematics classroom. As a narrative case based on a lesson observed in a real classroom, the case reflects the complexities of this context, yet was written to highlight certain themes relevant to teaching mathematics with technology. In particular, how students use dynamic geometry software to explore mathematical relationships, how they engage with the Standards for Mathematical Practice, and the important role of the teacher in this process are prominent themes in the lesson.

scholarly journals DOBLADO DE PAPEL Y SOFTWARE DE GEOMETRÍA DINÁMICA. UNA EXPERIENCIA CON FUTUROS PROFESORES DE MATEMÁTICA

PARADIGMA ◽  
2020 ◽  
pp. 1017-1045
Author(s):  
Martha Iglesias ◽  
José Ortíz
Keyword(s):  
Secondary School ◽  
Mathematics Teachers ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Argumentation Schemes ◽  
Initial Training ◽  
Geometric Problem ◽  
Paper Folding ◽  
Working Groups ◽  
Training Activities

El presente trabajo surge de un curso optativo de Resolución de Problemas Geométricos Asistido por Computadora (RPG-AC) que forma parte de la formación inicial de profesores de matemática en una universidad venezolana. Se estudian las actividades realizadas por 13 futuros profesores de matemática, en cinco grupos de trabajo, durante la implementación de un taller, el cual estuvo dirigido a la exploración de ángulos y triángulos con doblado de papel. Se utilizó el software de geometría dinámica CabriGéomètre II para mostrar la construcción con regla y compás de la herramienta triangular, y dejar ver su equivalencia con la construcción a partir del doblado de papel. En la validación de las construcciones realizadas en CabriGéomètre y en doblado de papel, se observaron esquemas de argumentación fácticos, empíricos y analíticos. Finalmente, el estudio realizado puso en evidencia que las actividades y experiencias formativas llevadas a cabo contribuyen a la formación didáctica y matemática de los futuros profesores.Palabras clave: Formación inicial de profesores de matemática, educación secundaria, software de geometría dinámica, doblado de papel, esquemas de argumentación.Ambientes de geometria dinâmica e dobragem de papel. Uma experiência com futuros professores de matemática.Resumo O presente trabalho nasce de um curso otátivo de Resoluçăo de Problemas Geométricos Assistido por Computador (RPG-AC) ó qual forma uma parte da formaçăo inicial de Professores de Matemática de uma Universidade venezuelana. Estudan-se as tarefas feitas por 13 (treze) futuros Professores de Matemática, em 5 (cinco) grupos de trabalho, durante a implementaçăo de um Talher, ó qual foi dirigido a exploraçăo de ângulos e triângulos com o dobrado de papel. Utilizou-se o software de Geometría dinámica: Cabri Géomètre II para ensinar a construçăo com régua e compás como ferramenta triângular, e deixar olhar a sua equivalènça com a construçăo desde o dobrado do papel. Na validaçăo das construçoĕs feitas em Cabri y no dobrado do papel, olharon-se quadros de argumentaçăo fácticos, impíricos e analíticos. Por fim, o estudo realizado mostrou que as atividades e experiências de treinamento realizadas contribuem para a formação didática e matemática de futuros professores. Palavras chave: formaçăo inicial de Professores de Matemática, Educaçăo secundária, software de Geometría dinámica, dobrado de papel, quadro de argumentaçăo.Paper folding and dynamic geometry software. An experience with pre-service mathematics teachersAbstractThis work arises from an optional course of Computer Aided Geometric Problem Solving (RPG-AC) that is part of the initial training of mathematics teachers in a Venezuelan university. The activities carried out by 13 future teachers of mathematics, in five working groups, are studied during the implementation of workshop, which was aimed at the exploration of angles and triangles with paper folding. The CabriGéomètre II dynamic geometry software was used to show the construction with the ruler and compass of the triangular tool, and to show its equivalence with the construction from the folded paper. In the validation of the constructions carried out in CabriGéomètre and in paper folding, factual, empirical and analytical argumentation schemes were observed. Finally, this study showed that the training activities and experiences carried out contribute to the didactic and mathematical training to pre-service teachers.Keywords: Pre-service mathematics teachers, secondary school, dynamical geometry software, folded paper, argumentation schemes.

scholarly journals Promoting Exploratory Teaching in Mathematics: A Design Experiment on a CPD course for Teachers

2015 ◽  
Vol 3 (6) ◽  
pp. 905-924 ◽  
Author(s):  
Henna Heikkinen ◽  
Peter Hästö ◽  
Vuokko Kangas ◽  
Marko Leinonen
Keyword(s):  
Mathematics Teachers ◽  
Mathematical Thinking ◽  
Research Question ◽  
Mathematical Problem ◽  
Substantial Effect ◽  
Design Experiment ◽  
Exploratory Learning ◽  
High School Mathematics ◽  
Factors Affecting ◽  
Main Research

In this paper we present a design experiment on a continued professional development (CPD) course for mathematics teachers. It consisted of three teaching cycles. Between them we analyzed the collected data in order to discover the factors affecting the course’s effectiveness and improve the next implementation. The general themes of the course, Introduction to Exploratory Learning in Mathematics, are teaching methods that promote active learning and exploratory learning environments. The course consists of one-day, on-site training and is aimed at elementary, middle and high school mathematics teachers. It is the first part of a larger CPD unit. We were especially motivated by the recent study of Stylianides & Stylianides (The Journal of Mathematical Behavior, 33 (1), 8–29) who proposed that even a very short intervention can impact positively on mathematical problem solving (attitudes) in initial elementary teacher training. Our main research question is thus to replicate and expand on their study: Can we impact positively on in-service teachers’ mathematical thinking over the course of a one-day seminar? In this article we describe the goals and implementation of our one-day course, some observations made during the implementations and conclusions. We replicate the findings of Stylianides and Stylianides (2014) that their “blond hair problem” makes a great impression on the participants. However, we found that the intervention did not have a substantial effect, at least in the short term, on what were considered good problems to use in an exploratory setting.

scholarly journals On the Learning of geometric concepts using Dynamic Geometry Software

RENOTE ◽  
2004 ◽  
Vol 2 (1) ◽  
Author(s):  
Alex Sandro Gomes ◽  
Gerard Vergnaud
Keyword(s):  
Problem Solving ◽  
Dynamic Geometry ◽  
Theoretical Framework ◽  
Dynamic Geometry Software ◽  
Mediated Learning ◽  
Computer Mediated ◽  
Geometric Concepts ◽  
Geometrical Concepts ◽  
Geometry Learning

Many results on computer mediated geometry learning conclude about different heuristic approaches to problem solving with Dynamic Geometry Software (DGS). However, little is described concerning conceptualization process. We used a theoretical framework built upon constructivist foundations for analyzing mediated learning of specific geometrical concepts. Our point is illustrated in a case study in which we analyzed studentsí interaction with a DGS. Our results points to a clear mapping of potential conceptualization of geometry in software using.

scholarly journals Does the use of technology make a difference in the geometric cognitive growth of pre-service mathematics teachers?

2012 ◽  
Vol 28 (7) ◽  
Author(s):  
Gerrit Stols
Keyword(s):  
Student Teachers ◽  
Mathematics Teachers ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Cognitive Growth ◽  
Van Hiele ◽  
Use Of Technology ◽  
Before And After ◽  
Quasi Experimental ◽  
The Difference

<blockquote>This study investigated the geometric cognitive growth of pre-service mathematics teachers in terms of the Van Hiele levels in a technology-enriched environment, as opposed to that of students in a learning environment without any technological enhancements. In order to investigate this, a quasi-experimental non-equivalent comparison group design was used. Similar course content was used for both the control and experimental groups. The students worked through a series of geometry activities and problems. The difference between the groups was that dynamic geometry software was integrated into the teaching of the experimental group. The <em>Cognitive Development and Achievement in Secondary School Geometry</em> (CDASSG) Van Hiele geometry test was used to determine all the students' level of geometric thinking before and after the course. The study found that the use of dynamic geometry software enhanced student teachers' geometric visualisation, analysis and deduction, but not their ability to informally justify their reasoning and to understand the formal aspects of deduction.</blockquote>

scholarly journals A generalisation of the nine-point circle and Euler line

Pythagoras ◽  
2005 ◽  
Vol 0 (62) ◽  
Author(s):  
Michael De Villiers
Keyword(s):  
Mathematics Teachers ◽  
Euclidean Plane ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Plane Geometry ◽  
Ancient Greek ◽  
Euler Line ◽  
Current Availability ◽  
Euclid’S Elements ◽  
Greek Geometry

To most people, including some mathematics teachers, geometry is synonymous with ancient Greek geometry, especially as epitomised in Euclid's Elements of 300 BC. Sadly, many are not even aware of the significant extensions and investigations of Apollonius, Ptolemy, Pappus, and many others until about 320 AD. Even more people are completely unaware of the major developments that took place in synthetic Euclidean plane geometry from about 1750-1940, and more recently again from about 1990 onwards (stimulated in no small way by the current availability of dynamic geometry software).

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