Prospective teachers’ approaches to problem-solving activies with the use of a dynamic geometry system

2020 ◽  
Author(s):  
Daniel Ortiz
Keyword(s):  
Problem Solving ◽  
Prospective Teachers ◽  
Dynamic Geometry

scholarly journals Creativity as a function of problem-solving expertise: posing new problems through investigations

ZDM ◽  
2021 ◽  
Author(s):  
Haim Elgrably ◽  
Roza Leikin
Keyword(s):  
Problem Solving ◽  
Dynamic Geometry ◽  
Problem Posing ◽  
Dynamic Geometry Environment ◽  
Mathematics Majors ◽  
Individual Interviews ◽  
University Mathematics ◽  
Domain Specific ◽  
Mathematics Test ◽  
Different Types

AbstractThis study was inspired by the following question: how is mathematical creativity connected to different kinds of expertise in mathematics? Basing our work on arguments about the domain-specific nature of expertise and creativity, we looked at how participants from two groups with two different types of expertise performed in problem-posing-through-investigations (PPI) in a dynamic geometry environment (DGE). The first type of expertise—MO—involved being a candidate or a member of the Israeli International Mathematical Olympiad team. The second type—MM—was comprised of mathematics majors who excelled in university mathematics. We conducted individual interviews with eight MO participants who were asked to perform PPI in geometry, without previous experience in performing a task of this kind. Eleven MMs tackled the same PPI task during a mathematics test at the end of a 52-h course that integrated PPI. To characterize connections between creativity and expertise, we analyzed participants’ performance on the PPI tasks according to proof skills (i.e., auxiliary constructions, the complexity of posed tasks, and correctness of their proofs) and creativity components (i.e., fluency, flexibility and originality of the discovered properties). Our findings demonstrate significant differences between PPI by MO participants and by MM participants as reflected in the more creative performance and more successful proving processes demonstrated by MO participants. We argue that problem posing and problem solving are inseparable when MO experts are engaged in PPI.

scholarly journals Nature of metacognition in a dynamic geometry environment

2015 ◽  
Vol 3 (5) ◽  
pp. 627-646
Author(s):  
Ana Kuzle
Keyword(s):  
Problem Solving ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Dynamic Geometry Environment ◽  
Mathematics Problem Solving ◽  
Managerial Decisions ◽  
Metacognitive Processes ◽  
Geometry Problem ◽  
Mathematics Problem

This case study examined the metacognitive processes of a preservice teacher when solving a nonroutine geometry problem in a dynamic geometry environment. The main purpose of the study was to uncover and investigate patterns of metacognitive processes and to understand what circumstances, situations, and interactions in a dynamic geometry environment promoted metacognitive behaviors. An adaptation of Schoenfeld’s (1981) model of episodes and executive decisions in mathematics problem solving, and the theory of instrumentation (Rabardel, 2001) was used to identify patterns of metacognitive processes in a dynamic geometry environment. During different phases of problem solving the participant engaged in different metacognitive behaviors whereas the dynamic geometry software supported strategies that are available and/or not available on paper and pen. The effectiveness of solution paths was dependent on the presence of managerial decisions, and well-orchestrated usage of different resources, both knowledge and technology. However, the results of the study call to question to which extent engagement in metacognitive behaviors is necessarily desirable or productive.

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.

scholarly journals Japanese and Swedish Mathematics Teacher Educators’ Pedagogical Content Knowledge – An Institutional Perspective

2019 ◽  
Vol 21 ◽  
Author(s):  
Yukiko Asami-Johansson ◽  
Iiris Attorps
Keyword(s):  
Problem Solving ◽  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Prospective Teachers ◽  
Teacher Educators ◽  
Institutional Perspective ◽  
Pedagogical Content ◽  
Mathematics Teacher Educators ◽  
Structured Problem Solving ◽  
Area Determination

The aim of this paper is to investigate which kind of conditions and constraints affect Japanese and Swedish teacher educators’ pedagogical content knowledge (PCK). We analyse the praxeologies of the lessons in which the educators teach area determination. Our study shows that the Japanese teacher educators’ PCK are more explicitly shared by the community of the teacher educators compared to the Swedish counterpart. Also, the detailed Japanese curriculum and the structured problem solving approach promote to illustrate how to construct rich mathematical and didactical organisations for prospective teachers.

scholarly journals The effect of Lego Mindstorm projects on problem solving skills and scientific creativity of teacher candidateÖğretmen adaylarının problem çözme becerilerine ve bilimsel yaratıcılıklarına Lego Mindstorm projelerinin etkisi

2019 ◽  
Vol 16 (1) ◽  
pp. 216
Author(s):  
Berkan Avcı ◽  
Fatma Şahin
Keyword(s):  
Problem Solving ◽  
Data Collection ◽  
Science Teachers ◽  
Prospective Teachers ◽  
Teacher Candidates ◽  
English Summary ◽  
Scientific Creativity ◽  
Problem Solving Skills ◽  
Grade Levels ◽  
Lego Mindstorms

In this study; the effects of Lego Mindstorms projects on problem solving skills and scientific creativity of teacher candidates were. The study group consisted of 20 pre-service science teachers. The data were collected quantitatively and qualitatively. Problem solving and scientific creativity  test were used as quantitative data collection instruments. , Teacher Participant Interview was used as qualitative data collection tool. The practice with teacher candidates lasted 9 weeks.  In this process, pre-service teachers learned the software. Then, these teacher candidates were presented with the science problems appropriate to different grade levels and produced solutions to these problems with Lego EV3 Education sets.Results of the study, the participating teacher candidates identified Lego Ev3 Education sets as creative (25.6%), functional (18.7%), educational (20.9%), developmental (20.9%) and informative (13.9%). As a result of the projects carried out with the Lego Ev3 education sets, the problem solving skills and scientific creativity of the prospective teachers developed.Extended English summary is in the end of Full Text PDF (TURKISH) file. ÖzetBu çalışmada; Lego Mindstorms projelerinin öğretmen adaylarının problem çözme becerilerine ve bilimsel yaratıcılıklarına etkisi incelenmiştir. Araştırmanın çalışma grubunu Fen Bilgisi 3.sınıf öğrencisi 20 öğretmen adayı oluşturmuştur. Araştırmada nicel ve nitel veriler toplanmıştır. Nicel veri toplama araçları olarak problem çözme envanteri ve bilimsel yaratıcılık testi kullanılmıştır. Nitel veri toplama aracı olarak da öğretmen görüş anketi kullanılmıştır. Araştırmanın uygulama süreci 9 hafta sürmüştür. Bu süreçte önce öğretmen adayları yazılımı öğrenmiştir. Sonra bu öğretmen adaylarına farklı sınıf düzeylerine uygun fen problemleri sunulmuş ve bu problemlere Lego EV3 Education setleri ile çözüm üretmişlerdir.Çalışmanın sonuçları, araştırmaya katılan öğretmen adaylarının Lego Ev3 Education setlerini: yaratıcı (%25.6), işlevsel (%18.7), eğitimde uygulanabilir (%20.9), gelişimsel (%20.9) ve bilgiyi uygulayabilir (%13.9) olarak tanımladıklarını ortaya çıkarmıştır. Lego Ev3 education setleri ile yapılan projeler sonucunda öğretmen adaylarının problem çözme becerileri ve bilimsel yaratıcılıkları gelişmiştir.

Forum on teacher preparation: A mathematics laboratory for prospective teachers

1970 ◽  
Vol 17 (1) ◽  
pp. 75-78
Author(s):  
David M. Clarkson
Keyword(s):  
Problem Solving ◽  
Prospective Teachers ◽  
Methods Course ◽  
Mathematical Activity ◽  
Schools Of Education ◽  
Mathematics Methods ◽  
Open Problems ◽  
School Officials ◽  
Mathematics Methods Course ◽  
And Mathematics

The Report of the Cambridge Conference on the Correlation of Science and Mathematics in the Schools recommends that schools of education plan programs of “apprentice teaching in the schools, including work with materials of the sort being developed in new curriculum projects.”1 A group of mathematics educators in England has urged the use of courses emphasizing problem solving: “It is the exploration of these more open problems which we feel to be the essential characteristic of real mathematical activity.”2 A loud chorus of opinion suggests that courses in methodology should be jointly planned and executed by both mathematicians and educators and that they should involve practical work with children. When the opportunity to design an experimental elementary mathematics methods course was offered the writer, he decided to emphasize the mathematics laboratory approach which gives an important role to problem solving. Conferences with members of the mathematics and education departments, as well as with school officials, paved the way for the experiment; the sympathetic support of the chairman of the division of education at the college made it possible financially.

Spinning the Cube with Technologies

2019 ◽  
Vol 112 (7) ◽  
pp. 551-554
Author(s):  
Lingguo Bu
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Teaching Experiment ◽  
Mathematical Tasks ◽  
Classroom Teaching ◽  
Sense Making ◽  
Pedagogical Issues ◽  
The Rich ◽  
Physical Manipulation

The rise of dynamic modeling and 3-D design technologies provides appealing opportunities for mathematics teachers to reconsider a host of pedagogical issues in mathematics education, ranging from motivation to application and from visualization to physical manipulation. This article reports on a classroom teaching experiment about cube spinning, integrating traditional tools, GeoGebra (www.geogebra.org), and 3-D design and printing technologies. It highlights the rich interplay between worthwhile mathematical tasks and the strategic use of diverse technologies in sustaining sense making and problem solving with a group of prospective teachers.

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