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

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.

2018 ◽  
Vol 9 (1) ◽  
pp. 125-148
Author(s):  
Birnaz Kanbur Tekerek ◽  
Ziya Argün

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.


2019 ◽  
Vol 9 (4) ◽  
pp. 92
Author(s):  
Gülçin Oflaz ◽  
Kübra Polat ◽  
Duygu Altaylı Özgül ◽  
Mario Alcaide ◽  
José Carrillo

It is of critical importance, in particular, for mathematics teachers who will teach future generations to understand and do mathematical proofs. It is important to determine future teachers' beliefs about and difficulties with proofs because their knowledge of this issue affects their teaching. This study aims to determine and compare the proof schemes of prospective mathematics teachers from two state universities, one in Turkey and the other in Spain. The case study was conducted within this study. The participants were 51 prospective teachers at their second year from the department of teaching mathematics education at Huelva University in Spain and 45 prospective teachers from the department of teaching mathematics education at Cumhuriyet University in Turkey. The Proof Test consisted of four questions about proofs for parallelograms. Semi-structured interviews were subsequently conducted to investigate the prospective teachers’ responses in-depth. The findings suggest that prospective teachers from Turkey and Spain indicated affinity in proving. The majority of the prospective mathematics teachers were either unable to complete the proof or completed the proof in an inaccurate way.


2021 ◽  
Vol 11 (3) ◽  
pp. 81-104
Author(s):  
Cahit Aytekin

Abstract Introduction: In the reflective writing process, teachers make identification, information, explanation and evaluation activities (Spanneberg, 2009). It is thought that the scenarios written by the teacher candidates in order to teach a certain subject can give them an opportunity to think deeply. However, these teaching scenarios can be a valuable tool for reflective thinking in terms of educational matters such as teaching methods, pedagogy, and beliefs. Methods: In this study, it was investigated whether script writing is an effective tool to make pedagogical elements visible in the prospects of mathematics teachers. Case study pattern, which is one of the qualitative research patterns, was used in the research. For this purpose, thirty prospective mathematics teachers who participated in the study were asked to write two scenarios. The first one is called as “car travel” and the other one is called as “triangles and similarity” scenario. Before the study, some basic frameworks were defined for both scenarios. These are explained to prospective teachers. The “car travel” scenario in this research was given within the scope of the theme which includes only two people and a limited environmental interaction. The second scenario is the triangles and the similarity scenario. In the second scenario, the role of a teacher who conducts applied and real-life education outside of school is defined. Results: In general, it is concluded that script writing activities are very useful in training teachers. The data obtained from both scenarios reveal that the pedagogical elements constructed during the scenario writing activities become concrete in the minds of the prospective teachers. Discussion: It is observed that prospective teachers often include the structure of teaching related to real life in their scenarios. It is stated that teaching in the context of real life increases academic success and students’ interest in the lesson, and thus, the content is learned perceptibly by the students (Acar & Yaman, 2011). Another cognitive element that prospective teachers include in their scenarios is the use of available materials. It is noteworthy that the prospective teachers used real-life tools and materials as materials in the place chosen for the scenarios of their scripts. Limitations: This research is limited to script texts written by thirty prospective teachers. Conclusions: Thanks to this visibility, feedback can be given on the pedagogical elements that the prospective teacher will use in the future.


2017 ◽  
Vol 5 (2) ◽  
pp. 10
Author(s):  
Emine Özdemir ◽  
Filiz Tuba Dikkartin Övez

The cognitive development of prospective teacher needs to be taken into estimate so that proofs are presented in forms that are potentially meaningful for them. This requires educators and mathematicians to rethink consider the use of types of proof related to the logical thinking improvement of the singular. The purpose of the study is to identify the proof writing levels of prospective teachers and to reveal the difference between varying proof writing levels and logical thinking skills. In this study mixed research design was used and the sample was selected through criterion sampling. “The Proof-Writing Scale” and “The Test of Logical Thinking” were used as data tools. The proofs written by the prospective teachers for the theorems included in the Proof-Writing Scale were subjected to a descriptive analysis. The proofs were assigned in accordance with Balacheff’s taxonomy. As a result of the study, the distribution of the proofs written by the prospective mathematics teachers to the theorems was as follows: pragmatic proofs (35%), intellectual proofs (49%) and demonstration proofs (16%). There was a significant difference, in terms of their logical thinking skills, among the prospective teachers who had varying levels of proof-writing.


2018 ◽  
Vol 6 (9) ◽  
pp. 78 ◽  
Author(s):  
Selin Cenberci

New ideas and inventions are needed in the globalizing world in order that societies can be survived. To achieve this, there is a need for teachers and prospective mathematics teachers who will guide these students, who have creative ideas, make new inventions and generate new ideas in the educational environment where individuals are educated. Creative thinking skills should be used at the highest level in order to achieve a more permanent learning and ensure interdisciplinary transition. Creativity is defined as sensitivity emerging against problems. For this reason, importance of the noteworthy that opportunities should be given prospective mathematics teachers to develop creative thinking skills and have more time for designing creative products. Although each individual has creative thinking skills, it is very important to determine how using tendency of creative thinking skills and factors that will activate this tendency do change in accordance with different variables. So it was aimed to determine the level of creative thinking tendencies of prospective mathematics teachers and examine this level in terms of different variables. Marmara Creative Thinking Tendency Scale were applied to prospective mathematics teachers. According to the results obtained, it was declared that the creative thinking tendencies of the prospective mathematics teachers were in the group consisting of the "good" range in the total score section.


2021 ◽  
Vol 11 (1) ◽  
pp. 259-298
Author(s):  
Kemal Özgen

The aim of the first stage of the research was to examine the opinions of prospective mathematics teachers about what features a question prepared to develop and measure ML should have to be effective and qualified. Moreover, it was aimed to determine the degree to which prospective teachers apply these qualifications in questions they design to develop and measure ML. The aim of the second stage of the research was to develop a valid and reliable checklist that can be used in the design of the question to develop and measure ML and to show this tool with an application. The research was conducted as a case study model. The study group consisted of 20 prospective mathematics teachers and five mathematics teachers who took ML courses. Interview forms were applied in order to collect data from the teachers and teacher candidates who took the ML course. Content analysis was used in the analysis of the prospective mathematics teachers' opinions about the qualifications of ML question. In the analysis of the data obtained, content, context, process, level and structure categories were formed for effective and qualified ML question. The checklist was decided to be in five categories and a total of 28 items and three options depending on them. It can be said that the checklist for the ML question design, which was developed and piloted in this study, is a valid and reliable measurement tool. Mathematics teachers and related researchers can use the developed checklist as a guide and guiding tool in designing ML questions.


2020 ◽  
Vol 10 (1) ◽  
pp. 32
Author(s):  
Wahyudi Wahyudi ◽  
S.B Waluya ◽  
Waluya Suyitno ◽  
Isnarto Isnarto

Creating an enjoyable atmosphere and fostering creativity are the two most required components in learning mathematics. Hence, creativity would enable students to formulate something new. In addition, creativity is one of the most important and highest competencies in Bloom’s latest taxonomy. Furthermore, it is necessary to be possessed by everyone including prospective teachers. Not only for producing products in the form of objects, but the term creative also refers to problem solving in mathematic problems. This research is conducted to obtain a detail description regarding the impact of 3CM learning model among blended learning toward the enhancement of students’ creative thinking skills in mathematical problem solving. To achieve this goal, a pre-experimental design with one group pre-test post-test design pattern is chosen. Creative thinking skills are measured by test techniques and are emulated with observation techniques. Observations were performed when students worked on the test. The impact of 3CM learning with blended learning seen from test results paired sample T tests with the help of SPSS program a that are acquired from close ended questionnaire techniques. The results show that the average of pre-test is 60.51 and the average of post-test is 75.96. As for the results of paired T tests is the test got sig value (2-tailed) 0.000, and hence there was a significant gap among the results of pre-test and post-test. All of these results imply that 3CM learning within blended learning is undoubtedly able to increase students’ creativity in solving mathematical problems. This is due to the learning situation and activities which push students to do systematic thinking. It was started by criticizing the enchanting contextual problems, creating creative products based on particular mathematical concepts, and ended by having meaningful reflection.


ZDM ◽  
2021 ◽  
Author(s):  
Haim Elgrably ◽  
Roza Leikin

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.


Author(s):  
Ana Kuzle

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.


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