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 Problem Solving and Problem Posing in a Dynamic Geometry Environment

2005 ◽  
Vol 2 (2) ◽  
pp. 125-143
Author(s):  
Constantinos Christou ◽  
Nicholas Mousoulides ◽  
Marios Pittalis ◽  
Demetra Pitta-Pantazi
Keyword(s):  
Problem Solving ◽  
Dynamic Geometry ◽  
Problem Posing ◽  
Dynamic Geometry Environment

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.

Posing Problems: Two Classroom Examples

1999 ◽  
Vol 5 (2) ◽  
pp. 112-117
Author(s):  
Shukkwan S. Leung ◽  
Rui-Xiang Wu
Keyword(s):  
Teacher Training ◽  
Problem Solving ◽  
Problem Posing ◽  
Eighth Grade ◽  
Insufficient Information ◽  
Teacher Training College ◽  
Mathematics Test ◽  
Geometry Problem ◽  
Proportion Problem ◽  
Do So

IN ONE NCTM YEARBOOK TITLED PROBLEM Solving in School Mathematics, Butts (1980) reminded teachers of the importance of posing problems properly. What happens if we fail to do so and pose a problem that cannot be solved? This embarrassing moment can be made profitable if we ask students to help fix the problem. Here we share two lessons in which students help teachers pose problems. In the first lesson, fifth graders found a mistake in a proportion problem, and the teacher asked students to help her pose it properly. In the second, a geometry problem with insufficient information taken from an eighth-grade mathematics test was posed intentionally to future teachers in a teacher-training college as a problem-posing challenge. We first describe the two lessons and then close with suggestions on having learners help teachers pose problems properly.

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