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.

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.

Problem-solving activities observed in British primary schools

1969 ◽  
Vol 16 (1) ◽  
pp. 34-38
Author(s):  
Rose Grossman
Keyword(s):  
Teacher Training ◽  
Problem Solving ◽  
Primary School ◽  
Primary Schools ◽  
School Mathematics ◽  
Ministry Of Education ◽  
Low Socioeconomic ◽  
Primary School Mathematics ◽  
Teacher Training College

The object of a trip to England was to visit schools that were actively involved in teach ing innovative primary school mathematics programs. We met with Dr. Geoffrey Matthews, Director of the Nuffield Mathematics Project, who had worked with the Ministry of Education in planning visits to schools in various parts of greater London, Bristol, and Cambridge, including schools in high, medium, and low socioeconomic areas, visits to Teachers Centres, and a visit to a teacher training college.

scholarly journals The perceptions of creativity and creative potentials of future kindergarten and class teachers

2014 ◽  
Vol 46 (1) ◽  
pp. 181-199
Author(s):  
Radmila Milovanovic ◽  
Emina Kopas-Vukasinovic
Keyword(s):  
Teacher Training ◽  
Problem Solving ◽  
Teaching Practice ◽  
Creative Problem Solving ◽  
Self Assessment ◽  
Knowledge And Beliefs ◽  
Teacher Training College ◽  
Creative Problem ◽  
Important Basis ◽  
Very High

Research studies on teaching practice have shown that not enough attention is paid to the problem of children?s creativity development in our schools in spite of the fact that the development of creative potentials in preschool institutions and school figures as one of the priority educational tasks. The perceptions of creativity and creative potentials of future kindergarten and class teachers can serve as an important basis for encouraging the development of their professional competences. This research was aimed at examining students? knowledge and beliefs on creativity, obtaining self-assessment of their own creative potentials and determining the level of expression of students? creativity based on their abilities of creative problem-solving. The sample included the students of the Faculty of Pedagogical Sciences in Jagodina and Teacher Training College in Vranje (N=300). For examining students? creative potentials we used the Epstein Creativity Competences Inventory and a version of the Saugstad & Rahaim Problem Solving Tests. Research results have confirmed that students possess the knowledge and the beliefs compatible with the modern scientific beliefs on creativity. They assess their own creative potentials as very high and they do possess them. The obtained results can serve as a better foundation for working with students towards fostering the development of their creative potentials and professional competences.

scholarly journals ENGLISH FOR ACADEMIC PURPOSES AND THE ENHANCEMENT OF FRENCH TRAINEE CONTENT TEACHERS’ PROFESSIONAL SKILLS

2019 ◽  
pp. 341
Author(s):  
Severine WOZNIAK
Keyword(s):  
Teacher Training ◽  
Professional Practice ◽  
English For Academic Purposes ◽  
Integrated Learning ◽  
Professional Skills ◽  
Initial Teacher Training ◽  
Teacher Training College ◽  
Language Studies ◽  
Do So

This paper explores the issue of syllabus design for English for Academic Purposes (EAP) classes by presenting a case study carried out at the Grenoble Faculty of Economics and the Grenoble Initial Teacher Training College (France). The study had two objectives: develop prospective and newly recruited content teachers’ professional skills, notably the ability to teach their subject in English on an occasional basis, and help them reflect on their professional practice. In order to do so, mandatory EAP modules for all trainee content teachers (TCT) of disciplines other than language studies were implemented to provide TCTs with an introduction to content and language integrated learning (CLIL) and to train them to teach in a CLIL format. In this paper two types of data are analyzed: the assessment of TCTs’ final assignment and the responses to a questionnaire aiming at gathering TCTs’ feedback on the EAP modules.

Toward a Reasoning Framework of Design As Synthesis

1999 ◽  
Author(s):  
Masaharu Yoshioka ◽  
Tetsuo Tomiyama
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Design Process ◽  
Process Modeling ◽  
Implementation Strategy ◽  
Multiple Model ◽  
Hypothetical Reasoning ◽  
Design Processes ◽  
Design Process Modeling ◽  
Do So

Abstract Most of the previous research efforts for design process modeling had such assumptions as “design as problem solving,” “design as decision making,” and “design by analysis,” and did not explicitly address “design as synthesis.” These views lack notion and understanding about synthesis. Compared with analysis, synthesis is less understood and clarified. This paper discusses our fundamental view on synthesis and approach toward a reasoning framework of design as synthesis. To do so, we observe the designer’s activity and formalize knowledge operations in design processes. From the observation, we propose a hypothetical reasoning framework of design based on multiple model-based reasoning. We discuss the implementation strategy for the framework.

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