Problem Posing in Geometry

1991 ◽  
Vol 84 (1) ◽  
pp. 10-14
Author(s):  
Larry Hoehn
Keyword(s):  
Problem Solving ◽  
Secondary School ◽  
Mathematics Teacher ◽  
Secondary School Teachers ◽  
Problem Posing ◽  
School Teachers ◽  
Scant Attention ◽  
Geometry Test

Problem solving received dramatic emphasis throughout the 1980s. However, its necessary counterpart, problem posing, has received scant attention. Some notable exceptions are the works of Brown and Walter (1983), Klamkin (1986), and, of course, Polya (1973). In this article a typical geometry theorem is used and problems are posed involving its application. The methods presented here work well to create geometry test questions, geometry contest problems, and calendar problems for the Mathematics Teacher. Although these methods are intended primarily for secondary school teachers, creative geometry students could use them for making their own mathematical discoveries.

scholarly journals Resolución de problemas matemáticos en GeoGebra

2020 ◽  
Vol 9 (1) ◽  
pp. 26-42
Author(s):  
William Enrique Poveda Fernández
Keyword(s):  
Costa Rica ◽  
Problem Solving ◽  
Secondary School ◽  
Secondary School Teachers ◽  
Mathematical Reasoning ◽  
Mathematical Thinking ◽  
School Teachers ◽  
Mathematical Objects ◽  
Problem Solving Strategies ◽  
Problem Solving Process

RESUMENEn este artículo se analizan y discuten las ventajas y oportunidades que ofrece GeoGebra durante el proceso de resolución de problemas. En particular, se analizan y documentan las formas de razonamiento matemático exhibidas por ocho profesores de enseñanza secundaria de Costa Rica, relacionadas con la adquisición y el desarrollo de estrategias de resolución de problemas asociadas con el uso de GeoGebra. Para ello, se elaboró una propuesta de trabajo que comprende la construcción y la exploración de una representación del problema, y la formulación y la validación de conjeturas. Los resultados muestran que los profesores hicieron varias representaciones del problema, examinaron las propiedades y los atributos de los objetos matemáticos involucrados, realizaron conjeturas sobre las relaciones entre tales objetos, buscaron diferentes formas de comprobarlas basados en argumentos visuales y empíricos que proporciona GeoGebra. En general, los profesores usaron estrategias de medición de atributos de los objetos matemáticos y de examinación del rastro que deja un punto mientras se arrastra.Palabras claves: GeoGebra; Resolución de problemas; pensamiento matemático. RESUMOEste artigo analisa e discute as vantagens e oportunidades oferecidas pelo GeoGebra durante o processo de resolução de problemas. Em particular, as formas de raciocínio matemático exibidas por oito professores do ensino médio da Costa Rica, relacionadas à aquisição e desenvolvimento de estratégias de resolução de problemas associadas ao uso do GeoGebra, são analisadas e documentadas. Para isso, foi elaborada uma proposta de trabalho que inclui a construção e exploração de uma representação do problema, e a formulação e validação de conjecturas. Os resultados mostram que os professores fizeram várias representações do problema, examinaram as propriedades e atributos dos objetos matemáticos envolvidos, fizeram conjecturas sobre as relações entre esses objetos e procuraram diferentes formas de os verificar com base em argumentos visuais e empíricos fornecidos pelo GeoGebra. Em geral, os professores utilizaram estratégias para medir os atributos dos objetos matemáticos e para examinar o rasto que um ponto deixa enquanto é arrastado.Palavras-chave: GeoGebra; Resolução de problemas; pensamento matemático. ABSTRACTThis article analyzes and discusses the advantages and opportunities offered by GeoGebra during the problem-solving process. In particular, the mathematical reasoning forms exhibited by eight secondary school teachers in Costa Rica, related to the acquisition and development of problem solving strategies associated with the use of GeoGebra, are analyzed and documented. The proposal was developed that includes the elements: construction and exploration of a representation of the problem and formulation and validation of conjectures. The results show that teachers made several representations of the problem, examined the properties and attributes of the mathematical objects involved, made conjectures about the relationships between such objects, and sought different ways to check them based on visual and empirical arguments provided by GeoGebra. In general, the teachers used strategies to measure the attributes of the mathematical objects and to examine the trail that a point leaves while it is being dragged.Keywords: GeoGebra; Problem Solving; Mathematical Thinking.

scholarly journals Teaching Strategies for Mathematical Problem-Solving through the Lens of Secondary School Teachers

TEM Journal ◽  
2021 ◽  
pp. 743-750
Author(s):  
Afiqah Hamizah Noor Ishak ◽  
Sharifah Osman ◽  
Chiang Kok Wei ◽  
Dian Kurniati
Keyword(s):  
Problem Solving ◽  
Secondary School ◽  
Thematic Analysis ◽  
Teaching Strategies ◽  
Secondary School Teachers ◽  
Mathematical Problem ◽  
Structured Interview ◽  
Mathematical Problem Solving ◽  
School Teachers ◽  
Teaching Problem

Many studies have been conducted on problem-solving but only a small number of studies emphasized the strategies of teaching problem-solving. This paper explores the teaching strategies for mathematical problem-solving in a secondary school in Johor, Malaysia. It involves a qualitative study in which a semi-structured interview was conducted with mathematics teachers. Data were analyzed using a sixstep thematic analysis. The results can be viewed from three contexts of findings, namely the teaching strategies, the problems faced by teachers, and the solutions to overcome the problems. The findings revealed that there are teachers who have implemented personal teaching strategies, namely the Easy-Maths Model and the Cut-Stop-Solve Model to effectively teach mathematical problem-solving. The findings also explained some problems in teaching mathematical problem-solving, whereby students’ weaknesses in basic mathematics emerged as the main drawback. This study provides useful information to teachers on the different strategies for teaching mathematical problem-solving.

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