Thoughts About Research On Mathematical Problem- Solving Instruction

Lester,; Frank, Kenneth A.

doi:10.54870/1551-3440.1267

Cited by 102 publications

(48 citation statements)

References 16 publications

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“…As Leppäaho (2018, p. 368) points out, mathematical problem-solving is learned only by practising it repeatedly. Mathematics can actually be taught through problemsolving (see for example Schoenfeld, 1985;Hiebert, 2003;Lester, 2013). This teaching method enables students themselves to engage with meaningful, rich problem tasks and instead of superficial procedure-learning, develop understanding of mathematical concepts and methods.…”

Section: Introductionmentioning

confidence: 99%

Developing mathematical problem-solving skills in primary school by using visual representations on heuristics

Kaitera

Harmoinen

2022

LUMAT

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Developing students’ skills in solving mathematical problems and supporting creative mathematical thinking have been important topics of Finnish National Core Curricula 2004 and 2014. To foster these skills, students should be provided with rich, meaningful problem-solving tasks already in primary school. Teachers have a crucial role in equipping students with a variety of tools for solving diverse mathematical problems. This can be challenging if the instruction is based solely on tasks presented in mathematics textbooks. The aim of this study was to map whether a teaching approach, which focuses on teaching general heuristics for mathematical problem-solving by providing visual tools called Problem-solving Keys, would improve students’ performance in tasks and skills in justifying their reasoning. To map students' problem-solving skills and strategies, data from 25 fifth graders’ pre-tests and post-tests with non-routine mathematical tasks were analysed. The results indicate that the teaching approach, which emphasized finding different approaches to solve mathematical problems had the potential for improving students’ performance in a problem-solving test and skills, but also in explaining their thinking in tasks. The findings of this research suggest that teachers could support the development of problem-solving strategies by fostering classroom discussions and using for example a visual heuristics tool called Problem-solving Keys.

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Section: Introductionmentioning

confidence: 99%

Developing mathematical problem-solving skills in primary school by using visual representations on heuristics

Kaitera

Harmoinen

2022

LUMAT

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“…Cognitive engagement plays an essential role in the problem-solving process and has strict influence on learning mathematics (Li, Lajoie, Zheng, Wu, & Cheng, 2021). This problem-solving ability is the primary goal of learning mathematics, and realizing this goal becomes the teacher's attention by considering a wide range of factors and strategies (Lester, 2013). Mastering problemsolving skills, students could apply their mathematical abilities in better approaches; they create a more profound understanding of mathematical concepts and feel the involvement of being a mathematician through solving problems (Son, Darhim, & Fatimah, 2020).…”

Section: Introductionmentioning

confidence: 99%

“…Problem-solving instruction is likely to be most successful when given in a systematically organized way beneath the heading of the teacher, considering students' metacognitive process as well. Problem-solving instruction that emphasizes the improvement of metacognitive abilities ought to include the teacher in three distinctive, but related, parts: (a) as an outside screen, (b) as a facilitator of students' metacognitive awareness, and (c) as a role model of a metacognitively capable problem solver (Lester, 2013). As Shekhar & Rahnev (2021) stated, students have the metacognitive ability to assess the exactness of their choices through correct evaluations in solving problems.…”

Section: Introductionmentioning

confidence: 99%

Mathematics pre-service teacher's metacognitive failure in mathematics online learning

Alifiani

Faradiba

2021

J. ris. pendidik. mat

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This study aims to reveal the metacognitive failures experienced by mathematics pre-service teachers based on their mistakes when solving problems in online learning during the pandemic era. This case study involved 29 participants who attended the mathematical problem test and cognitive style test, the two participants were categorized based on their cognitive style: Field Dependence (FD) and Field Independence (FI). The instrument used was a mathematical problem test to collect data on metacognitive that adapted from Stewart and a cognitive styles test to categorize the cognitive style that adapted from the Group Embedded Figures Test (GEFT). An interview was conducted to determine the nature of mathematical error based on metacognitive failure. The description of data analysis and interpretation of the meaning of the findings applied the text analysis. The results showed the different metacognitive failures of the two participants. The metacognitive failure of FI student was categorized as metacognitive blindness and the FD student was categorized as metacognitive stagnation, a new condition of metacognitive failure that was found in this study.

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“…A pesar de la importancia del conocimiento de los profesores para enseñar la RP, los trabajos centrados en este conocimiento profesional son escasos (LESTER, 2013), frente a los que se han dedicado a evaluar la competencia del profesor en RP (PIÑEIRO, 2019). Los estudios que se han ocupado de este tema, lo han abordado, indirectamente, de varias maneras, y hacen notar la existencia de un conocimiento específico relativo a elementos propios de la RP (BLANCO; GUERRERO; CABALLERO, 2013;BOOTE;BOOTE, 2018;CHAPMAN, 2012;CRESPO;SINCLAIR, 2008;DEPAEPE;DE CORTE;VERSCHAFFEL, 2010;HALLMAN-THRASHER, 2017;GINÉ;DEULOFEU, 2014;GONZÁLEZ;ELI, 2017;MALLART;FONT;MALASPINA, 2016;OSANA et al, 2006;PATKIN;GAZIT, 2011;TICHÁ;HOŠPESOVÁ, 2013).…”

Section: Introductionunclassified

“…La resolución de problemas matemáticos genuinos se ha definido, en este trabajo, como un proceso y una forma de pensar (CHAPMAN, 2015;LESTER, 2013;SCHOENFELD, 1985), cuyo objetivo es encontrar soluciones a "algo o alguna situación [...] cuando alguien experimenta un estado de problemático, asumiendo la tarea de dar sentido a la situación e involucrándose en alguna actividad de construcción de sentido" (MASON, 2016, p. 263).…”

Section: Introductionunclassified

Conocimiento sobre la resolución de problemas de matemáticas manifestado por estudiantes para profesor

Piñeiro

Castro-Rodríguez

Castro

2021

Bolema

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Resumen La resolución de problemas es un proceso central en la educación matemática, sin embargo, implementarla de forma efectiva en el aula no es un proceso trivial. Los profesores requieren conocimientos específicos para ello. Este trabajo presenta un estudio de casos múltiple, centrado en indagar el conocimiento de futuros maestros de primaria sobre problemas matemáticos, su proceso de resolución y la disposición hacia ellos. Se realizaron entrevistas semiestructuradas a nueve futuros maestros que terminaban su formación universitaria del grado de Educación Primaria en España. Los resultados muestran que los profesores sostienen una caracterización de problema desconectada del resolutor y una conceptualización lineal del proceso de resolución, demostrando la poca integración existente en sus conocimientos profesionales.

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Thoughts About Research On Mathematical Problem- Solving Instruction

Cited by 102 publications

References 16 publications

Developing mathematical problem-solving skills in primary school by using visual representations on heuristics

Developing mathematical problem-solving skills in primary school by using visual representations on heuristics

Mathematics pre-service teacher's metacognitive failure in mathematics online learning

Conocimiento sobre la resolución de problemas de matemáticas manifestado por estudiantes para profesor

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