Problem solving and the development of cognitive structure

1969 ◽  
Vol 16 (1) ◽  
pp. 11-15
Author(s):  
Thomas C. O'brien ◽  
Bernard J. Shapiro

A basic purpose of teaching mathematics is to develop a learner's problemsolving behavior. On the other hand, knowledge of mathematical ideas can evolve from problem-solving activities of the learner. As indicated by Piaget, the building of cognitive structure is a process of evolution by stages from sensorimotor activities through concrete operations to formal operations (mental operations not directly rooted in physical experience). The purpose of the following introduction is to consider two of the many implications that Piaget's findings have for educational practice, and then to relate these implications to a problem-solving activity that the teacher may wish to try with his class.

This chapter of the book is about cognitive processes and the ways they are related to learning and creating. The text discusses how scientific concepts can be translated to the realm of mental imagery and visual thinking and how solutions inspired by nature and science-based issues support developing sensitivity and the use of original ideas in our work. Because cognition and learning may not be limited to humans, the text examines some mental operations in animals. On the other hand, the text discusses how the science- and technology-related producers might enhance their imagination and problem solving with graphical thinking and visual literacy.


1987 ◽  
Vol 7 (2) ◽  
pp. 137-154 ◽  
Author(s):  
Oliver W. Hill

This study attempts to evaluate psychological concepts of intuition. Of the many definitions of intuition, two extremes emerge. One holds intuition to be an inferential heuristic, and the other defines it as a cognitive mode capable of immediate, non-inferential, holistic processing. Three inventories were administered that purport to measure intuition. The Intuitive Problem Solving Scale corresponds to the definition of intuition as inferential heuristic. The Psycho-Epistemological Profile and the Meyers-Briggs Type Indicator define intuition as a non-inferential epistemic mode. Scores on these scales are correlated with scores on various inferential tasks, as well as with scores on measures of three traits usually associated with intuition (originality, private self-awareness, and creativity). Results indicate that intuition is not completely reducible to inference.


2010 ◽  
Vol 17 (1) ◽  
pp. 4-7
Author(s):  
Lynn McGarvey

As teachers and educators, we have a unique opportunity to continue to see the world through the eyes of a child. Together with our students, we engage in an ongoing quest to make sense of the world around us. We have opportunities to experience wonder and fascination with mathematical ideas new to us, concepts never truly understood, and alternative strategies for problem solving. The start of the new school year is a time to renew that sense of curiosity, enthusiasm, and optimism for teaching mathematics to children.


Revemop ◽  
2019 ◽  
Vol 1 (3) ◽  
pp. 458
Author(s):  
Flávia Sueli Fabiani Marcatto

<p>Este artigo tem como objetivo a construção de uma perspectiva diferenciada sobre o ensino de Matemática por meio da resolução de problemas para professores e futuros professores. O estudo segue uma metodologia de investigação de natureza qualitativa e interpretativa. No desenvolvimento das ações, foram incentivados registros escritos em portfólios com ênfase no processo de resolução de problemas. Dois problemas foram selecionados para intervenções em turmas da Educação Básica. O processo estimulou-os a questionar suas próprias respostas, explorar ideias matemáticas, questionar o problema e seus modos de encontrar a solução, fazer generalizações e transformar um dado problema em novas situações-problema, adaptando-as para suas aulas. Isto evidencia uma concepção de ensino-aprendizagem obtida por via de ação reflexiva e compartilhada que constrói conhecimentos, aprimorando a formação inicial e continuada de professores de Matemática.</p><p><strong>Palavras-chave: </strong>Ensino-Aprendizagem-Avaliação por meio da Resolução de Problemas. Práticas de Discussão. Ações de professores de Matemática.</p><p><strong><br /></strong></p><p><strong>A reflection on problem solving in teacher education teaching Mathematics</strong></p><p align="center"> </p><p><strong>Abstract: </strong>This article aims to build a differentiated perspective on mathematics teaching by solving problems for teachers and future teachers. The study follows an investigation methodology of qualitative and interpretative nature. In the development of the actions, written records were encouraged in portfolios with an emphasis on the problem-solving process. Two problems were selected for interventions in basic education classes. The process stimulated them to question their own answers, explore mathematical ideas, question the problem and their ways of finding the solution, make generalizations, and transform a given problem into new problem situations, by adapting them to their classrooms. This shows a concept of teaching and learning obtained through reflexive and shared action that builds knowledge, improving the initial and continued formation of mathematics teachers.<strong></strong></p><p><strong>Keywords:</strong> Teaching-Learning-Assessment through Problem Solving. Discussion Practices. Actions of Mathematics teachers.</p><p><strong><br /></strong></p><p><strong>Una reflexión sobre la resolución de problemas en la formación de profesores que enseñan Matemáticas</strong></p><p align="center"> </p><p><strong>Resumen:</strong> Este artículo tiene como objetivo la construcción de una perspectiva diferenciada obre enseñanza de Matemáticas por medio de la resolución de problemas para profesores y futuros profesores. El estudio sigue una metodología de investigación de naturaleza cualitativa e interpretativa. En el desarrollo de las acciones se incentivaron registros escritos en portafolios con énfasis en el proceso de resolución de problemas. Dos problemas fueron seleccionados, para intervenciones en grupos de Educación Básica. El proceso estimuló a cuestionar sus propias respuestas, explorar ideas matemáticas, cuestionar el problema y sus maneras de encontrar la solución, hacer generalizaciones y transformar un determinado problema en nuevas situaciones-problema, adaptándolas a sus clases. Esto evidencia una concepción de enseñanza-aprendizaje obtenida por vía de acción reflexiva y compartida que construye conocimientos, perfeccionando la formación inicial y continuada de profesores de Matemáticas.<strong></strong></p><p><strong>Palavras chave: </strong>Enseñanza-Aprendizaje-Evaluación a través de la resolución de problemas. Prácticas de Discusión. Acciones de profesores de Matemáticas.</p>


Imbizo ◽  
2017 ◽  
Vol 7 (1) ◽  
pp. 40-54
Author(s):  
Oyeh O. Otu

This article examines how female conditioning and sexual repression affect the woman’s sense of self, womanhood, identity and her place in society. It argues that the woman’s body is at the core of the many sites of gender struggles/ politics. Accordingly, the woman’s body must be decolonised for her to attain true emancipation. On the one hand, this study identifies the grave consequences of sexual repression, how it robs women of their freedom to choose whom to love or marry, the freedom to seek legal redress against sexual abuse and terror, and how it hinders their quest for self-determination. On the other hand, it underscores the need to give women sexual freedom that must be respected and enforced by law for the overall good of society.


Author(s):  
J. Navaneetha Krishnan ◽  
P. Paul Devanesan

The major aim of teaching Mathematics is to develop problem solving skill among the students. This article aims to find out the problem solving strategies and to test the students’ ability in using these strategies to solve problems. Using sample survey method, four hundred students were taken for this investigation. Students’ achievement in solving problems was tested for their Identification and Application of Problem Solving Strategies as a major finding, thirty one percent of the students’ achievement in mathematics is contributed by Identification and Application of Problem Solving Strategies.


BMC Zoology ◽  
2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Ansa E. Cobham ◽  
Christen K. Mirth

Abstract Background Organisms show an incredibly diverse array of body and organ shapes that are both unique to their taxon and important for adapting to their environment. Achieving these specific shapes involves coordinating the many processes that transform single cells into complex organs, and regulating their growth so that they can function within a fully-formed body. Main text Conceptually, body and organ shape can be separated in two categories, although in practice these categories need not be mutually exclusive. Body shape results from the extent to which organs, or parts of organs, grow relative to each other. The patterns of relative organ size are characterized using allometry. Organ shape, on the other hand, is defined as the geometric features of an organ’s component parts excluding its size. Characterization of organ shape is frequently described by the relative position of homologous features, known as landmarks, distributed throughout the organ. These descriptions fall into the domain of geometric morphometrics. Conclusion In this review, we discuss the methods of characterizing body and organ shape, the developmental programs thought to underlie each, highlight when and how the mechanisms regulating body and organ shape might overlap, and provide our perspective on future avenues of research.


2018 ◽  
Vol 13 (2) ◽  
pp. 179-190 ◽  
Author(s):  
T.M. Wong

Purpose The purpose of this paper is to identify the teaching innovations that have been implemented in higher education institutions in Asia and the perspectives of educators on them. Design/methodology/approach Semi-structured interviews were conducted with 28 educators who were affiliated with 23 higher education institutions in ten Asian countries/regions. The interviews covered information about the teaching innovations of the participants’ institutions, the characteristics of the innovative practices and the participants’ views on them. The relationships between the characteristics of institutions and their teaching innovations were also examined. Findings The results showed that the teaching innovations included two main categories, namely, those which involved the use of advanced technologies and those which did not. The innovations that involved the use of advanced technologies were mainly from larger institutions, while the other category was mainly from smaller ones and had been practised for less than 1.5 years. Differences were also identified between the two categories in terms of the aims and importance of innovations, innovative features, the evaluation of innovations and improvements needed for them. Originality/value The results highlighted that technology is only one of the many aspects of teaching innovations, which is different from the view prevailing in the literature. They also suggested that differences in the scale of institutions (in terms of number of students) possibly influences the kind of teaching innovations adopted.


2021 ◽  
pp. 104649642110102
Author(s):  
Michael Stinson ◽  
Lisa B. Elliot ◽  
Carol Marchetti ◽  
Daniel J. Devor ◽  
Joan R. Rentsch

This study examined knowledge sharing and problem solving in teams that included teammates who were deaf or hard of hearing (DHH). Eighteen teams of four students were comprised of either all deaf or hard of hearing (DHH), all hearing, or two DHH and two hearing postsecondary students who participated in group problem-solving. Successful problem solution, recall, and recognition of knowledge shared by team members were assessed. Hearing teams shared the most team knowledge and achieved the most complete problem solutions, followed by the mixed DHH/hearing teams. DHH teams did not perform as well as the other two types of teams.


2000 ◽  
Vol 11 (3) ◽  
pp. 261-264 ◽  
Author(s):  
Tricia S. Clement ◽  
Thomas R. Zentall

We tested the hypothesis that pigeons could use a cognitively efficient coding strategy by training them on a conditional discrimination (delayed symbolic matching) in which one alternative was correct following the presentation of one sample (one-to-one), whereas the other alternative was correct following the presentation of any one of four other samples (many-to-one). When retention intervals of different durations were inserted between the offset of the sample and the onset of the choice stimuli, divergent retention functions were found. With increasing retention interval, matching accuracy on trials involving any of the many-to-one samples was increasingly better than matching accuracy on trials involving the one-to-one sample. Furthermore, following this test, pigeons treated a novel sample as if it had been one of the many-to-one samples. The data suggest that rather than learning each of the five sample-comparison associations independently, the pigeons developed a cognitively efficient single-code/default coding strategy.


Sign in / Sign up

Export Citation Format

Share Document