8 research outputs found
The Need for an Inclusive Framework for Students\u27 Thinking in School Geometry
This study is the outcome of a research that investigated how students who were assigned varying levels of geometric thinking attempted problems requiring some amount of algebraic thinking in geometry. The study reports that students’ thinking in geometry also requires facility with algebra and as such there is a need for a framework that provides a more inclusive view of what constitutes geometric thinking in school mathematics
Making visible a teacher’s pedagogical reasoning: an aspect of pedagogical documentation
Much of a teacher’s practice and professional learning remains unseen despite recent calls to incorporate practice-based and inquiry-based approaches to improve mathematics instruction. Although the idea of pedagogical reasoning and action can provide a way to unpack these unseen aspects of practice, it remains to be seen how a teacher’s actions and thinking can be made visible. In this paper, we present a case of how a teacher’s pedagogical reasoning is made visible through pedagogical documentation, which suggests the possibility of using documentation to unpack these unseen aspects of a teacher’s practices.This study was funded by Singapore Ministry of Education (MOE) under the MOE Academy Fund Programme (AFD 06/17 CBH) and administered by National Institute of Education (NIE), Nanyang Technological University, Singapore
An approach to teach with variations: using typical problems
Mathematics teachers use typical problems from past examination papers and textbook exercises to develop procedural skills. In this paper, we discuss other uses of typical problems. We focus on the affordances that an experienced teacher, John, perceives in typical problems and how he uses them to enhance student learning by harnessing the idea of teaching with variations or bianshi. Drawing on data from a larger qualitative design-based research on investigating teacher noticing, we present snapshots of John’s classroom practices to show what he noticed about the variations afforded by typical problems and how he used these problems with students to promote both procedural skills and conceptual understanding. Findings suggest the value of supporting teachers in harnessing variations of typical problems, which has implications for teacher education and professional development
Avances de investigación en educación matemática
Resumen basado en el de la publicaciĂłnResumen en español, francĂ©s y portuguĂ©sMonográfico con el tĂtulo: Conocimiento, competencia docente del profesor de matemáticas y llegar a ser un formador de profesoresLos profesores de matemáticas usan problemas tĂpicos para desarrollar destrezas procedimentales. Se discuten otros usos de los problemas tĂpicos. Se analizan las oportunidades que un profesor experimentado percibe en los problemas tĂpicos y cĂłmo los usa para potenciar el aprendizaje de sus estudiantes aprovechando las variaciones del problema. A partir de los datos de la investigaciĂłn, se presenta una instantánea de la práctica de ese profesor para mostrar lo que observa de las posibles variaciones en los problemas tĂpicos y cĂłmo las usa con los estudiantes para promover tanto las destrezas procedimentales como la comprensiĂłn conceptual. Los resultados subrayan el potencial de apoyar a los profesores para que aprovechen las variaciones de los problemas tĂpicos, lo cual tiene implicaciones para la formaciĂłn inicial y continua de profesoresES
An approach to teach with variations: using typical problems
Mathematics teachers use typical problems from past examination papers and textbook exercises to develop procedural skills. In this paper, we discuss other uses of typical problems. We focus on the affordances that an experienced teacher, John, perceives in typical problems and how he uses them to enhance student learning by harnessing the idea of teaching with variations or bianshi. Drawing on data from a larger qualitative design-based research on investigating teacher noticing, we present snapshots of John’s classroom practices to show what he noticed about the variations afforded by typical problems and how he used these problems with students to promote both procedural skills and conceptual understanding. Findings suggest the value of supporting teachers in harnessing variations of typical problems, which has implications for teacher education and professional development.Les professeurs de mathĂ©matiques utilisent des problèmes typiques des propositions d'examen prĂ©cĂ©dentes et des manuels pour dĂ©velopper des compĂ©tences procĂ©durales. Dans cet article, nous discutons d'autres utilisations de problèmes typiques. Nous nous concentrons sur les opportunitĂ©s qu'un enseignant expĂ©rimentĂ©, John, perçoit dans les problèmes typiques et comment il les utilise pour amĂ©liorer l'apprentissage de ses Ă©tudiants en profitant des variations du problème (ou bianshi). Ă€ partir des donnĂ©es d'une recherche qualitative axĂ©e sur la compĂ©tence «noticing» de l'enseignant, nous prĂ©sentons un aperçu de la pratique de John pour montrer ce qu'il observe des variations possibles dans les problèmes typiques et comment il les utilise avec les Ă©lèves promouvoir les compĂ©tences procĂ©durales et la comprĂ©hension conceptuelle. Les rĂ©sultats soulignent la possibilitĂ© d'aider les enseignants Ă tirer parti des variations de problèmes typiques, qui ont des implications pour la formation initiale et continue des enseignants.Os professores de matemática usam problemas tĂpicos de propostas de exames anteriores e de livros didáticos para desenvolver procedimentos. Neste artigo, discutimos outros usos de problemas tĂpicos. NĂłs nos concentramos nas oportunidades que um professor experiente, John, percebe nos problemas tĂpicos e como ele os usa para melhorar a aprendizagem de seus alunos aproveitando as variações do problema (ou bianshi). A partir dos dados de uma pesquisa qualitativa voltada para a competĂŞncia “olhar profissionalmente” do professor, apresentamos um instantâneo da prática de John para mostrar o que ele observa de possĂveis variações em problemas tĂpicos e como ele os usa com os alunos para promover habilidades processuais e compreensĂŁo conceitual. Os resultados destacam o potencial de apoiar os professores para tirar proveito das variações de problemas tĂpicos, que tĂŞm implicações para a formação inicial e contĂnua dos professoresLos profesores de matemáticas usan problemas tĂpicos desde propuestas de exámenes anteriores y desde los libros de texto para desarrollar destrezas procedimentales. En este articulo, discutimos otros usos de los problemas tĂpicos. Nos centramos en las oportunidades que un profesor experimentado, John, percibe en los problemas tĂpicos y cĂłmo los usa para potenciar el aprendizaje de sus estudiantes aprovechando las variaciones del problema(o bianshi). A partir de los datos de una investigaciĂłn con enfoque cualitativo centrada en la competencia “mirar profesionalmente” del profesor, presentamos una instantánea de la práctica de John para mostrar lo que observa de las posibles variaciones en los problemas tĂpicos y cĂłmo las usa con los estudiantes para promover tanto las destrezas procedimentales como la comprensiĂłn conceptual. Los resultados subrayan el potencial de apoyar a los profesores para que aprovechen las variaciones de los problemas tĂpicos, lo cual tienen implicaciones para la formaciĂłn inicial y continua de profesores