Turn vs. shape: teachers cope with incompatible perspectives on angle

Kontorovich, Igor’; Zazkis, Rina

doi:10.1007/s10649-016-9699-2

Cited by 22 publications

(7 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Lakatos's research was deeply involved with the development of definitions (e.g. Kontorovich & Zazkis, 2016;Larsen & Zandieh, 2008;Ouvrier-Buffet, 2006). He described the history of the concepts of polyhedron and of uniform convergence of sequences of functions in terms of the development of definitions, for example through what he called 'monster barring' (ad hoc alteration of definitions to rule out problematic counterexamples) and proof-generated concepts.…”

Section: Discussionmentioning

confidence: 99%

Task Design Principles for Heuristic Refutation in Dynamic Geometry Environments

Komatsu

Jones

2018

Int J of Sci and Math Educ

View full text Add to dashboard Cite

Task design is increasingly recognised as crucial for enhancing student learning of mathematics. Even so, and despite the significance of mathematical activity related to proofs and counterexamples in school mathematics, the task design principles underpinning students' success in proof-related activity remains under-explored in mathematics education research. What is more, although the affordances of using dynamic geometry environments (DGEs) have been established in the literature, task design in DGEs remains somewhat under-studied. In this paper, we address both these issues by theoretically developing, and empirically testing, task design principles for supporting students' heuristic refutation (revising conjectures/proofs through addressing counterexamples) in DGEs. We use the existing literature to elaborate three design principles: using tasks whose conditions are purposefully implicit, providing tools that enhance the production of counterexamples, and increasing students' recognition of contradictions. To test these principles empirically, we analyse two sets of task-based interviews, one with a triad of secondary school students and the other with a pair of undergraduates, where tasks designed according to the principles were implemented. Our analysis shows that using the tasks enabled the students to engage successfully in heuristic refutation. The matter of examining mathematical definitions when handling counterexamples emerged as an issue for further research.

show abstract

Section: Discussionmentioning

confidence: 99%

Task Design Principles for Heuristic Refutation in Dynamic Geometry Environments

Komatsu

Jones

2018

Int J of Sci and Math Educ

View full text Add to dashboard Cite

show abstract

“…O grupo temático # 2 está composto pelos estudos de Kontorovich & Zazkis (2016), Prado & Lobo da Costa (2016) e Tekin-Sitrava & Isiksal-Bostan (2016). São três pesquisas empíricas em que se exploram os conhecimentos do professor de matemática em contextos de formação continuada de professores e ensino de matemática na escola.…”

Section: Metassíntese Do Eixo 2: "Teacher Knowledge" -Mathematicsunclassified

“…São três pesquisas empíricas em que se exploram os conhecimentos do professor de matemática em contextos de formação continuada de professores e ensino de matemática na escola. Kontorovich & Zazkis (2016), visando a explorar a maneira em que um grupo de 16 professores de matemática lidam com as tensões entre duas perspectivas do ângulo, objetivam caracterizar as aproximações do ângulo empregadas por esses professores como forma estática e rotação dinâmica. Para tal, os professores, em contexto de formação continuada, foram engajados a resolver uma tarefa que solicitava a criação de diálogos hipotéticos entre um docente e estudantes em que se abordasse a conjectura de que a soma dos ângulos exteriores de um polígono é igual a 360º.…”

Section: Metassíntese Do Eixo 2: "Teacher Knowledge" -Mathematicsunclassified

Tarefas investigativas de geometria dinâmica e saberes do professor que ensina matemática: uma revisão de literatura

Araujo

Pazuch

2020

JIEEM

View full text Add to dashboard Cite

ResumoEste artigo reporta a revisão de literatura de uma pesquisa sobre os saberes mobilizados por um grupo de professores que ensinam matemática, em um contexto formativo, quando se engajam na elaboração de tarefas investigativas de geometria dinâmica para o ensino de geometria. O objetivo do artigo é analisar as contribuições da literatura para a elaboração de tarefas investigativas de geometria dinâmica como atividade específica do professor que ensina matemática, com foco nos saberes mobilizados nessa atividade. Para tal, optou-se por uma estratégia de busca de informação baseada na definição de dois eixos temáticos, quais sejam, “Dynamic Geometry” – GeoGebra (uma vez que interessam tarefas elaboradas com esse software) e “Teacher Knowledge” – Mathematics. Cada expressão anterior indica um descritor de busca, posteriormente inserido em três bases de dados (Redalyc, SciELO e Web of Science). O processo de busca resultou em 21 estudos, analisados e relacionados entre si conforme o método de revisão metassíntese. Os resultados obtidos mostram, entre outros aspectos, que as tarefas de cunho investigativo são predominantes nos cenários de ensino de geometria que incorporam Software de Geometria Dinâmica (SGD). Porém, esses resultados também revelam a ausência de pesquisas focadas na maneira em que professores que ensinam matemática elaboram esse tipo de tarefa e mobilizam saberes para tal fim, constituindo essa ausência um campo de pesquisa sobre esse tema. Palavras-chave: Formação de professores. Software GeoGebra. Educação Básica.Abstract This article reports a literature review about mathematics teacher’s knowledge mobilized from a teacher group in a formative context, when they are engaged in the elaboration of investigative dynamic geometry tasks’ elaboration for teaching geometry. The objective of the article is to analyze the contributions from the literature regarding the elaboration of investigative dynamic geometry tasks, as a specific activity of teaches mathematics teacher, focusing on the mobilized knowledge in this activity. For that, we opted for an information search strategy based on the definition of two thematic axes, namely, “Dynamic Geometry” –GeoGebra (since the tasks developed with this software are interesting) and “Teacher Knowledge” –Mathematics, being that each previous sentence (separated by a hyphen) indicates a search descriptor, later inserted in three databases (Redalyc, SciELO and Web of Science). The search process resulted in 21 studies, analyzed and related to each other according to the meta-synthesis review method. The results obtained show, among other aspects, that investigative tasks are the predominant type of task in geometry teaching scenarios that incorporate Dynamic Geometry Software (SGD). However, these results also reveal the absence of research focused on the way in which mathematics teachers elaborate this type of tasks and mobilize knowledge for this purpose, the former constituting a research field on this topic.Keywords: Teacher Education. GeoGebra Software. Middle and High School.

show abstract

“…Harel (1998Harel ( , 2013 identified many intellectual needs in mathematics including (a) need for certainty, (b) need for causality, (c) need for computation, and (d) need for communication. Kontorovich and Zazkis (2016) introduced an additional need: the need for efficiency.…”

Section: Opportunities To Promote Intellectual Needmentioning

confidence: 99%

“…The evolution of number systems was also driven by the need for efficiency. The need for efficiency is associated with the parsimony principle of doing a minimal amount of work to solve a given problem (Kontorovich & Zazkis, 2016). Number systems not only provide a means for computation, but also each increase in sophistication over time (variations) increased the efficiency of computation.…”

Section: Opportunities To Promote Intellectual Needmentioning

confidence: 99%

Leveraging variation of historical number systems to build understanding of the base-ten place-value system

Thanheiser

Melhuish

2018

ZDM Mathematics Education

View full text Add to dashboard Cite

Prospective elementary school teachers (PTs) come to their mathematics courses fluent in using procedures for adding and subtracting multidigit whole numbers, but many are unaware of the essential features inherent in understanding the base-10 place-value system (i.e., grouping, place value, base). Understanding these features is crucial to understanding and teaching number and place value. The research aims of this paper are (1) to present a local instructional theory (LIT), designed to familiarize PTs with these features through comparison with historical number systems and (2) to present the effects of using the LIT in the PT classroom. A theory of learning (variation theory) is paired with a framework related to motivation (intellectual need) to illustrate the mutually supporting roles they may play in mathematical learning and task design. The LIT, a supporting task sequence, and the rationale for task design are shared. This theoretical contribution is then paired with evidence of PTs' changing growth in their conceptions of whole number before and after courses leveraging this task sequence.

show abstract

Turn vs. shape: teachers cope with incompatible perspectives on angle

Cited by 22 publications

References 15 publications

Task Design Principles for Heuristic Refutation in Dynamic Geometry Environments

Task Design Principles for Heuristic Refutation in Dynamic Geometry Environments

Tarefas investigativas de geometria dinâmica e saberes do professor que ensina matemática: uma revisão de literatura

Leveraging variation of historical number systems to build understanding of the base-ten place-value system

Contact Info

Product

Resources

About