Mathematical connections of a higher cognitive level: A tool we may use to identify these in practice

Mhlolo, Michael Kainose

doi:10.1080/10288457.2012.10740738

Cited by 31 publications

(43 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The importance task representation is unconventional, that, according to Zazkis (2008), it is a vehicle towards constructing a "richer or more abstract schema" (p.154). As reported in various studies (Haciomeroglu et al, 2010;Mhlolo, 2012;Moon et al, 2013), students and teachers find it difficult to make mathematical connections between different representations.…”

Section: Results For Task 6: Instantaneous Rates Of Variationmentioning

confidence: 99%

Comparing the Didactic-Mathematical Knowledge of Derivative of In-Service and Pre-service Teachers

Castro

Pino-Fan

2021

Acta Sci.

View full text Add to dashboard Cite

Background:The knowledge that a mathematics teacher should master has taken an increasing interest in recent years. Very few studies focused on comparing didactic-mathematic knowledge of in-service and pre-service teachers aimed at identifying features of the teachers' didactic-mathematical knowledge on specific topics that can establish a line between pre-service and in-service teachers' knowledge for teaching. Objective: The research aims to compare derivative knowledge of preservice and in-service teachers to identify similarities and differences between teachers' knowledge. Design: This research is a mixed and interpretative study. Settings and Participants: The participants were 22 pre-service teachers, and 11 in-service teachers enrolled in a pre-service teacher education programme and a master's programme, respectively. Data collection and participants: Data were collected based on a questionnaire designed purposefully for the study. Results: The results show that preservice teachers lack both epistemic derivative knowledge, while in-service teachers not only have this knowledge but relates it to its use in teaching. Pre-service teachers may not be making sense of the concept of derivative means, much less related to teaching. Conclusions: The insufficiencies found in pre-service teachers' knowledge justify the pertinence to design specific formative cycles to develop prospective teachers' epistemic facet of didactic-mathematical knowledge. It is recommended that both in-service and pre-service teachers discuss activities in which they can identify and reflect on possible mistakes and errors made by students. The development of these formative cycles should consider the complexity of the global meaning of the derivative.

show abstract

Section: Results For Task 6: Instantaneous Rates Of Variationmentioning

confidence: 99%

Comparing the Didactic-Mathematical Knowledge of Derivative of In-Service and Pre-service Teachers

Castro

Pino-Fan

2021

Acta Sci.

View full text Add to dashboard Cite

show abstract

“…3) Implication: This type of connection is a logical relationship if-then (A B) (Businskas, 2008;Mhlolo, 2012;García-García, 2018). The procedure that exists in this relationship is presented through logical reasoning in mathematics that suggests connections of an if-then nature.…”

Section: Conceptual Frameworkmentioning

confidence: 99%

“…The procedure that exists in this relationship is presented through logical reasoning in mathematics that suggests connections of an if-then nature. Mhlolo (2012) argues that, in deductive reasoning, the conclusion is reached from previously known facts (the premises). An example of this type of connection is: if is differentiable in , then is continuous in .…”

Section: Conceptual Frameworkmentioning

confidence: 99%

Pre-service Mathematics Teacher's Mathematical Connections in the Context of Problem-Solving About the Derivative

Rodríguez-Nieto¹

2021

TURCOMAT

View full text Add to dashboard Cite

The mathematical connections made by five Pre-Service Mathematics Teachers (PSMTs) when solving problems on the derivative were analyzed. The conceptual framework used was the typology of intra-mathematical connections. For data collection, semi-structured interviews were conducted, and a questionnaire was designed, which included three tasks about of the derivative, which were analyzed through the thematic analysis method. The results showed that PSMTs made mathematical connections: meaning, different representations, procedural, part-whole, implication and feature. We identified that the PSMT's difficulties in establishing connections are caused by the meaning they have on the derivative concept, acquired in their received teaching and, if they are not attended, they can be reproduced in their future practice as in-service teachers.

show abstract

“…Em nível de aprendizagem, as conexões nos permitem formar uma visão da Matemática como um todo integrado e não como uma coleção de par- tes separadas, que é como os alunos veem (Evitts, 2004;Mwakapenda, 2008;Mhlolo, 2012). Esses autores argumentam que as conexões matemáticas devem ser desenvolvidas nos estudantes porque permitiriam que eles melhorassem sua compreensão matemática.…”

Section: Conexões E Formação De Professoresunclassified

Conexões extramatemáticas na formação inicial de docentes

Vanegas

Giménez

2018

Estud. av.

View full text Add to dashboard Cite

RESUMO O objetivo deste artigo é mostrar as conexões que futuros professores do Ensino Fundamental utilizam no planejamento de sequências didáticas para o ensino de Matemática. Uma observação etnográfica participante é feita para caracterizar o tipo de conexões extradisciplinares consideradas. A análise feita nos permite afirmar que os futuros professores valorizam o uso de contextos reais, como motivadores e geradores deconhecimento matemático, embora os desenvolvimentos nem sempre sejam justificados epistemicamente. Verificamos uma dificuldade em considerar as conexões metafóricas.

show abstract

Mathematical connections of a higher cognitive level: A tool we may use to identify these in practice

Cited by 31 publications

References 25 publications

Comparing the Didactic-Mathematical Knowledge of Derivative of In-Service and Pre-service Teachers

Comparing the Didactic-Mathematical Knowledge of Derivative of In-Service and Pre-service Teachers

Pre-service Mathematics Teacher's Mathematical Connections in the Context of Problem-Solving About the Derivative

Conexões extramatemáticas na formação inicial de docentes

Contact Info

Product

Resources

About