Developing mathematical knowledge for teaching in a methods course: the case of function

Steele, Matt; Hillen, Amy F.; Smith, Margaret S.

doi:10.1007/s10857-013-9243-6

Cited by 41 publications

(61 citation statements)

References 23 publications

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“…For instance, Nyikahadzoyi (2015) indicated that teachers, who have SCK, should know the different definition and representations of a function, be able to choose the neccessary representation for particular purposes and concepts, have a great collection of neat examples, know the importance of the topic in relation to the whole subject and be able to explain this to the students, and conceive a function as a procedure, process, object, or procept (s. 268). While Steele et al (2013) defined the components of SCK, they also focused on the importance of definition, using multiple representation and being able to felxibly move them. In this study, Table 1 was constructed as the theoretical framework of this study by considering these three studies.…”

Section: Figure 1 Domains Of Mkt Framework (Adapted Frommentioning

confidence: 99%

Examination of Pre-Service Mathematics Teachers’ Knowledge of Teaching Function Concept

Taşdan¹,

Koyunkaya²

2017

ADN

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Abstract:Teaching of mathematics could be improved with teachers who have a strong mathematical knowledge and have an ability to reflect this knowledge on their teaching. Therefore, it is important to develop mathematics teachers' theoretical and pedagogical knowledge. This study was designed to examine pre-service secondary mathematics teachers' (PSMT) mathematical knowledge for teaching (MKT) in terms of function concept. In order to examine PSMT's MKT regarding function concept, case study design was used in the study. Three PSMTs', who were at the fifth year in the program, were selected as the participants. The data was collected by observing and recording PSMTs' teaching of function concept as well as by examining their lesson plan of the concept. Descriptive and content analysis were used to analyze the collected data. The results revealed that PSMTs' had limited knowledge regarding teaching of function concept. Particularly, they had difficulties to reflect their knowledge of function concept on their teaching. The results also showed that experience is directly related to teaching of function concept, time and classroom management and communication with students. Therefore, it is important to improve both in-service and pre-service teachers' MKT by considering the effect of experience and abilities in teaching.

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Section: Figure 1 Domains Of Mkt Framework (Adapted Frommentioning

confidence: 99%

Examination of Pre-Service Mathematics Teachers’ Knowledge of Teaching Function Concept

Taşdan¹,

Koyunkaya²

2017

ADN

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“…No entanto, apesar das potencialidades das realizações desse panorama, a sua ênfase no ensino pode acarretar a subordinação do conceito de função à realização algébrica (EVEN, 1990;STEELE;HILLEN;SMITH, 2013), ou seja, o não reconhecimento do caráter arbitrário de uma relação funcional, tanto no que diz respeito à natureza da relação entre às variáveis, que não precisa ser descrita por uma fórmula (como na parte A do Quadro 2), quanto aos conjuntos (domínio e contradomínio) que não têm que ser numéricos (como podemos observar no exemplo da Parte A do Quadro 1).…”

Section: Panorama Algébricounclassified

“…Quando a classificação é mais fraca (C-) nessa relação, há uma redução no isolamento entre os panoramas, as pontes "diminuem de tamanho", havendo articulação entre os seus textos. Estudos sustentam que um componente fundamental para a aprendizagem do tema função, em nossos termos, é a fluência na transição entre os textos do que chamamos de diferentes panoramas (EVEN, 1990, MAGGIO;NEHRING, 2012;STEELE;HILLEN;SMITH, 2013). Isto nos possibilita inferir sobre a importância da implementação de uma C-nas relações intraconceito na realização do ensino desse conceito.…”

Section: Panorama Formalunclassified

“…Em virtude do papel desempenhado por uma variedade de realizações na compreensão de conceitos (DAVIS; RENERT, 2014), em particular no conceito de função, por revelar, por exemplo, aspectos e interpretações particulares deste conceito (STEELE, HILLEN;SMITH, 2013) e, que esse tópico (realizações), ainda não foi sistematicamente incorporado aos cursos de formação (DAVIS; RENERT, 2014).…”

Section: Considerações Finaisunclassified

“…Estudos indicam que a natureza estrutural lógica dos seus textos ocasiona dificuldade no seu entendimento, pelo menos para uma abordagem inicial, de forma que é necessário reconsiderar o seu lugar no processo de ensino e aprendizagem (NACHIELI, TABACH, 2015;VIIRMAN, 2014), no decorrer da Educação Básica. À vista disso, pesquisadores têm sugerido descrições mais operacionais para o seu ensino (VIIRMAN, 2014), considerando que as bases conceituais do conceito de função devem ser acessíveis desde os anos inicias do Ensino Fundamental (STEELE; HILLEN; SMITH, 2013), tal como comunicá-lo como uma relação de dependência por meio da análise de regularidades e padrões em sequências numéricas e geométricas (ASGHARY; SHAHVARANI; MEDGHALCHI, 2013;MAGGIO;NEHRING, 2012), mesmo antes que a palavra função tenha sido oficialmente introduzida no ensino. Outra sugestão, indicada por Asghary, Shahvarani e Medghalchi (2013), é comunicar o conceito de função usando a metáfora de uma máquina que transforma cada input em um único output.…”

Section: Introductionunclassified

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Um modelo teórico de Matemática para o Ensino do Conceito de Função a partir de realizações em livros didáticos <br> A theoretical model of Mathematics for Teaching of the concept of function from realizations in textbooks

Santos

Barbosa

2017

EMP

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The role of task classification and design in curriculum making for preservice teachers of mathematics

Dempsey

O’Shea

2019

The Curriculum Journal

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This paper reports on a research project undertaken with a group (n = 19) of Irish preservice student teachers (PSTs) during the third year of a five-year undergraduate education course. A series of workshops were carried out on the classification and design of mathematics tasks. The research is presented as a case study using mixed methods to gather data at three points, before the workshops, after the workshops, and two years later, when PSTs were in their final year. We argue that task classification and design are curriculum-making activities for mathematics teachers. Through critically classifying and designing mathematics tasks, PSTs developed skills of evaluating the cognitive demand of tasks and showed evidence of using these skills in curriculum making. Through using frameworks to classify tasks, the PSTs demonstrated a capacity to take a more critical role in curriculum making. Our data show that the development of skills in these areas has lasting effects on PSTs' practices and willingness to engage meaningfully with the curriculum in mathematics. The research highlights the need for PSTs to work on evaluating and designing tasks. How frameworks can support and enhance PSTs' capacity to make curricular decisions is evidenced.

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Developing mathematical knowledge for teaching in a methods course: the case of function

Cited by 41 publications

References 23 publications

Examination of Pre-Service Mathematics Teachers’ Knowledge of Teaching Function Concept

Examination of Pre-Service Mathematics Teachers’ Knowledge of Teaching Function Concept

Um modelo teórico de Matemática para o Ensino do Conceito de Função a partir de realizações em livros didáticos <br> A theoretical model of Mathematics for Teaching of the concept of function from realizations in textbooks

The role of task classification and design in curriculum making for preservice teachers of mathematics

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