Mathematical Knowledge for Teaching and Task Unfolding: An Exploratory Study

2010 ◽  
Vol 110 (3) ◽  
pp. 247-278 ◽  
Author(s):  
Charalambos Y. Charalambous
Keyword(s):  
Exploratory Study ◽  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Knowledge For Teaching ◽  
And Task

scholarly journals Mathematical Knowledge for Teaching and the Mathematical Quality of Instruction: An Exploratory Study

2008 ◽  
Vol 26 (4) ◽  
pp. 430-511 ◽  
Author(s):  
Heather C. Hill ◽  
Merrie L. Blunk ◽  
Charalambos Y. Charalambous ◽  
Jennifer M. Lewis ◽  
Geoffrey C. Phelps ◽  
...  
Keyword(s):  
Exploratory Study ◽  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Quality Of Instruction ◽  
Knowledge For Teaching ◽  
Mathematical Quality Of Instruction ◽  
Mathematical Quality

scholarly journals What Mathematical Knowledge Do Prospective Teachers Reveal When Creating and Solving a Probability Problem?

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3300
Author(s):  
Marlén Alonso-Castaño ◽  
Pedro Alonso ◽  
Maria Mellone ◽  
Luis J. Rodríguez-Muñiz
Keyword(s):  
Prospective Teachers ◽  
Exploratory Study ◽  
Mathematical Knowledge ◽  
Methodological Approach ◽  
Mathematical Knowledge For Teaching ◽  
Problem Posing ◽  
Teaching Model ◽  
Training Task ◽  
Knowledge For Teaching ◽  
Probability Problem

The teaching of probability is conditioned by teachers’ mathematical knowledge. In this paper, an exploratory study is carried out with prospective teachers. A training task was designed requiring them to create and solve a probability problem using the values of euro coins, which was adapted to students aged 11 to 12. The study aimed at determining what mathematical knowledge prospective teachers show when dealing with the task. The data were collected through the Moodle online Campus. We framed the data analysis in the Mathematical Knowledge for Teaching model and we used content analysis as the methodological approach. The results indicate that, despite finding evidence of adequate common and specialised mathematical knowledge, in approximately half of the prospective teachers participating in the study, too many of them still show a lack of knowledge in both subdomains. There was also little evidence of knowledge of the curriculum. The main finding of the research is that, when prospective teachers get involved in complex creative tasks, they mobilised together specialised and common mathematical knowledge, working into different mathematical processes such as problem posing and solving, communication, and argumentation, which reinforces the need to continue working on these types of complex tasks.

scholarly journals Mathematical knowledge for teaching: Adding to the description through a study of probability in practice

Pythagoras ◽  
2006 ◽  
Vol 0 (63) ◽  
Author(s):  
Mercy Kazima ◽  
Jill Adler
Keyword(s):  
Problem Solving ◽  
Mathematical Knowledge ◽  
Mathematical Problem ◽  
Mathematical Knowledge For Teaching ◽  
Mathematical Work ◽  
Mathematical Problem Solving ◽  
Knowledge For Teaching ◽  
Scaling Down ◽  
Multilingual Classroom ◽  
Everyday Knowledge

In their description of the mathematical work of teaching, Ball,  Bass & Hill (2004) describe the mathematical problem solving that teachers do as they go about their work. In this paper we add to this description through our study of teaching of probability in a grade 8 multilingual classroom in South Africa. We use instances of teaching to highlight the mathematical problem solving that teachers might face as they work with learners’ ideas, both expected and unexpected. We discuss  the restructuring of tasks as an inevitable feature of teachers’ work, and argue that in addition to scaling up or scaling down of the task as Ball et al. (2004) describe, restructuring can also entail shifting the mathematical outcomes from those intended. We also point out how well known issues in mathematics education, for example working with learners’ everyday knowledge, and the languages they bring to class, are highlighted by the context of probability, enabling additional insights into the mathematical work of teaching.

scholarly journals Conhecimentos de Professores de Matemática em Início de Carreira Sobre o Campo Aditivo

2020 ◽  
Vol 13 (1) ◽  
pp. 53-63
Author(s):  
Rafael Neves Almeida ◽  
Ruy Cesar Pietropaolo
Keyword(s):  
Data Collection ◽  
Knowledge Base ◽  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Early Career ◽  
Early Career Teachers ◽  
Knowledge For Teaching ◽  
Problem Situations ◽  
Scholarship Recipients ◽  
Career Teachers

Este trabalho apresenta um estudo realizado com cinco professores de Matemática, em início de carreira, ex-bolsistas do Programa Institucional de Bolsa de Iniciação à Docência (Pibid), cujo objetivo foi evidenciar os Conhecimentos Didáticos e Curriculares dos participantes sobre o ensino de problemas do campo aditivo, conforme indicado pelos parâmetros curriculares nacionais. A coleta de dados se deu por meio de entrevistas e protocolos respondidos pelos professores. Como referenciais teóricos, no tocante ao início de carreira, foram utilizados os trabalhos de Huberman e Garcia. Em relação aos conhecimentos de professores necessários à docência optou-se por Ball, Thames e Phelps. A análise dos dados nos permitiu verificar que os professores no processo de ensino do campo aditivo dão bastante ênfase à ideia de combinar dois estados para obter um terceiro, não destacando outros importantes significados. Portanto, faz-se necessário uma ampliação na base de conhecimentos desses docentes para o ensino das operações.   Palavras-chave: Professores em Início de Carreira. Conhecimentos Matemáticos para o Ensino. Campo Aditivo. PIBID.   Abstract In this work, we will present a study carried out with five early-career teachers, former scholarship recipients of the Programa Institucional de Bolsa de Iniciação a Docência (Pibid), whose objective was to highlight the participants' Didactic and Curricular Knowledge about the notion of addition. The data collection was done through interviews and protocols answered by the teachers. As theoretical references, regarding the beginning of the career, the works of Huberman (1995) and Garcia (1999) were used. Regarding the teachers' knowledge required for teaching, Ball, Thames and Phelps (2008) were chosen. The analysis of the data allowed us to verify that the teachers' knowledge about addition operation is restricted to the meaning of joining and that the idea most used to work with this theme in the classroom involves problem situations with money. Therefore, it is necessary to increase the knowledge base of these teachers.   Keywords: Teacher Early-Career Teachers. Mathematical Knowledge for Teaching (MKT).  

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