Teachers’ use of their mathematical knowledge for teaching in learning a mathematics learning trajectory

2013 ◽  
Vol 17 (2) ◽  
pp. 149-175 ◽  
Author(s):  
P. Holt Wilson ◽  
Paola Sztajn ◽  
Cyndi Edgington ◽  
Jere Confrey
Keyword(s):  
Mathematical Knowledge ◽  
Mathematics Learning ◽  
Mathematical Knowledge For Teaching ◽  
Learning Trajectory ◽  
Knowledge For Teaching

What role does professional noticing play? Examining connections with affect and mathematical knowledge for teaching among preservice teachers

ZDM ◽  
2021 ◽  
Author(s):  
Cindy Jong ◽  
Edna O. Schack ◽  
Molly H. Fisher ◽  
Jonathan Thomas ◽  
David Dueber
Keyword(s):  
Preservice Teachers ◽  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Professional Noticing ◽  
Knowledge For Teaching

scholarly journals Strategic competence for multistep fraction word problems: an overlooked aspect of mathematical knowledge for teaching

2021 ◽  
Author(s):  
Yasemin Copur-Gencturk ◽  
Tenzin Doleck
Keyword(s):  
Word Problem ◽  
Word Problems ◽  
Mathematical Knowledge ◽  
Teaching And Learning ◽  
Mathematics Learning ◽  
Mathematical Knowledge For Teaching ◽  
Important Indicator ◽  
Strategic Competence ◽  
The Usa ◽  
Valid Solution

AbstractPrior work on teachers’ mathematical knowledge has contributed to our understanding of the important role of teachers’ knowledge in teaching and learning. However, one aspect of teachers’ mathematical knowledge has received little attention: strategic competence for word problems. Adapting from one of the most comprehensive characterizations of mathematics learning (NRC, 2001), we argue that teachers’ mathematical knowledge also includes strategic competence, which consists of devising a valid solution strategy, mathematizing the problem (i.e., choosing particular strategies and presentations to translate the word problem into mathematical expressions), and arriving at a correct answer (executing a solution) for a word problem. By examining the responses of 350 fourth- and fifth-grade teachers in the USA to four multistep fraction word problems, we were able to explore manifestations of teachers’ strategic competence for word problems. Findings indicate that teachers’ strategic competence was closely related to whether they devised a valid strategy. Further, how teachers dealt with known and unknown quantities in their mathematization of word problems was an important indicator of their strategic competence. Teachers with strong strategic competence used algebraic notations or pictorial representations and dealt with unknown quantities more frequently in their solution methods than did teachers with weak strategic competence. The results of this study provide evidence for the critical nature of strategic competence as another dimension needed to understand and describe teachers’ mathematical knowledge.

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).  

scholarly journals Reflecting Upon Different Perspectives on Specialized Advanced Mathematical Knowledge for Teaching

2017 ◽  
pp. 747-748
Author(s):  
Miguel Ribeiro ◽  
Arne Jakobsen ◽  
Alessandro Ribeiro ◽  
Nick H. Wasserman ◽  
José Carrillo ◽  
...  
Keyword(s):  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Knowledge For Teaching
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