scholarly journals Teachers’ Mathematics Knowledge for Teaching Early Algebra: A Systematic Review from the MKT Perspective

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2590
Author(s):  
Nataly Pincheira ◽  
Ángel Alsina
Keyword(s):  
Systematic Review ◽  
Primary Education ◽  
Mathematical Knowledge ◽  
Empirical Studies ◽  
Mathematical Knowledge For Teaching ◽  
Early Algebra ◽  
Specialized Knowledge ◽  
Knowledge For Teaching ◽  
Mathematics Knowledge For Teaching ◽  
Mathematics Knowledge

The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher’s professional knowledge model, and refers to the mathematical knowledge that the teacher employs to carry out the instruction process in the classroom. MKT has become an international benchmark for research into mathematics education and boasts a great scope and impact to date. The objective of this study is to conduct a systematic review of the way in which the MKT of early algebra teachers has been conceptualized and empirically studied in the scientific literature from 2010 to 2021. A systematic search in the Web of Science and Scopus databases led to a review of 17 papers. The results show great advances in the conceptualization of mathematical knowledge for teaching early algebra, focusing mainly on primary education teachers and on specialized knowledge of the content. In turn, there is a predominance of studies that address functional thinking as a content area. We conclude that more empirical studies are needed that address the mathematical knowledge that childhood and primary education teachers have of early algebra.

scholarly journals Base de Conhecimento de Professores de Matemática: do Genérico ao Especializado

2017 ◽  
Vol 18 (2) ◽  
pp. 126
Author(s):  
Geison Mello ◽  
Jeferson Gomes Moriel Junior ◽  
Gladys Denise Wielewski
Keyword(s):  
Theoretical Model ◽  
Mathematics Teacher ◽  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Theoretical Models ◽  
Specialized Knowledge ◽  
Knowledge For Teaching ◽  
Current State ◽  
Theoretical Perspectives ◽  
Mathematics Knowledge

Diversos pesquisadores se apoiaram na premissa de que existe uma base de conhecimentos necessários para se ensinar – knowledge base – para convalidar um corpus de saberes/conhecimentos mobilizados pelo professor no ato educativo, visando sua incorporação em cursos de preparação docente, dando origem a diversos modelos teóricos para descrever o referido conjunto de conhecimento. Entretanto, os modelos mais difundidos na literatura são genéricos e não dizem respeito a determinada disciplina, como a Física, Biologia, Geografia, ou a Matemática. Este artigo tem por objetivo discutir o atual estado do desenvolvimento dos modelos teóricos, que descrevem o conhecimento necessário para um professor ensinar Matemática. Para tanto, realizou-se um estudo analítico-interpretativo de três modelos teóricos, partindo do genérico e culminando no especializado, quais sejam: a tipologia de Lee Shulman, o Mathematical Knowledge for Teaching e o Mathematics Teacher’s Specialized Knwledge. Os resultados indicam que o Mathematics Teacher’s Specialized Knwledge – com seus dois domínios, seus seis subdomínios e as crenças nucleares – é atualmente o modelo teórico que responde com maior profundidade, clareza e consistência interna a pergunta: qual é o conjunto de conhecimentos especializados, que deve ter um professor para ensinar matemática? Este modelo teórico reforça que ser professor de matemática exige a construção de uma gama de conhecimentos que são altamente especializados, o que por sua vez implica em uma formação igualmente especializada, na valorização da profissão e na criação/manutenção de condições adequadas de preparação e trabalho.Palavras-chave: Conhecimento de Professores de Matemática. MKT. MTSK.AbstractSeveral researchers are based on the premise that there is a knowledge basis necessary to teaching to validate a corpus of knowledge mobilized in the Teacher’s practice, aiming at their incorporation into Teacher’s preparation courses, giving rise to different models to describe such set of knowledge. However, the most widespread models in the literature are generic and do not relate to a particular discipline, such as Physics, Biology, Geography or Mathematics. This article aims to discuss the current state of development of theoretical perspectives on the knowledge necessary for a mathematics Teacherr. To do so, an analytical-interpretative study was performed of three theoretical models, starting from the generic and culminating in the specialized, that are: the typology of Lee Shulman, the Mathematical Knowledge for Teaching and the Mathematics Teacher’s Specialized Knwledge. The results indicate that Mathematics Teacher’s Specialized Knwledge - its two domains, its six subdomains and nuclear beliefs - is the theoretical model that responds in greater depth, clarity and internal consistency the question: what is the set of specialized knowledge that is necessary to develop a mathematics Teacher? This theoretical model reinforces that being a mathematics Teacher requires the construction of a range of knowledge that is highly specialized, which in turn implies an equally specialized training, in the valuation of the profession and in the creation / maintenance of adequate conditions of preparation and work.Keywords: Mathematics Knowledge Teacher. MKT. MTSK.

Strengthen your mathematical muscles

2010 ◽  
Vol 17 (3) ◽  
pp. 178-183
Author(s):  
Kay A. Wohlhuter ◽  
M. Lynn Breyfogle ◽  
Amy Roth McDuffie
Keyword(s):  
Mathematical Knowledge ◽  
Teaching And Learning ◽  
Learning Needs ◽  
Elementary School Mathematics ◽  
Deep Knowledge ◽  
Knowledge For Teaching ◽  
Mathematics Knowledge For Teaching ◽  
Mathematics Knowledge ◽  
Unique Approach ◽  
Math Concepts

What mathematics must teachers understand in order to teach elementary school mathematics? Historically, the answer to that question was that they needed to know only the mathematics concepts and procedures they taught. Research on the teaching and learning of mathematics challenges that myth and indicates that the role and substance of mathematics knowledge needed for teaching has expanded. In addition to a profound understanding of fundamental mathematics content (Ma 1999), teachers need deep knowledge about how students learn particular math concepts and processes and, correspondingly, which teaching approaches and strategies are most effective in meeting students' learning needs. Ball, Hill, and Bass (2005) refer to this kind of knowledge as mathematics knowledge for teaching. For example, to determine whether a child's unique approach for adding fractions can be generalized or how an area model might be used to develop the partial-product algorithm for multiplying two-digit numbers, teachers need a form of mathematical knowledge different from other professionals (e.g., engineers). Aligned with this research, the Teaching Principle identifies the necessity for teachers to develop deep knowledge and understanding of mathematics to meet the needs of their students today and in the future (NCTM 2000).

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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