scholarly journals The development of pedagogical content knowledge of a mathematics teaching intern: the role of collaboration, curriculum, and classroom context

2005 ◽  
Author(s):  
◽  
Bridgette Bond Almond Stevens
Keyword(s):  
Pedagogical Content Knowledge ◽  
Instructional Strategies ◽  
Content Knowledge ◽  
Mathematics Teaching ◽  
Mathematics Classroom ◽  
Essential Elements ◽  
Classroom Context ◽  
Structured Interviews ◽  
Pedagogical Content

In this study I examined the role of collaboration, curriculum, and the classroom context in the development of pedagogical content knowledge of a mathematics teaching intern. Additionally, I investigated the nature of the collaborative process between the teaching intern and his mentor teacher as they collaborated on action (during structured planning time) and in action (while students were present). The teaching internship resided in a seventh-grade mathematics classroom during the teaching of a probability unit from a standards-based curriculum, Connected Mathematics Project. Using existing research, a conceptual framework was developed and multiple data sources (audio taped collaborations, observations of the intern's teaching practices, semi-structured interviews, and a mathematics pedagogy assessment) were analyzed in order to understand the teaching intern's development of knowledge of instructional strategies, knowledge of student understandings, curricular knowledge, and conceptions of purpose for teaching probability.Results identified numerous dilemmas related to planning and implementing instruction. Although the teaching intern developed pedagogical content knowledge, he often experienced difficulty accessing it while teaching. Through collaboration, curriculum, and the classroom context, the teaching intern learned to incorporate his pedagogical content knowledge in instruction. Analysis revealed that as he gained new knowledge he was able to shift his focus from content to the use of instructional strategies for teaching and learning. The curriculum was the primary focus of collaboration and initiated the intern's examination of the learning-to-teach process. Collaboration on action and collaboration in action proved to be essential elements in the development of pedagogical content knowledge.

scholarly journals Conceptualizing content-related PD facilitator expertise

2021 ◽  
Author(s):  
Susanne Prediger ◽  
Bettina Roesken-Winter ◽  
Rebekka Stahnke ◽  
Birte Pöhler
Keyword(s):  
Secondary School ◽  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Situated Learning ◽  
Mathematics Teaching ◽  
Learning Opportunities ◽  
Preparation Programs ◽  
Pedagogical Content ◽  
Situational Demands ◽  
Classroom Level

AbstractStudies of facilitators of professional development (PD) for mathematics teachers have been increasing in order to improve their preparation for conducting PD. However, specifications of what facilitators should learn often lack a conceptualization that captures facilitators’ expertise for different PD content. In this article, we provide a framework for facilitator expertise that is in line with current conceptualizations but makes explicit the content-related aspects of such expertise. The framework for content-related facilitator expertise combines cognitive and situated perspectives and allows unpacking different components at the PD level and the classroom level. Using two illustrative cases of different PD content (probability education in primary school and language-responsive mathematics teaching in secondary school), we exemplify how the framework can help to analyze facilitators’ practices in content-related ways in a descriptive mode. This analysis reveals valuable insights that support designers of facilitator preparation programs to specify what facilitators should learn in a prescriptive mode. We particularly emphasize the importance of working on content-related aspects, unpacking the PD content goals into the content knowledge and pedagogical content knowledge elements on the classroom level and developing facilitators’ pedagogical content knowledge on the PD level (PCK-PD), which includes curricular knowledge, as well as knowledge about teachers’ typical thinking about a specific PD content. Situated learning opportunities in facilitator preparation programs can support facilitators to activate these knowledge elements for managing typical situational demands in PD.

scholarly journals EXAMINING PROSPECTIVE TEACHERS’ BELIEF AND PEDAGOGICAL CONTENT KNOWLEDGE TOWARDS TEACHING PRACTICE IN MATHEMATICS CLASS: A CASE STUDY

2019 ◽  
Vol 10 (2) ◽  
pp. 185-202 ◽  
Author(s):  
Muhtarom Muhtarom ◽  
Dwi Juniati ◽  
Tatag Yuli Eko Siswono
Keyword(s):  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Prospective Teachers ◽  
Teaching Practice ◽  
Mathematics Classroom ◽  
Pedagogical Content ◽  
Good Communication ◽  
Good Communication Skill ◽  
Two Factors ◽  
The Relationship

Beliefs and pedagogical content knowledge (PCK) are two factors influencing teaching practice in the classroom. This research aims to describe the beliefs and PCK of the prospective mathematics teachers and the relationship between the two factors on the teaching practices in the mathematics classroom. Participant in this research includes a prospective teacher who has taken a micro teaching subject and has good communication skill. Data were collected through interview and video analysis on the teaching practice in the classroom. The data obtained were coded, simplified, presented, and triangulated for the credibility and concluded. The result of the research shows that the prospective teachers who hold a constructivist belief view mathematics as a dynamic knowledge which evolves and is regarded as the space of creation for humans. Their beliefs on the nature of mathematics support the belief in the teaching-learning process in mathematics classrooms. Furthermore, a good understanding of the prospective teachers have on the components of the PCK has been sufficient, which can be identified in every step of practical activities in the classroom. More elaboration on the relationship between the belief and PCK is presented in this research.

Designing Meaningful Instruction

2017 ◽  
Author(s):  
Birch P. Browning
Keyword(s):  
Instructional Design ◽  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Subject Matter ◽  
Self Assessment ◽  
Relevant Feedback ◽  
Pedagogical Content ◽  
Learning Plan ◽  
Instructional Context

The chapter outlines and discusses many steps in instructional design as well as assessing its effectiveness. The role of knowledge of subject matter, pedagogy, how students learn, and instructional context is stressed. The six challenging questions relating to pedagogical content knowledge are presented and discussed. Designing instruction is a temporally backward process, in that the first step is to determine the desired outcomes. The reader is taken through the three major stages of planning instruction: defining outcomes, planning assessment, and designing the learning plan. The importance of timely and relevant feedback is stressed. Teacher self-assessment is key as well. The author states that the height of professionalism is the consistent willingness to evolve for the students’ benefit.The chapter concludes with a detailed sample lesson project.

scholarly journals Interconnections between Content Knowledge and Pedagogical Content Knowledge of a University Lecturer in Linear Algebra

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2542
Author(s):  
Diana Vasco-Mora ◽  
Nuria Climent-Rodríguez ◽  
Dinazar Escudero-Ávila
Keyword(s):  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Linear Algebra ◽  
Classroom Practice ◽  
Structured Interviews ◽  
Classroom Performance ◽  
Pedagogical Content ◽  
University Teachers ◽  
Video Recordings ◽  
Learning Capabilities

The aim of this study is to deepen our understanding of the practice of a lecturer in linear algebra by exploring the connections he makes between his content knowledge and his pedagogical content knowledge while working on the topic of matrices. Data were collected through video recordings of his classes and semi-structured interviews, and were analysed with the Mathematics Teacher’s Specialised Knowledge model. Instances of classroom performance, supported by the teacher’s own affirmations, provided evidence relating to the categories comprising the model, and enabled us to establish connections between the lecturer’s knowledge, his understanding of his students’ learning capabilities, and his knowledge of teaching mathematics, which together account for his classroom practice: the use of varied examples to introduce new content, the highlighting of the most salient aspects of the topic, and alerts about potential errors and difficulties. The contribution that these results could make to the training of university teachers, which would be done with the knowledge of the areas of difficulty shown by the teacher in mind, could be used to deepen other elements of their pedagogical content knowledge. The interconnections between areas of knowledge identified by the study also serve to validate the usefulness of a theoretical model for studying teachers’ knowledge.

scholarly journals Estratégias formativas: um elemento potencializador para ressignificação da prática docente Formation strategies: a potentiation element for resignification the teaching practice

2017 ◽  
Vol 19 (1) ◽  
Author(s):  
Vera Lucia Merlini ◽  
Aparecido Dos Santos ◽  
Sandra Maria Pinto Magina
Keyword(s):  
Public School ◽  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Teaching Practice ◽  
Mathematics Classroom ◽  
Qualitative Change ◽  
Sao Paulo ◽  
Early Years ◽  
São Paulo ◽  
Pedagogical Content

Identificar ressignificação e transformação da prática docente de professoras participantes de uma formação. Apoiado nas ideias teóricas de: Nacarato e Santos referente aos processos formativos com viés colaborativo; Schön, Zeichner e Pimenta no que tange à reflexão sobre a prática docente; Vergnaud no que concerne às Estruturas Multiplicativas e Magina, Santos e Merlini às categorias de base do Campo Conceitual Multiplicativo. Os dados foram coletados no âmbito de uma formação continuada com um grupo de 14 professoras dos anos iniciais, numa escola pública da cidade de São Paulo. As análises permitem sustentar uma mudança qualitativa nas práticas dessas professoras, nas dimensões: gestão da sala de aula de Matemática; conhecimento didático e pedagógico do conteúdo e ressignificação do currículo.Identify reinterpretation and transformation of teaching practice of participants of training teachers. Data were collected as part of a continuing training with a group of 14 teachers of early years, a public school in São Paulo. The analyzes allow sustain a qualitative change in the practices of these teachers, dimensions: management of mathematics classroom; didactic and pedagogical content knowledge and reframing the curriculum.

scholarly journals The Development of Pedagogical Content Knowledge about Teaching Redox Reactions in German Chemistry Teacher Education

2020 ◽  
Vol 10 (7) ◽  
pp. 170 ◽  
Author(s):  
Luciane F. Goes ◽  
Carmen Fernandez ◽  
Ingo Eilks
Keyword(s):  
Teacher Education ◽  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Redox Reactions ◽  
Teaching Experience ◽  
Experienced Teachers ◽  
Structured Interviews ◽  
Online Questionnaire ◽  
Master's Students ◽  
Pedagogical Content

This paper presents a qualitative cross-level study with a focus on prospective and in-service teachers’ pedagogical content knowledge (PCK) of redox reactions in Germany. The objective was to investigate and analyze the differences in PCK between those in pre-service teacher education and those working as teachers. The sample included four different groups: bachelor’s students, master’s students, graduate teacher trainees, and in-service teachers. Data were collected by an online questionnaire and semi-structured interviews. The online questionnaire was developed based on misconceptions and learning difficulties regarding redox reactions. Sixty-two participants answered the questionnaire and the interviews were carried out with twelve participants. The results revealed that teaching experience makes a difference. Pre-service teachers described quite traditional and content-focused approaches while experienced teachers emphasized the application of the content. Experienced teachers showed a more developed repertoire of instructional strategies. Participants differed also in their knowledge about learners and the curriculum. Concerning assessment, practices were at a quite general pedagogical knowledge level and not domain-specific. Although teacher education in Germany includes several chances for internships, it is suggested that central aspects of teachers’ PCK start to develop and settle only when they begin to work as teachers. To avoid perpetuating traditional practices, investment in continuous professional development is needed.

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