Pedagogical Content Knowledge Within “Mathematical Knowledge for Teaching”

2020 ◽  
pp. 655-658
Author(s):  
Hamsa Venkat ◽  
Jill Adler
Keyword(s):  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Pedagogical Content ◽  
Knowledge For Teaching

An Empirical Study of the Dimensionality of the Mathematical Knowledge for Teaching Construct

2018 ◽  
Vol 70 (5) ◽  
pp. 485-497 ◽  
Author(s):  
Yasemin Copur-Gencturk ◽  
Tammy Tolar ◽  
Erik Jacobson ◽  
Weihua Fan
Keyword(s):  
Elementary School Teachers ◽  
Content Knowledge ◽  
Mathematical Knowledge ◽  
Secondary Analysis ◽  
Mathematical Knowledge For Teaching ◽  
Upper Elementary ◽  
Specialized Content Knowledge ◽  
Pedagogical Content ◽  
Knowledge For Teaching ◽  
Content Knowledge For Teaching

This study explores the dimensionality of mathematical knowledge needed by elementary school teachers. Specifically, we focus on the construct of Mathematical Knowledge for Teaching to investigate whether common mathematical content knowledge (the generic mathematical knowledge that is held by an educated adult), specialized content knowledge (the content knowledge that is unique to teaching), and pedagogical content knowledge (knowledge of the content, students, and teaching) can be distinguished empirically. Findings from a secondary analysis of data collected from upper elementary teachers in the Measures of Effective Teaching project ( N = 397) suggest the most parsimonious explanation of Mathematical Knowledge for Teaching construct is that it is unidimensional. We argue, based on the findings and limitations we identified, that researchers should reconsider both the structure of the components that make up the content knowledge for teaching and the effects of item design on the dimensionality of the construct.

scholarly journals Predictive Validity of Entry Level Mathematical on Mathematical Knowledge of Pre-service Teachers for Teaching Basic School mathematics in Ghana

2020 ◽  
Vol 7 (2) ◽  
pp. 17-26
Author(s):  
Millicent Narh Kert
Keyword(s):  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Mathematical Knowledge ◽  
Scale Up ◽  
Mathematical Knowledge For Teaching ◽  
Colleges Of Education ◽  
Pedagogical Content ◽  
Mathematics Content Knowledge ◽  
Entry Level ◽  
Mathematics Pedagogical Content Knowledge

Introduction: Knowledge about teaching mathematics remains a contentious issue in the preparation of pre-service teachers in Ghana. This study explored relationships among entry-level mathematical knowledge (ELMK), mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) scores of pre-service teachers in colleges of education (CoEs) in Ghana. Methods: The cross-sectional survey design was adopted for this study. A total of 998 pre-service teachers from ten (10) public colleges of education were sampled via multi-stage sampling technique. Structured questionnaire and unstructured observation schedule were used for the survey. College mathematics test results were used as secondary data. The data were analysed using descriptive statistics (frequency count, percentage) and inferential statistics (Pearson’s correlation, paired-samples t-test and regression analysis) with the aid of Statistical Package for Social Sciences software version 22. Results: The majority of pre-service teachers in Ghanaian colleges of education had average but relatively weak grades in ELMCK. ELMCK did not significantly predict pre-service teachers’ MCK statistically (p ≥ 0.05) although a statistically significant positive correlation existed between the variables. Although a negative correlation existed between ELMCK and PMCK, ELMCK significantly predicted pre-service teachers’ PMCK statistically (p ≤ 0.05) but the effect size was statistically negligible. Conclusions: This study concluded that, CoEs in Ghana admit pre-service teachers with average but weak grades in ELMK. Therefore, Ghanaian CoEs should structure and introduce PMCK alongside MCK for pre-service teachers. Mathematics tutors in CoEs should organize remedial lessons for pre-service teachers to scale-up their MCK and PMCK that adequately equip them with MKT. Keywords: Entry-level mathematical knowledge (ELMK), mathematics content knowledge (MCK), mathematics pedagogical content knowledge (MPCK), mathematical knowledge for teaching (MKT), pre-service teachers.

scholarly journals Developing a model of pedagogical content knowledge for secondary and post-secondary mathematics instruction

2014 ◽  
Vol 2 ◽  
Author(s):  
Shandy Hauk ◽  
Allison Toney ◽  
Billy Jackson ◽  
Reshmi Nair ◽  
Jenq-Jong Tsay
Keyword(s):  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Mathematical Reasoning ◽  
Theory Development ◽  
Mathematical Knowledge For Teaching ◽  
Extended Model ◽  
Pedagogical Content ◽  
Post Secondary ◽  
Knowledge For Teaching ◽  
Mathematics Pedagogical Content Knowledge

The accepted framing of mathematics pedagogical content knowledge (PCK) as part of mathematical knowledge for teaching has centered on the question: What mathematical reasoning, insight, understanding, and skills are required for a person to teach elementary mathematics? Many have worked to address this question in K-8 teaching. Yet, there remains a call for examples and theory in the context of teachers with greater mathematical preparation and older students with varied and complex experiences in learning mathematics. In this theory development report we offer background and examples for an extended model of PCK – as the interplay among conceptually-rich mathematical understandings, experience in and of teaching, and multiple culturally-mediated classroom interactions.

scholarly journals Matematikklæreres refleksjoner om egne undervisningsutfordringer

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Marianne Maugesten ◽  
Reidar Mosvold ◽  
Janne Fauskanger
Keyword(s):  
Content Knowledge ◽  
Mathematics Teaching ◽  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Language Teachers ◽  
Mathematical Tasks ◽  
Second Grade ◽  
Specialized Content Knowledge ◽  
Pedagogical Content ◽  
Knowledge For Teaching

Matematikkundervisning stiller krav til matematikkfaglig og matematikkdidaktisk kunnskap. Mens mange forskere har studert kunnskapen lærere har, eller den kunn­skapen de bruker i undervisningen, retter denne studien fokuset mot hvilke matematiske undervisningsutfordringer som er i fokus når lærere reflekterer over egen matematikk­undervisning, og hvilke deler av den profesjonelle kunnskapsbasen de trekker inn i refleksjonene. Andretrinnslærerne i denne studien reflekterer omkring mange sentrale matematiske undervisningsutfordringer, men det matematiske fokuset i refleksjonene er ofte uklart – selv når de reflekterer over undervisningsutfordringer som stiller krav til spesialisert matematisk kunnskap. Resultatene fra studien indikerer også at lærerne ofte bruker et upresist og hverdagslig språk når de reflekterer over egen matematikk­undervisning. Nøkkelord: matematiske undervisningsutfordringer, undervisningskunnskap, tallforståelse   Mathematics teachers’ reflections about experienced tasks of teaching   Abstract Teaching requires a special content knowledge as well as pedagogical content knowledge. Whereas many studies have investigated the knowledge teachers have or use in teaching, this study investigates what mathematical tasks of teaching that are in focus when teachers reflect on their own mathematics teaching, and what aspects of the professional knowledge base they draw upon. The second grade teachers in this study reflect on several core tasks of teaching mathematics, but their reflections tend to have an unclear mathematical focus — even when they reflect upon tasks of teaching that require specialized content knowledge. The results from this study also indicate that the language teachers use to reflect on their own mathematics teaching tends to lack precision and rigor. Keywords: mathematical tasks of teaching, mathematical knowledge for teaching, number sense

Teaching and Learning in the Digital Age

2019 ◽  
pp. 1-23
Keyword(s):  
Preservice Teachers ◽  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Teaching And Learning ◽  
Teacher Educators ◽  
Technological Pedagogical Content Knowledge ◽  
Theoretical Description ◽  
Pedagogical Content ◽  
Knowledge For Teaching ◽  
K 12

Technological pedagogical content knowledge (TPACK) is a dynamic theoretical description of teachers' knowledge for designing, implementing, and evaluating curriculum and instruction with digital technologies. TPACK portrays the complex interaction among content knowledge, pedagogical knowledge, and technological knowledge for guiding all teachers (K-12 and higher education faculty) in the strategic thinking of when, where, and how to direct students' learning with technologies. Teacher educators' and educational researchers' acceptance of the TPACK construct mirrors the acceptance of its parent construct of pedagogical content knowledge (PCK). The importance of teachers' continued practice in integrating technologies is essential for extending and enhancing their TPACK. Connections with the knowledge-of-practice construct suggest calling TPACK TPACK-of-practice to more accurately describe the process of the knowledge development efforts for guiding inservice and preservice teachers in gaining, developing, and transforming their knowledge for teaching as new and more powerful technologies emerge for integration in education. Ultimately, the very nature of the TPACK construct describes a transformation of teachers' knowledge for teaching in the 21st century – a century reframed by robust and advanced technologies that have been integrated into the fabric of a more complex social, cultural, and educational environment.

Don't Reinvent the Wheel: Capitalizing on What Others Already Know about Teaching Topics in Evolution

2019 ◽  
Vol 81 (2) ◽  
pp. 133-136
Author(s):  
Michelle A. Ziadie ◽  
Tessa C. Andrews
Keyword(s):  
High School ◽  
High School Students ◽  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Career Stages ◽  
Collective Knowledge ◽  
School Students ◽  
Teaching Evolution ◽  
Pedagogical Content ◽  
Knowledge For Teaching

What knowledge do you need to be an effective instructor? One key type of knowledge is pedagogical content knowledge (PCK), which includes awareness of how students are likely to think about a topic and where they will struggle as they learn that topic. We propose PCK as a valuable framework for reflecting on your own knowledge for teaching topics in evolution. We have created a searchable file that uses PCK as a framework to organize over 400 peer-reviewed papers from 40+ journals to give you better access to relevant resources for teaching evolution to undergraduates and advanced high school students. None of us have time to read 400 papers to inform our teaching, so we provide tips to maximize your use of this collective knowledge in the time you have available. We have written these to be useful to instructors across career stages.

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