Primary school teachers' subject matter knowledge and pedagogical content knowledge of number bases: a case study of Lusaka district.
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Date
2023
Authors
Mulenga, George
Journal Title
Journal ISSN
Volume Title
Publisher
The University of Zambia
Abstract
The study was inspired by the necessity to advance professional learning for primary school teachers that might support them to proficiently teach the mathematics topic of number bases. This was after a base line study conducted at National In-Service Teachers College (NISTCOL) in 2014 by the College Lectures in the Department of Mathematics amongst primary school teachers who came from all provinces of the country revealed that Grade 7 primary school teachers encounter challenges when teaching number bases. This qualitative case study evaluated the mathematics Subject Matter Knowledge (SMK) and Pedagogical Content Knowledge (PCK) of Grade seven primary school teachers with a focus on Number Bases, a topic which consolidates the concept of place value, the basis for all arithmetic algorithms (Wilson, 2006). Dimensions of the Knowledge Quartet: foundation, transformation, connection and contingency (Rowland, Turner, Thwaites, & Huckstep, 2009) and the strands of mathematical proficiency (Kilpartick, 2001) were applied to code, interpret and discuss the findings. Thematic analysis of lesson observations, questionnaire, concept maps and interviews was done by applying the pre-specified categorisation scheme of the Subject Audit Instrument (knowledge Quartet). Initially thirty participants took part in the questionnaire. Out of these nineteen took part in the concept maps. Then based on the performance in the questionnaire and concept maps two high performers, two moderate performers and two low achievers were selected to take part in lesson observations and post-lesson observation interviews. The study was guided by four research questions:
1. What foundation knowledge of Number Bases do primary school teachers have?
2. How do primary school teachers transform the content knowledge they have into forms that are pedagogically convenient to their pupils when teaching Number Bases?
3. How do the primary school teachers connect instructions when teaching Number Bases?
4. What are the primary school teachers’ contingency actions when teaching Number Bases?
With regard to the nature of primary school teachers’ foundation knowledge the findings indicated that most primary school teachers were uncertain as to the status or importance of topic of number bases and when making instructional decisions they mainly relied on imitation of one another or trial and error, rather than relying on the theoretical foundation required to guide instructional decisions. On the nature of primary school teachers’ transformation knowledge the findings indicated that in most cases examples were mathematically correct, selected intentionally, and matched the purpose of the lesson and that participants exhibited knowledge of various forms of mathematical representations such as tabular, symbolic and tally marks. With regard to the nature of primary school teacher’s connection knowledge the findings revealed that during lesson observation participants mainly used a single method; they rarely used several methods when solving problems on number bases. Moreover, they could not change tack when teaching number bases, amidst pupils facing challenges in comprehending the number bases concepts. On the nature of primary school teachers’ contingency knowledge of number bases the findings indicated that participants responded to student ideas mainly in two ways: ignore or acknowledge but sideline. In addition the findings revealed that most participants could not reflect in action of either example or representation being used during lesson enactment even when faced with challenges. In line with the research findings, a reference manual that could enhance primary school teachers’ SMK and PCK in the context of number bases has been
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proposed. Practically, the study has made contributions to areas in which primary school teachers need assistance such as the aspect of relational approaches to teaching mathematics.
Recommendations for primary school teachers, Institutions training primary school teachers and for further research have been made. For instance, in order to enhance professionalism in the teaching of number bases primary school teachers should be sensitized on how to notice and interpret key features of classroom interaction as well as ensuring that they acquire skills of stopping to reflect-in-action and change tack (example or representation being used) amidst challenges.
Key words: Knowledge Quartet, Foundation, Transformation, Connection, Contingency, Number bases, Subject Matter Knowledge (SMK) and Pedagogical Content Knowledge (PCK)
Description
Doctor of Philosophy in Mathematics Education
Keywords
Mathematics--Study and teaching. , Mathematics teaching and learning. , Pedagogical content knowledge. , Subject matter knowledge.