scholarly journals Unpacking Mathematics Pedagogical Content Knowledge for Elementary Number Theory: The Case of Arithmetic Word Problems

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1750
Author(s):  
Wing Yee Lo
Keyword(s):  
Number Theory ◽  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Word Problems ◽  
Sixth Graders ◽  
Elementary Number Theory ◽  
Pedagogical Content ◽  
Primary Mathematics ◽  
Elementary Number ◽  
Mathematics Pedagogical Content Knowledge

“Number” is an important learning dimension in primary mathematics education. It covers a large proportion of mathematical topics in the primary mathematics curriculum, and teachers use most of their class time to teach fundamental number concepts and basic arithmetic operations. This paper focuses on the nature of mathematics pedagogical content knowledge (MPCK) concerning arithmetic word problems. The aim of this qualitative research was to investigate how well the future primary school teachers in Hong Kong had been prepared to teach mathematical application problems for third and sixth graders. Nineteen pre-service teachers who majored in both mathematics and primary education were interviewed using two sets of scenario-based questions. The results revealed that innovative approaches were suggested for teaching third graders while the strategies suggested for teaching sixth graders were mostly based on a profound understanding of mathematical content knowledge. Many participants demonstrated sound knowledge about the sixth grader’s mathematical misconception, but most of them were unable to precisely indicate the third grader’s error in presenting a complete solution for a typical mathematics word problem. A deep understanding of elementary number theory seems to be a precondition for developing pre-service teachers’ MPCK in teaching arithmetic word problems.

scholarly journals Teachers’ pedagogical content knowledge in teaching word problem solving strategies

ZDM ◽  
2019 ◽  
Vol 52 (1) ◽  
pp. 165-178 ◽  
Author(s):  
Csaba Csíkos ◽  
Judit Szitányi
Keyword(s):  
Problem Solving ◽  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Word Problem ◽  
Word Problems ◽  
Teaching Practice ◽  
Word Problem Solving ◽  
Pedagogical Content ◽  
Explicit Teaching ◽  
Problem Solving Strategies

AbstractThis research addressed Hungarian pre-service and in-service (both elementary and lower secondary) teachers’ pedagogical content knowledge concerning the teaching of word problem solving strategies. By means of a standardized interview protocol, participants (N = 30) were asked about their judgement on the difficulty of teaching word problems, the factors they find difficult, and their current teaching practice. Furthermore, based on a comparative analysis of Eastern European textbooks, we tested how teachers’ current beliefs and views relate to the word problem solving algorithm described in elementary textbooks. The results suggest that in the teachers’ opinion, explicit teaching of a step-by-step algorithm is feasible and desirable as early as in the 1st school grade. According to our results, two approaches (namely, paradigmatic- and narrative-oriented) concerning how to teach the process of word problems solving, originally revealed by Chapman, were found. Furthermore, teachers in general agreed with the approach taken in the textbooks on the subject of what kinds of word problems should be used, and that explicit teaching of word problem solving strategies should be introduced by using simple, routine word problems as examples.

scholarly journals Developing mathematics teachers’ pedagogical content knowledge in lesson study

2016 ◽  
Vol 5 (3) ◽  
pp. 212-226 ◽  
Author(s):  
Aoibhinn Ni Shuilleabhain
Keyword(s):  
Pedagogical Content Knowledge ◽  
Teacher Learning ◽  
Empirical Evidence ◽  
Content Knowledge ◽  
Mathematics Teachers ◽  
Lesson Study ◽  
Content Type ◽  
Pedagogical Content ◽  
Primary Mathematics ◽  
Knowledge Of Content

Purpose – The purpose of this paper is to investigate the development of mathematics teachers’ pedagogical content knowledge (PCK) over successive cycles of lesson study. Utilising the framework of mathematical knowledge for teaching (MKT) (Ball et al., 2008), this research classifies features of PCK as utilised by post-primary mathematics teachers in their planning and reflection conversations in lesson study. The development of these features of PCK is then traced over successive cycles. Design/methodology/approach – In total, 12 teachers in two Irish post-primary schools participated in this research. Over the course of one academic year, these two groups of teachers completed a number of cycles of lesson study and qualitative data were generated through audio recordings of all lesson study meetings and through individual interviews with participants. Findings – Analysis of teacher dialogue reveals distinct features of knowledge of content and students (KCS) and knowledge of content and teaching (KCT) incorporated by these teachers in their planning and reflection conversations, providing empirical evidence of MKT in lesson study. The occurrence of these features of KCS and KCT in lesson study conversations increased over successive cycles, demonstrating teacher learning. Originality/value – This research contributes to the literature in expanding the theoretical underpinnings of teacher learning in lesson study. It also provides further empirical evidence of MKT (Ball et al., 2008) in teacher practice, specifically related to post-primary mathematics teachers.

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