An Investigation of Prospective Mathematics Teachers’ Knowledge of Basic Algorithms with Whole Numbers: A Case of Turkey

Year 2018, , 513 - 528, 15.07.2018

Reyhan Tekin Sitrava

https://doi.org/10.12973/eu-jer.7.3.513

Abstract

The
aim of this qualitative case study is to investigate prospective mathematics
teachers’ subject matter knowledge of the underlying concepts of standard and
nonstandard algorithms used to solve the problems with whole numbers. Twenty
three prospective mathematics teachers enrolled in the Elementary Mathematics
Education Program of one of the most successful universities in Turkey were the
participants of the study. The data was collected through four tasks containing
basic algorithms. More specifically, the Ones Task assessed participants’
understanding of the underlying place value concepts of standard algorithms.
The Andrew Task and the Doubling Task required participants to conceptualize
and interpret nonstandard strategies. In the Division Task, participants were
expected to provide in-depth explanation for the difference between
multiplication and division and between partitive division and measurement
division. The content analysis method was used to analyze the data. The results
of the study revealed that more than half of the prospective mathematics
teachers had knowledge about the place value of 1 in addition and subtraction,
and also multiplication. However, most of the prospective teachers could not
explain the underlying principle and the meaning of the nonstandard algorithm
in subtraction. Similar to their knowledge on subtraction, prospective
teachers’ knowledge on division was limited.

Keywords

Content knowledge, basic algorithms, whole numbers, prospective mathematics teacher

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