Development of Arithmetical Thinking: Evaluation of Subject Matter Knowledge of Pre-Service Teachers in Order to Design the Appropriate Course

  • Raisa GubermanEmail author


One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of “number” and the development thereof, calculation methods and strategies. properties of operations on different sets of numbers, as well as the properties of the numbers themselves. Hence, the question arises: how to educate PMTs in order to supplement their mathematical knowledge with the required components? The present study explored the development of arithmetic thinking among pre-service teachers intending to teach mathematics at elementary school. This was done by matching the van Hiele theory of the development of geometric thinking to arithmetic. Analysis of findings obtained both in the present study and in many studies of geometry teaching indicates that this approach to considering the learners’ level of thinking development might lead to meaningful learning in arithmetic course for PMTs.


Prospective mathematics teachers (PMTs) Mathematical knowledge for teaching Development of mathematical thinking Arithmetic 



This paper presents part of my doctoral thesis written under the supervision of Prof. Shlomo Vinner. I express my deep personal and professional appreciation to Prof. Vinner and am grateful for the honor of having been his research student. I also wish to thank Dr. Marita Barabash for her constructive comments during my work on this paper.

Supplementary material

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Copyright information

© Ministry of Science and Technology, Taiwan 2014

Authors and Affiliations

  1. 1.Achva Academic CollegePOB ShikmimIsrael

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