Difficulties in Learning and Teaching Numbers: A Literature Review on the Obstacles and Misconceptions of Learners and Instructors


Cognitive obstacles
Misconceptions of arithmetic
Number reasoning
Whole numbers
Rational numbers




This paper attempts to summarize a number of research studies on numbers. The purpose of this study was to investigate and identify the obstacles encountered by students when they are dealing with number reasoning (whole numbers, integers, and rational numbers) and the difficulties faced by pre-service teachers in teaching arithmetic, including their misconceptions and weaknesses when they teach arithmetic and operations. There are two main sections in this paper: students’ cognitive obstacles for number reasoning, and pre-service teachers’ misconceptions of arithmetic. With the summarized misconceptions and obstacles of both, students and teachers, this paper provides efficient and effective thinking strategies that may help both, learners and instructors overcome obstacles, revise misconceptions, and strengthen their understanding, in order to develop proficiency in number reasoning and arithmetic operations.


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