Analysis of Pre-service Mathematics Teachers' Representational Ability Regarding the Prime Numbers Concept

Abstract

A deep understanding of prime numbers remains a significant challenge, particularly for pre-service mathematics teachers responsible for conveying this essential knowledge to their students. Prime numbers have an essential role in mathematics, including in factorization, proof, and cryptography. Therefore, this study aims to describe and analyze the representational abilities of prospective mathematics teacher students at Alkhairaat University, regarding the prime numbers in Number Theory. This study uses a descriptive exploratory method with a mixed-methods approach based on a sequential explanatory design. Data collection was carried out through diagnostic tests, semi-structured interviews, and documentation, which were then analyzed using descriptive statistics for quantitative data and the Miles & Huberman model for qualitative data. Triangulation of methods and time was used to ensure the validity of the data. The findings showed that out of 17 students, only 29.41% were able to provide accurate verbal representations related to the prime and composite numbers, and only 5.88% were able to link the two meaningfully. In addition, while students were able to mention definitions, most of them had difficulties applying the prime numbers in the abstract problem context, including examples in algebraic notation. This study concludes that there is still a significant gap in the representation ability of prime number concepts of pre-service mathematics teachers. The implications emphasize the need for integrating multidimensional representation learning strategies into the mathematics education curriculum so that prospective teachers are better prepared to teach prime numbers in a comprehensive and meaningful way.   

Keywords: representation, prime numbers, number theory, pre-service mathematics teachers.