In this study wefocused on one of the recurring issues in the learning of mathematics, which is students’ errors and misconceptions in learning algebra. We investigated Year 7 students on how they manipulate and interpret letters in solving routine algebraic problems to understand their thinking process. This is a case study of qualitative nature, focusing on one pencil and paper test, observation, and in-depth interviews of students in one particular school in Brunei Darussalam. The themes that emerged from interviews based on the test showed students’ interpretation of letters categorized as “combining” - which involved the combining of numbers during addition, “equating a letter as 1” – where a letter in any algebraic expression is considered to be equal to 1, “misconception of equal sign” – where students see equal sign as taking the value or letter which is closest to the equal sign, “inconsistency with own rule” – where students made up their own misguided rules but utilize other rules for similar situation and finally, “seeing letters as an abbreviations for objects” – where students consider the letters as representing objects.


Letters and Symbols, Algebra Misconception, Students’ Errors in Algebra, Case Study, Qualitative Research

Author Bio(s)

Madihah Khalid is currently employed at the Department of Curriculum and Instruction, International Islamic University Malaysia. She obtained her PhD in Mathematics Education from Curtin University of Technology, Western Australia in 2004. Her areas of interest include Curriculum and Instruction, Education for special needs, Mathematics Education, Teacher Education, Assessment and Evaluation, Lesson Study and Statistics for Social Research. She regularly publishes papers in refereed journals, conference proceedings as well as book chapters. Google Scholar: https://scholar.google.com/citations?user=iq4QqyMAAAAJ&hl=en; Orcid: https://orcid.org/0000-0002-4538-1922; ResearcherGate: https://www.researchgate.net/profile/Madihah_Khalid; Please direct correspondence to madihahkhalid@iium.edu.my.

Faeizah Haji Yakop has been teaching Mathematics since 2000 at Sayyidina Husain Secondary School, Brunei Darussalam after graduating with a B.Sc. in Education (Majoring in Mathematics) from University Brunei Darussalam. She then pursued her Master in Mathematics Education in 2011 at the same university. She was then posted to Sengkurong Sixth Form Center as a Mathematics instructor and has been there until now. Her research interest is in the area of students' misconceptions in mathematics especially when they enter the lower secondary level. She can be reached via her email, pie_74@hotmail.com.

Hasniza Ibrahim is currently a PhD Student (Education) in International Islamic University Malaysia. She acquired her Master’s degree in Educational Psychology from the same university. She has plenty of experience in conducting research both in qualitative and quantitative, and published articles in the refereed journals covering educational psychology and mathematics education. She is a registered engineer in the Malaysian Board of Engineers since 2008 and worked in various fields since 2006 after graduating with a B.Sc. in Engineering (Chemical). Google Scholar: https://scholar.google.com/citations?user=YIlOU_0AAAAJ&hl=en; Orcid: https://orcid.org/0000-0003-1044-9445; ResearcherGate: https://www.researchgate.net/profile/Hasniza_Ibrahim; Please direct correspondence to hasniezaibrahim@gmail.com.


This research was supported by [FRGS/1/2016/SSI09/UIAM/02/10]. We would like to thank the Ministry of Education for providing us with the grant and make this research possible.

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