‘Crossing’ the equals sign: insights into pre-service teachers’ understanding of linear equations

ABSTRACT

This paper reports on an exploratory study designed to determine and enhance the conceptual understanding of a group of pre-service mathematics teachers at one Irish university utilizing an established framework for understanding mathematics. 23 students on a one year Professional Diploma in Mathematics Education participated in the study, which involved the distribution of a pre- and post-test and engagement in a ten week intervention designed to enhance their subject matter knowledge (SMK) and pedagogical content knowledge (PCK). The findings highlight that although there was an improvement in overall conceptual understanding across the entire cohort at the end of the intervention, within certain mathematical topics there was a statistically insignificant improvement and many deep-rooted issues remain. In this paper we focus on the pre-service teachers’ understanding of elementary algebra, in particular, how to solve a linear equation.

KEYWORDS:

• Linear equations
• pedagogical content knowledge
• preservice mathematics teachers
• understanding mathematics
• Usiskin

Additional information

Notes on contributors

Olivia Fitzmaurice

Olivia Fitzmaurice Olivia Fitzmaurice is a lecturer in mathematics education in the School of Education at the University of Limerick.

Niamh O’Meara

Niamh O’Meara Niamh O’Meara is a lecturer in mathematics education and is based in EPISTEM, the National Centre for STEM Education, at the University of Limerick.

Patrick Johnson

Patrick Johnson Patrick Johnson is a lecturer in mathematics education in the School of Education at the University of Limerick.

Sean Lacey

Sean Lacey Sean Lacey is a lecturer of mathematics and statistics at Cork Institute of Technology. He is also chair of the Department of Mathematics Research Committee.