Diagnosing Mathematics Ability of Technology Students: Misconceptions in Algebra

Catering to a long-standing need in the country, the technology stream was introduced to the G.C.E. (A/L) in Sri Lanka in 2015 with one compulsory subject Science for Technology formed by combining six Science subjects including Mathematics. There is no argument that a sound Mathematics background is essential to produce a good technology graduate. Not only do technologists need Mathematics knowledge in technological applications, but also the logical, analytical, and critical thinking developed through the learning of mathematics is essential for them in solving problems. Hence, technology faculties around the country observe that the command in mathematics of their new entrants needs improvement. As a diagnosis and to uplift their mathematics achievement, this study aims to explore one aspect of their mathematics knowledge: common mistakes and misconceptions. This paper reports on the extent to which algebraic mistakes are made by students entering Technology Faculties. The data for this study comes from a three-week online intensive mathematics course that students follow, prior to commencing their degree program. Students ask to respond to ten questions designed to capture errors in algebraic manipulations. The analysis of data shows a lack of understanding of the intricacies of division by zero consequently resulting in cancellation errors, erroneous manipulations of algebraic expressions, and improper use of parenthesis and priority of exponents in the order of operations. Another mistake is extending the distributive property of multiplication over addition erroneously to distributing multiplication over multiplication. More importantly, the data reveals a training these students have received in school that is mathematically less precise and therefore highlights the need to make students unlearn these erroneous habits that is ingrained in them for many years. Further, these results urge instructors to incorporate purposeful remedial actions into their early mathematics courses to better prepare them for their future technology.   Full paper submission of ICIET 2021