An investigation of adult learning of mathematics

This case study investigated some of the factors facilitating the learning of mathematics by adult students. In particular, the research looked into the use of visualising strategies related to work place experiences, and real-world referents, to facilitate the understanding and use of algebraic variables, and algebraic notation and conventions. The subjects were six male and two female students, chosen from the engineering and science students at the Burnie campus of the North West Coast Regional College of TAFE. They were mature age students, with reasonable work experience, and all had finished school-based study of mathematics in Grade 10. Four of them had a trade background, and four had had no formal training since leaving school. Background factors were investigated with a written questionnaire, followed by an interview. Basic mathematical competence was measured using the ACER Mathematics Profile Series Operations Test, direct visualising ability was measured with Betts Questionnaire on Mental Imagery, and spatial ability was measured with the ACER Mathematics Profile Series Space Test Unit IV. A twenty item algebra test investigated the students' meanings and use of algebraic letters, and their facility with algebraic notation and conventions. Following error analysis, the subjects were interviewed to obtain insights into their cognitive processes, particularly where errors had occurred. Results of analysis of the first three test instruments revealed high levels of mathematical competence for these students, but no correlation between the two tests of visual and spatial abilities. The TAFE students' results on the algebra test were consistently higher than results recorded for similar research with a wide range of students in both England and Australia. Evidence from interviews suggested that the TAFE stadents' greater facility with algebraic concepts could be related to their experience of mathematics with real-world referents, both in the workplace and in exposure to applied mathematics in other subjects. Less able students appeared inhibited in moving beyond a concrete base to more abstract relationships, but the able students successfully transcended their real-world referents and were able to interpret and manipulate variables logically and consistently.