Identifying troublesome knowledge to strengthen mathematics support

Abstract

Identifying troublesome knowledge (Meyer & Land, 2003; Perkins, 1999) affecting students within the mathematics discipline and related science disciplines, can be a positive step for a subject developer, but it is almost essential for those developing or presenting mathematics support programs. Mathematics support should ideally accommodate the many facets of student development of mathematical competency and skill by addressing the issues of troublesome knowledge - ritual knowledge, inert knowledge, conceptually difficult knowledge and foreign knowledge (as defined by Perkins, 1999). Overcoming misconceptions and knowledge barriers is a challenge for any student, but particularly for those underprepared students who seek support because of their lack of mathematical skills. Students are inevitably at different stages in their transition towards deeper learning and often need individual guidance and instruction. Being aware of the problems students face, and trying to alleviate them, is part of the challenge for support program instructors. This presentation discusses the different aspects of troublesome knowledge that have become evident whilst running the Maths Skills Program at La Trobe University, a program of mathematics support for first year students of Chemistry, Physics, Biology, Statistics and Mathematics (Jackson & Johnson, 2013; Jackson, Johnson & Blanksby, 2014). The ways such problems are confronted within this program are also addressed. REFERENCES Jackson, D.C. & Johnson, E.D. (2013). A hybrid model of mathematics support for science students emphasizing basic skills and discipline relevance. International Journal of Mathematical Education in Science and Technology, 44(6), 846-864. Jackson, D.C., Johnson, E.D. & Blanksby, T.M. (2014). A Practitioner’s Guide to Implementing cross- disciplinary links in a Mathematics Support Program. International Journal of Innovation in Science and Mathematics Education, 22(1), 67-83 Meyer, J. & Land, R. (2003). Threshold concepts and troublesome knowledge: linkages to ways of thinking and practising within disciplines. Enhancing Teaching-Learning Environments in Undergraduate Courses Project, Occasional Report 4, University of Edinburgh. Retrieved 5 June 2014 from http://www.colorado.edu/ftep/documents/ETLreport4-1.pdf Perkins, D. (1999). The many faces of constructivism. Educational Leadership, 57 (3). Retrieved 26 May 2014 from http://www.wou.edu/~girodm/library/Perkins.pdf