In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (Vol. 1). Palmerston North, NZ: MERGA. © MERGA Inc. 2009 Concept Maps: Implications for the Teaching of Function for Secondary School Students Jill P Brown 1 Australian Catholic University <jill.brown@acu.edu.au> This paper reports analysis of the concept maps of the understanding of function developed in secondary school constructed by seven experienced secondary mathematics teachers who were part of a larger study. The concept maps were analysed according to (a) key notions related to the definition of function, (b) process or object view of function, and (c) identification of the importance of working within and across representations. The findings suggest a teaching emphasis that might not be supportive of students developing a deep understanding of functions. This paper presents part of a larger study involving teachers and Years 9-11 students of mathematics in six Victorian schools. The teachers were participants in a three year research project involving the use of technology in the teaching and learning of mathematics for the development of deeper understanding (see http://extranet.edfac .unimelb.edu.au/DSME/RITEMATHS/). The focus here is related to answering the following research question: What allows teachers to perceive particular affordances of technology-rich teaching and learning environments (TRTLE’s) and act on these to develop student understandings of functions and the development of higher order thinking? (see Brown, 2005, for details). One method of data collection related to addressing this question involved asking the teacher participants in the study to create a concept map. Concept Maps Concept mapping is attributed to Novak, who recently described concept maps as “graphical tools for organising and representing knowledge” (Novak & Cafias, 2008, p. 1). They were developed in 1972 as part of Novak’s research seeking “to follow and understand changes in children’s knowledge of science” (p. 3). Whilst originally used mainly in science, there is much evidence to suggest increasing use of concept maps in mathematics (e.g., Afamasaga-Fuata’i, 2007; delos Santos & Thomas, 2005; Hasemann & Mansfield, 1995; Mwakapenda, 2003; Williams, 1998). Concept maps were initially used by teachers to more effectively present knowledge “with the intention being to map something from the outside world into the student’s mind” (Hasemann & Mansfield, 1995, p. 45). Later, students generated their own concept maps, either in a scaffolded or open fashion. Subsequently, they have been used as a research tool to gain insight into the understandings and knowledge of the concept mapper, as is the case in the study reported here. Student generated concept maps have been considered by many (e.g., delos Santos & Thomas, 2005) “to be an externalisation of conceptual schemas” (p. 378) and hence a useful tool to help identify students’ current conceptual schemas and changes in these over time. Concept maps are often used to “trace students’ understanding” (Hasemann & Mansfield, 1995). For example, Afamasaga-Fuata’i (2007) and delos Santos and Thomas (2005) used pairs of concept maps produced by each student, (undergraduate and final year 1 Jill Brown was a student at The University of Melbourne when the data were collected.