Research groups
Secondary education
Leaders: Dr Michael Cavanagh & Dr Wilhelmina van Rooy
This group is concerned with mathematics and science learning and teaching in secondary schools. There is some overlap with the Primary group and the ICT group.
Mathematics projects in this area fall into the following categories, although there is a great deal of overlap between them:
- student understanding of single topics (fractions, rates of change)
- the teaching of single topics (percentages, ratios and rates)
- more general aspects of teaching (Working Mathematically)
- mathematics teacher education (preservice and inservice)
Several projects focus on the role of abstraction and generalisation in mathematics learning. A four-step method of teaching for empirical abstraction (familiarisation, recognition, reification, application) has been developed and tested across a number of middle school topics, and theoretical abstraction has been studied at the senior level.
Science education research is concerned with pedagogy, curriculum and teacher education.
Research on the nexus between mathematics and science education is at the planning stage.
Current Projects
- Enhancing success in mathematics
This project aims to improve the quality of mathematics learning and teaching across Stages 3 and 4 in a Sydney secondary school and three of its feeder primary schools. A particular focus of the project is on student engagement in mathematics lessons.
Chief Investigator: Michael Cavanagh
A collaborative project with the NSW Department of Education and Training
- Teaching algebra in junior secondary school
This study investigates a multifaceted approach to teaching algebra in the junior secondary years. The approach emphasises the development of the variable concept in a variety of contexts before moving on to simplifying algebraic expressions, the prediction being that such an approach can better promote understanding in basic algebra. The teaching program is based on the Working mathematically in patterns and algebra materials developed by McMaster and Mitchelmore.
Chief investigator: PhD student Salma Tahir
- Teachers for the future: Experiences of mature-aged entrants to teacher training for secondary mathematics
This study will examine the characteristics of mature-aged entrants to mathematics teacher education programs. It will investigate their experiences at university, during their practicum, and in their first year of teaching. Outcomes will be a deeper understanding of the needs of mature-aged students and their supervising teachers, and improvements in the design of teacher education programs.
Chief investigator: Michael Cavanagh
Funded by a Macquarie University Research Development Grant
- Development of children's understanding of fractions
This project aims to assess the extent to which upper primary and lower secondary school students conceive of fractions as a single number as opposed to a pair of whole numbers. A test has been developed and administered to a large, statewide sample and followed up by clinical interviews with selected students. The data show fundamental misconceptions that can be traced to the formation of incomplete concept images.
Chief investigator: PhD student Peter Gould
- Transforming the technologies and modalities of learning: The case of the New Life Sciences in secondary schooling
This project aims to provide theoretical and analytic frameworks for understanding changing intellectual, technological and communicational parameters of contemporary education. It also aims to make these frameworks accessible enough to become part of the conceptual repertoire of professional practitioners and flexible enough to allow practitioners to maintain currency in evolving fields of knowledge in the New Life Sciences.
Chief Investigators: PR Freebody (Sydney), John Hedberg, KC Nichols (QU), Wilhelmina Van Rooy
Funded by an ARC Discovery Grant
- NSW HSC Biology students’ understanding of the HSC course
The aim of this project is to ascertain the level of understanding of some basic biological concepts by HSC biology candidates after studying the Stage 6 syllabus. Comments from teachers and HSC markers suggesting that students have a better understanding of disease than genetics or physiology will be tested by comparing students’ conceptual understanding in the three core areas.
Chief Investigator: Wilhelmina van Rooy
Recent Projects
- Year 7 students' understanding of basic area measurement concepts
Four teachers in two secondary schools in Sydney worked with the investigators to design a written test and interview tasks that could be used to identify Year 7 students' understanding of areas of basic shapes. Results indicated common misconceptions associated with area-perimeter confusion, a poor grasp of the relationship between areas of rectangles and triangles, and a limited appreciation of the need to identify perpendicular height when calculating areas.
Chief investigators: Michael Cavanagh, Heather McMaster
Funded as part of an Australian School Innovation in Science, Technology and Mathematics (ASISTM) project
- Students' understanding of rate of change
In an individual teaching experiment, 14 Year 11 students were taught the concepts of average and instantaneous rate of change as embedded in three realistic contexts. Analysis of student protocols showed that, while all students had a good global understanding of rate of change concepts, many had some difficulty with both the average and instantaneous concepts. Their abstraction processes seemed to fit the RBC model of Dreyfus et al. much better than the empirical abstraction model.
Chief investigator: PhD student Ibrahim Hassan
- Teaching percentages as part-whole relationships
Five teachers in regional New South Wales implemented the Teaching for Abstraction method for the Year 6 topic “Percentages”. Particular emphasis was given to additive versus multiplicative approaches to comparison situations and to efficient methods of calculating simple percentages. The results show that, even though the approach is radically different from that to which students and teachers are accustomed, it has the potential to benefit student engagement and learning as well as both student and teacher attitudes.
Chief Investigators: Paul White, Sue Wilson (ACU), Rhonda Faragher (ACU) and Michael Mitchelmore
Funded by a grant from the National Centre for Science, Information and Communication Technology, and Mathematics Education for Rural and Regional Australia (SiMERR)
- Teaching ratio and rates for abstraction
The Teaching for Abstraction method for the Year 8 topic "Ratio and rates" was implemented in six classes of varying abilities and gender mixture. Student learning varied considerably. High ability students had no difficulty with the calculations but often omitted units. Low ability students often confused the ratio of two parts with the fraction for each part of the whole, and could not readily convert ratios to their simplest form because they did not recognise common factors. The major difficulty for teachers lay in adapting the approach to the various abilities and interests of their students.
Chief Investigators: Michael Mitchelmore, Paul White
Funded through a Macquarie University Collaboration Research Grant and the NSW Department of Education.
- Implementation of the Mathematics 7-10 syllabus
A large, statewide sample of mathematics teachers in Years 7 and 9 was interviewed to assess schools' implementation of the 2002 syllabus. The majority of teachers involved in this study were pleased with the easy-to-read format of the new syllabus and the flexibility of the learning continuum. However, they were not convinced of the importance of the Working Mathematically outcomes and most reported that the introduction of the new syllabus had not influenced their classroom pedagogy in any meaningful way. Most teachers were unsure precisely what Working Mathematically meant and how they could implement it with their classes.
Chief investigator: Michael Cavanagh
- Maintaining a constructivist pedagogy
This study sought to identify key factors that determine whether and how beginning secondary mathematics teachers develop and maintain a constructivist pedagogy. Samples of DipEd students from two universities reported a significant mismatch between the constructivist approaches discussed at university and the more traditional pedagogies they observed during their practicum. However, most of them indicated a desire to follow student-centred teaching in the future. Their actual behaviour during their first year of teaching is currently being studied. It is hoped that the results will lead to a more relevant mathematics teacher education curriculum and improved outcomes for beginning teachers.
Chief investigators: Michael Cavanagh, Anne Prescott
Publications
Cavanagh, M. (2008). Area measurement in Year 7. Reflections, 33(1), 55-58.
Cavanagh, M. (2008). One secondary teacher's use of problem solving teaching approaches. In M. Goos, R. Brown & K. Makar (Eds.), Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, Brisbane, Vol. 1, pp. 117-124). Adelaide: MERGA.
Cavanagh, M. (2008). Trigonometry from a different angle. The Australian Mathematics Teacher, 64(1), 25-30.
Mitchelmore, M. C., & McMaster, H. (2008) Working mathematically in Patterns & Algebra (Part 2). Reflections, 33(1), 41-42.
Nichols, K., Barton, G., Van Rooy, W., Freebody, J., & Hedberg, J. (in press). Investigating the use of technology and modalities in Queensland Senior Biology. In C. J. Liu (Ed.), Proceedings of the 2008 Conference of Asian Science Education. Kaohsiung, Taiwan: National Kaohsiung Normal University.
Prescott, A., & Cavanagh, M. (2008). A sociocultural perspective on learning to teach secondary mathematics. In M. Goos, R. Brown & K. Makar (Eds.), Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, Brisbane, June 28-July 1). Adelaide: MERGA.
Van Rooy, W., Freebody, P., Hedberg, J., & Nichols, K. (in press). Transforming the technology and modalities of learning biology for Senior High School students in NSW: A report of work in progress. In C. J. Liu (Ed.), Proceedings of the 2008 Conference of Asian Science Education. Kaohsiung, Taiwan: National Kaohsiung Normal University.
White, P., Mitchelmore, M., Wilson, S., & Faragher, R. (2008). Teaching for abstraction: Percentages. In O. Figueras, J. Cortina, S. Alatorre, T. Rojano, & A. Sepúlveda. (Eds.), Proceedings of the joint meeting of PME 32 and PME-NA XXX (Vol. 1, p. 323). México: Cinvestav-UMSNH.
Cavanagh, M. (2007). Secondary teachers' responses to the new syllabus. Reflections, 32(1), 78-80.
Cavanagh, M. (2007). Year 7 students' understanding of area measurement. In K. Milton, H. Reeves, & T. Spencer (Eds.), Mathematics: Essential for learning, essential for life (Proceedings of the 21st biennial conference of the Australian Association of Mathematics Teachers, Hobart, pp. 136-142). Adelaide: AAMT.
Cavanagh, M., & Prescott, A. (2007). Professional experience in learning to teach secondary mathematics: Incorporating pre-service teachers into a community of practice. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice (Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, Hobart, pp. 182-191). Adelaide: MERGA.
Ho, K. F., Tan, P., & Hedberg, J. G. (2007). An "Understand, Strategise, Execute and Reflect" (USER) approach to the teaching of mathematical problem solving — One teacher's experience. In C. Shegar & R. B. Abdul Rahim (Eds.), Redesigning pedagogy: Voices of practitioners (pp. 147-156). Singapore: Pearson Education.
Mitchelmore, M. C., & McMaster, H. (2007) Working mathematically in Patterns & Algebra. Reflections, 32(1), 26-28.
Mitchelmore, M. C., & White, P. (2007). Abstraction in mathematics education [Editorial]. Mathematics Education Research Journal, 19(2), 1-9.
Mitchelmore, M. C., White, P., & McMaster, H. (2007). Teaching ratio and rates for abstraction. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice (Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia, Hobart, pp. 503-512). Adelaide: MERGA.
Cavanagh, M. (2006). Implementing a reform-oriented mathematics syllabus: A survey of secondary teachers. In J. Novotná, H. Moraová, M. Krátká & N. Stehlíková (Eds.), Proceedings of the 30th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 273-280). Prague: Program Committee.
Cavanagh, M. (2006). Mathematics teachers and Working Mathematically: Responses to curriculum change. In P. Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.), Identities, cultures and learning spaces (Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 115-122). Adelaide: MERGA.
Hassan, I., & Mitchelmore, M. C. (2006). The role of abstraction in learning about rates of change. In P. Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.), Identities, cultures and learning spaces (Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 278-285). Adelaide: MERGA.
Lim, C.P., Nonis, D., & Hedberg, J. (2006). Gaming in a 3D Multi-User Virtual Environment (MUVE): Engaging students in science lessons. British Journal of Educational Technology, 37, 211-231.
Lioe, T. L., Ho, K. F., & Hedberg, J. G., (2006). Students’ metacognitive problem-solving strategies in solving open-ended problems in pairs. In W. D. Bokhorst-Heng, M. D. Osborne, & K Lee, (Eds.) Redesigning pedagogy: Reflections on theory and praxis (pp. 243-260). Rotterdam, The Netherlands: Sense Publishers.
McMaster, H., & Mitchelmore, M. C. (2006). Working mathematically with data. Reflections, 31(1), 42-45.
Owens, K., & Outhred, L. N. (2006). The complexity of learning geometry and measurement. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the Psychology of Mathematics Education: Past, present and future (pp. 83-115). Rotterdam, The Netherlands: Sense Publishers.
Prescott, A., & Cavanagh, M. (2006). An investigation of pre-service secondary mathematics teachers' beliefs as they begin their teacher training. In P. Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.), Identities, cultures and learning spaces (Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, Vol. 2, pp. 424-431). Adelaide: MERGA.
Prescott, A. & Mitchelmore, M. C. (2006). Teacher misconceptions about projectile motion. In P. Grootenboer, R. Zevenbergen, & M. Chinnappan (Eds.), Identities, cultures and learning spaces (Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia, Vol. 2, p. 602). Canberra: MERGA.
Riley, J., & Van Rooy, W. (2006). Children’s ideas about health. Education Today, 6(37), 34-35.
Tan, D. K C, Hedberg, J.G., Koh, T. S., & Seah, W. C. (2006). Datalogging in Singapore schools: Supporting effective implementations. Research in Science & Technological Education, 24, 111-127.
Tirtasanjaya, L., Ho, K. F., & Hedberg, J. G., (2006). Students’ metacognitive problem-solving strategies in solving open-ended problems in pairs. In W. D. Bokhorst-Heng, M. D. Osborne, & K Lee, (Eds.) Redesigning pedagogy: Reflections on theory and praxis (pp. 243-260). Rotterdam, The Netherlands: Sense Publishers.
Van Rooy, W. (2006, July). Biology teachers and their response to curriculum change. Paper presented at the Australian Science Education Research Association conference, Canberra.
Anderson, J., White, P., & Sullivan, P. (2005). Using a schematic model to represent influences on, and relationshipds between, teachers’ problem-solving beliefs and practices. Mathematics Education Research Journal, 17(2), 9-38.
Cavanagh, M. (2005). Enhancing teachers' knowledge of students' thinking: The case of graphics calculator graphs. In P. L. Jeffrey (Ed.), Creative dissent, constructive solutions (Proceedings of the annual conference of the Australian Association for Research in Education, Parramatta NSW, January 2005). Available at http://www.aare.edu.au/05pap/cav05043.pdf
Cavanagh, M. (2005). Working mathematically: The role of graphics calculators. In M. Coupland, J. Anderson, & T. Spencer (Eds.), Making mathematics vital (Proceedings of the 20th biennial conference of the Australian Association of Mathematics Teachers, Sydney, pp. 80-86). Adelaide: AAMT.
Chen, M. P., Guo, L., Freebody, P. & Hedberg, J.G. (2005, May). The discourse of multimodalities in science and history classrooms. Paper presented at conference on “Redesigning pedagogy: research, policy, practice”, Nanyang Technological University, Singapore.
Ho, K. F., Tan, P. & Hedberg, J.G. (2005, May). An understand, strategize, execute and reflect (USER) approach to the teaching of mathematical problem solving—One teacher’s experience. Paper presented at conference on “Redesigning pedagogy: research, policy, practice”, Nanyang Technological University, Singapore.
Ho, K.F., & Hedberg, J. G. (2005). Teachers’ pedagogies and their impact on students’ mathematical problem solving. Journal of Mathematical Behavior, 24, 238-252.
McMaster, H. J., & Mitchelmore, M. C. (2005). The rewards and difficulties of working mathematically. In Making Mathematics Vital (Proceedings of the twentieth biennial conference of the Australian Association of Mathematics Teachers, Sydney, pp.194-200). Adelaide: AAMT.
McMaster, H. J., & Mitchelmore, M. C. (2005). Working mathematically in measurement. Reflections, 30(1), 20-23.
Mitchelmore, M. C., & White, P. (2005, July). Abstraction in mathematics learning. Discussion group presented at the 29th annual conference of the International Group for the Psychology of Mathematics Education, Melbourne.
Prescott, A., & Mitchelmore, M. (2005). Student misconceptions about projectile motion. In P. Clarkson, A. Downton, D. Gronn, A. McDonough, R. Pierce, & A. Roche (Eds.), Building connections: Theory, research and practice (Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia, Melbourne, pp. 633-640). Sydney: MERGA.
Prescott, A., & Mitchelmore, M. (2005). Teaching projectile motion to eliminate misconceptions. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 97-104). Melbourne: The University.
Van Rooy, W. (2005, November/December). Curriculum reform in the secondary school - The voices of experienced teachers. Paper presented at the annual meeting of the Australian Association for Educational Research, Sydney.
White, P. (2005). Quality Teaching and pedagogy in mathematics K – 12. In M. Coupland, J. Anderson, T. Spencer (Eds.), Making mathematics vital (Proceedings of the 20th biannual conference of the Australian Association of Mathematics Teachers, Sydney, pp. 261-267). Adelaide: AAMT.
White, P., & Mitchelmore, M. (2005). Teaching percentage as a multiplicative relationship. In P. Clarkson, A. Downton, D. Gronn, A. McDonough, R. Pierce, & A. Roche (Eds.), Building connections: Theory, research and practice (Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia, Melbourne, pp. 783-790). Sydney: MERGA.
Wong, K. Y., Quek, K. S., Hedberg, J.G. & Chua, P. H. (2005, May). Understanding in-class experiences of mathematically weak pupils. Paper presented at conference on “Redesigning pedagogy: research, policy, practice”, Nanyang Technological University, Singapore.
Anderson. J., Sullivan. P., & White. P. (2004). The influence of perceived constraints on teachers’ problem-solving beliefs and practices. Proceedings of the 27th annual conference of the Mathematics Education Research Association of Australasia, Townsville (pp. 39-46).
Anderson, J., & White, P. (2004). Problem solving in the teaching and learning of mathematics. In B. Perry, G. Anthony & C. Diezmann (Eds). Research in mathematics education in Australasia 2000 – 2003 (pp. 127-150). Flaxton QLD: Post Pressed.
Cavanagh, M. (2004). The new syllabus: Problem solving, investigations and a whole lot more! Reflections, 29(2), 5-7.
Mitchelmore, M. C. (2004). Teaching mathematical concepts: Instruction for abstraction. Invited regular lecture at the International Congress on Mathematical Education, Copenhagen.
Mitchelmore, M. C., & McMaster, H. J. (2004). Working mathematically in space and geometry. Reflections, 29(1), 24-27.
Mitchelmore, M. C., & White, P. (2004). Abstraction in mathematics and mathematics learning. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 329-336). Bergen, Norway: Program Committee.
Prescott, A. (2004). Teaching the mathematics of projectile motion in upper secondary school. Unpublished PhD thesis, Macquarie University.
Van Rooy, W. (2004). Bringing controversial issues into science teaching. In G. Venville & V. Dawson (Eds.), The Art of Science Teaching (pp. 194-208). Sydney: Allen & Unwin.
White, P. (2004). Pentimals, or why 10 is a better base than 5. Australian Mathematics Teacher, 60(4), 20-24.
White, P., & Mitchelmore, M. C. (2004). Background knowledge and connectedness: The case of mathematics. In I. Putt, R. Faragher, & M. McLean (Eds.), Mathematics education for the third millennium: Towards 2010 (Proceedings of the 27th annual conference of the Mathematics Education Research Group of Australasia, Townsville, QLD, pp. 589-596). Sydney: MERGA.
White, P., Mitchelmore, M. C., Branca, N., & Maxon, M. (2004). Professional development: Mathematical content versus pedagogy. Mathematics Teacher Education and Development, 6, 49-60.
White. P., & Sattler. J. (2004). Extra perspectives on secondary school mathematics. Reflections, 29(1), 35-38.
Cavanagh, M., & Mitchelmore, M. C. (2003). Graphics calculators in the learning of mathematics: Teacher understandings and classroom practices. Mathematics Teacher Education and Development, 5, 3-18.
D’Souza, S.M. & Wood, L. N. (2003). Secondary students’ perceptions of instructional approaches: Implications for mathematics learning. In L. Bragg, C. Campbell, G. Herbert, & J. Mousely (Eds.), Mathematics Education Research: Innovation, Networking, Opportunity (Proceedings of the 26th annual conference of the Mathematics Education Research Group of Australasia, Geelong, pp. 286-293). Sydney: MERGA.
Mitchelmore, M. C. (2003). Working Mathematically in space and geometry. Paper presented at the annual conference of the Mathematical Association of New South Wales, Brighton-le-Sands.
Mitchelmore, M. C. (2002). The role of abstraction and generalisation in the development of mathematical knowledge. In D. Edge & Y. B. Har (Eds.). Mathematics education for a knowledge-based era (Proceedings of the Second East Asia Regional Conference on Mathematics Education and the Ninth Southeast Asian Conference on Mathematics Education, Vol. 1, pp. 157-167). Singapore: Association of Mathematics Educators.
Prescott, A. (2002). Student misconceptions about projectile motion. Reflections, 27(1), 92-96.
Reiss, M., Tunnicliffe, S., Moller-Anderson, A., Bartoszeck, A., Simoes de Carvalho, G., Chen, S., Mulemwa, J. Novikova, T., Otuka, J., Teppa, S. and Van Rooy, W. (2002). An international study of young people's drawings of what is inside themselves. Journal of Biological Education, 36(2) 58-64.
Van Rooy, W. (2002). Inside the AS biology classroom. School Science Review, 83(304), 1-8.
Van Rooy, W. (2002). What's in the biota bag? Examining Australian fossil biota. Australian Science Teachers' Association Journal, 48(1), 46-48.
Van Rooy, W., & Pollard, I. (2002). Stories from the bioscience ethics classroom: Exploring undergraduates' perceptions of their learning. Eubios Journal of Asian and International Bioethics, 12(1), 26-30.
Van Rooy, W., & Pollard, I. (2002). Teaching and learning about bioscience ethics with undergraduates. Education for Health.
White, P., & Mitchelmore, M. C. (2002). Teaching and learning mathematics by abstraction. In D. Tall & M. Thomas (Eds.), Intelligence, learning and understanding in mathematics: A tribute to Richard Skemp (pp. 235-255). Flaxton, QLD: Post Pressed.