Research groups

• Early childhood and primary education
• Secondary education
• Tertiary education
• ICT in education

Research Group 1. Early childhood and primary education

Leaders: A/Prof Joanne Mulligan & Dr Kathy Stewart

This group is concerned with mathematics and science learning and teaching during the crucial period from before school to about Year 6. There is some overlap with the Secondary group and the ICT group.

Earlier projects focussed on young children’s understanding of mathematical concepts such as multiplication, area measurement, and angles. Important findings included these:

• The intuitive model children employ to solve a particular problem tends to reflect the mathematical structure they are able to impose on it rather than its inherent mathematical structure.
• Children often do not realise the linear nature of length units and how a linear measurement scale is constructed.
• Angle concepts may be effectively taught by first identifying similarities between real-life angle contexts where both arms of the angle are visible, and then looking for similarities between these and contexts where one or no arms are visible.

While single-concept studies continue, more recent efforts have centred on researching children’s awareness of the mathematical patterns and structures that underlie these concepts. The most significant results so far are these:

• There is a strong correlation between young children's awareness of pattern and structure across a wide variety of mathematical tasks.
• Children classified by their teachers as low-achieving have very little awareness of structure.
• It is possible to teach children to become more aware of pattern, and such teaching leads to an improvement in their mathematics achievement.

A proposal to publish a Pattern and Structure Mathematical Awareness Program (PASMAP) was highly commended in the Macquarie University Innovations Awards 2006. Click here to view a video summarising this proposal. Click here to read a summary of the research on which PASMAP is based.

Research on early science learning and teaching is in its infancy, but is concentrating on the potential of mobile technology to enhance out-of-classroom science experiences. There is also an interest in the development of statistical understanding through ecological studies.

Current projects

• Reconceptualising early mathematics learning: The fundamental role of pattern and structure
  A full-year Kindergarten PASMAP program is to be developed and field-tested in two schools in Sydney and two schools in Brisbane. Two teachers in each school will teach the PASMAP program and two will teach the regular entry-level program. Professional development will be provided to all teachers to ensure that both programs are taught to their full potential. Evaluation will be based on assessments made at the beginning and end of the year as well as the middle of the following year, together with records of classroom observations, teacher interviews and student artifacts.
  Chief investigators: Joanne Mulligan, Lyn English (QUT), Michael Mitchelmore, Coral Kemp
  Funded by an ARC Discovery Grant  
   
• Word problem solving for Filipino children who have reading difficulties in English
  This research will design and evaluate a pedagogical approach aimed at developing Filipino children's strategies for solving word problems in English by providing them with a range of problem solving situations and encouraging the use of different modes of representation. It is anticipated that the project will be implemented through organisations which provide small-group tutoring for children from Philippine public schools.
  Chief investigator: PhD student Debbie Bautista

• The impact of technological tools on early data exploration through integrated mathematical investigations
  A two-year longitudinal study, targeting a cohort of Year 5 students and their teachers, will investigate the teaching and learning of data modelling and statistical reasoning using innovative ICT programs. The emphasis will be on content knowledge, graphical representation and critical interpretation.
  Chief investigator: PhD student Karen Ahearn
   
• Learning astronomy in prior-to-school settings: Using storytelling and imagery to stimulate young children’s understanding
  This research seeks to evaluate the impact of an innovative early science curriculum in which children experience aspects of astronomy through practical, hands-on, inquiry-based learning activities. The curriculum is being implemented in the year prior to formal schooling in two childcare centres. The study investigates children’s learning experiences as they grapple with the big picture of their place in the Solar System, and tracks their developing conceptual understandings of the creation of Earth and Space.
  Chief investigator: PhD student Camilla Gordon
   
• Developing a conceptual understanding of the measurement of length, area and volume: Studies of learning and teaching
  An interview assessment of understanding of length, area and volume measurement was administered to a large sample of students in Years 1-4. The analysis has suggested the order in which six measurement principles are learnt within and across domains. The study has also found some basic misconceptions which have not previously been reported.
  Chief investigators: Michael Mitchelmore, Lynne Outhred, and PhD student Margaret Curry
  Funded through an ARC Linkages-Project grant.  
   
• The development of length concepts in young children
  A sample of 120 students from Years 1-5 were interviewed on their understanding of length. It has been found that many students have a poor concept of length and do not know what they are measuring or what the role of the measurement unit is.
  Chief investigator: PhD student Philippa Bragg

Recent projects

• Mathematical thinking of preschool children in rural and regional Australia: Research and practice.
  CRiMSE was a partner in a consortium led by La Trobe University which prepared a review of the research literature on the mathematical capabilities of children prior to formal schooling. The group also surveyed childcare workers to assess their beliefs and knowledge of mathematics and the ways in which they nurture mathematical thinking in their children. Among CRiMSE’s contribution was a video targeted at carers and parents explaining critical aspects of mathematical development and providing examples of best practice.
  Chief investigators: Joanne Mulligan, Marina Papic
   
• Teaching pattern and structure in the first year of schooling
  Ten Year 1 children identified as under-achieving on a standardised mathematics test were engaged in a Pattern and Structure Mathematical Awareness Program (PASMAP) over 15 weekly episodes. Nine of the 10 children showed impressive growth in their ability to represent various patterns and substantial improvement in basic mathematical skills.
  Chief investigators: Joanne Mulligan, Coral Kemp, Michael Mitchelmore
  Funded by a Macquarie University Safety Net Grant  
   
• Preschoolers' mathematical patterning: An intervention study
  Teachers at one preschool developed a 6-month intervention program to teach basic repeating and spatial patterns. At the end of the program, the children were better able to solve patterning tasks than children in a similar school that did not experience it. After a further 12 months, they outperformed the comparison children on these patterning tasks as well as on new pattern-related tasks and on a standard mathematics assessment.
  Chief investigators: Marina Papic, Joanne Mulligan  
   

Publications

Howell, S., & Kemp, C. (in press). A participatory approach to the identification of measures of number sense in children prior to school entry. International Journal of Early Years Education.

Looveer, J., & Mulligan, J. (in press). Evaluating the efficacy of link items in the construction of a numeracy achievement scale from Kindergarten to Grade 6. In B. Duckor & N. Brown (Eds.), Advances in Rasch measurement, Volume 2. Maple Grove, MN: JAM Press.

White, P., Mitchelmore, M. C., Wilson, S., & Faragher, R. (2008). Teaching percentages: Professional learning in three regional Catholic schools. Journal of Catholic School Studies, 80(2), 55-62.

Mitchelmore, M. C., & White, P. (2008). Teaching mathematics concepts: Instruction for Abstraction. In M. Niss (Ed.), ICME-10 Proceedings [CD]. Roskilde, Denmark: Roskilde University, IMFUFA, Department of Science, Systems and Models.

Goodwin, K. Highfield, K., Mulligan, J., & Hedberg, J. (2008). A meta-analysis of recent research in early mathematics learning and technology. 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. 343). México: Cinvestav-UMSNH.White, P., & Wilson, S. (2008). A new approach to teaching percentages. Reflections, 33(1), 15-18.

Mulligan, J., Mitchelmore, M. C., Kemp, C.,  Marston, J., & Highfield, K. (2008). Encouraging mathematical thinking through pattern and structure: An intervention in the first year of schooling. Australian Primary Mathematics Classroom, 13(3), 10-15.

Mulligan, J., Mitchelmore, M. C., Marston, J., Highfield, K., & Kemp, C. (2008). Promoting mathematical pattern and structure in the first year of schooling: An intervention study. 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. 4, pp. 129-136). México: Cinvestav-UMSNH.

 Ahearn, K. (2007). Exploring data representation and statistical reasoning through integrated investigations in a Grade 2 classroom. 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, p. 911). Adelaide: MERGA.

Marston, J. (2007) Promoting early mathematical patterning in Kindergarten: Making, breaking and translating towers in problem-solving situations. Reflections, 32(1), 21-24.

Mulligan, J. T. (2007) Pattern and structure in the K-2 classroom. Reflections, 32(1), 18-20.

 Mulligan, J. T., Mitchelmore, M. C., Kemp, C., Marston, J., & Highfield, K. (2007). The impact of an intervention on the development of mathematical pattern and structure in the first year of schooling. 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, p. 920). Adelaide: MERGA.

Papic, M (2007). Promoting repeating patterns with young children – More than just alternating colours. Australian Primary Mathematics Classroom, 12(3), 8-13.

 Papic, M., & Mulligan, J. T. (2007). The growth of early mathematical patterning: An intervention study. 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. 591-600). Adelaide: MERGA.

Preston, C. & Van Rooy, W. (2007). Planning to teach primary science. In V. Dawson & G. Venville (Eds), The Art of Teaching Primary Science (2nd ed., pp. 87-107). Sydney: Allen & Unwin.

Riley, J, & Van Rooy, W. (2007). Perceptions about health in primary school children. Teaching Science, 53(4), 32-35.

 White, P., Wilson, S., Faragher, R., & Mitchelmore, M. C. (2007). Percentages as part whole relationships. 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. 805-814). Adelaide: MERGA.

Beaman, R., Wheldall, K., & Kemp, C. (2006). Differential teacher attention to boys and girls in the classroom. Educational Review, 58, 339-366.

Cavanagh, M. (2006). A review of the Count Me In Too Online Professional Development Program. Sydney: New South Wales Department of Education. Available at http://www.curriculumsupport.education.nsw.gov.au/primary/mathematics/assets/pdf/cmitonlineval.pdf

 Curry, M., Mitchelmore, M. C. & Outhred, N. L. (2006). Development of children's understanding of length, area and volume measurement principles. 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. 377-384). Prague: Program Committee.

 Gould, P., Outhred, L. N., & Mitchelmore, M. C. (2006). One-third is three-quarters of one-half. 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. 262-269). Adelaide: MERGA.

Hodge, K.A., & Kemp, C.R. (2006). Recognition of Giftedness in the Early Years of School: The Perspectives of Teachers, Parents and Children. Journal for the Education of the Gifted, 30, 164-204.

Howell, S., & Kemp, C. (2006). An international perspective on early number sense. Identifying components predictive on difficulties in early mathematics achievement. Australian Journal of Learning Disabilities, 11, 197-207.

Kemp, C., & Carter, M. (2006). The contribution of academic skills to the successful inclusion of children with disabilities. Journal of Developmental and Physical Disabilities, 28, 123-147.

 Mulligan, J. T. (2006). Promoting structural thinking in the early mathematics curriculum. Curriculum Leadership Journal, 4(26). Available at http://cmslive.curriculum.edu.au/leader/default.asp?id=15604

 Mulligan, J. T., & Mitchelmore, M. C. (2006). A Pattern and Structure Mathematics Awareness Project (PASMAP). Proceedings of the 30th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 1, p. 308). Prague: Program Committee.

 Mulligan, J. T., & Vergnaud, G. (2006). Research on children's early mathematical development. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the Psychology of Mathematics Education: Past, present and future (pp. 117-146). Rotterdam, The Netherlands: Sense Publishers.

 Mulligan, J. T., Mitchelmore, M. C., & Prescott, A. (2006). Integrating concepts and processes in early mathematics: The Australian Pattern and Structure Mathematics Awareness Project (PASMAP). 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. 4, pp. 209-216). Prague: Program Committee.

 Mulligan, J. T., Prescott, A., Papic, M., & Mitchelmore, M. C. (2006). Improving early numeracy through a Pattern And Structure Mathematics Awareness Program (PASMAP). 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, Canberra, pp. 376-383). Adelaide: MERGA.

 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.

Riley, J., & Van Rooy, W. (2006). Children’s ideas about health. Education Today, 6(37), 34-35.

Zhao, D., Mulligan, J. T., & Mitchelmore, M. C. (2006). Case studies on mathematics assessment practices in Australian and Chinese primary schools. In F. K. S. Leung, K.-D. Graf, & F. J. Lopez-Real (Eds.), Mathematics education in different cultural traditions?A comparative study of East Asia and the West (pp. 261-275). New York: Springer.

Curry, M., & Outhred, L. N. (2005). Conceptual understanding of spatial measurement. 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. 265-272). Sydney: MERGA.

 Gould, P. (2005). Year 6 students' methods of comparing the size of fractions. 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. 393-400). Sydney: MERGA.

 Howell, S., & Kemp, C. (2005). Defining number sense: A participatory Australian study. Educational Psychology, 25, 555-571.

Mulligan, J. T. (2005). Key aspects of early number learning. In A. McIntosh & L. Sparrow (Eds.), Beyond written computation (pp. 17-29). Perth: Mathematics, Science and Technology Education Centre, Edith Cowan University.

 Mulligan, J. T., Prescott, A., Mitchelmore, M. C., & Outhred, L. N. (2005). Taking a closer look at young students' images of area measurement. Australian Primary Mathematics Classroom, 10(2), 4-8.

 Mulligan, J., Mitchelmore, M. C., & Prescott, A. (2005). Case studies of children's development of structure in early mathematics: A two-year longitudinal study. 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. 1-8). Melbourne: The University.

Outhred, N. L., & Sardelich, S. (2005). A problem is something you don't want to have. Teaching Children Mathematics, 12, 146-154.

 Papic, M. (2005). The development of patterning in early childhood. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th conference of the International Group for the Psychology of Mathematics Education (Vol. 1, p. 269). Melbourne: The University.

Papic, M., & Gordon, C. (2005). A process of discovery. Every Child, 11(3), 20.

Papic, M., & Mulligan, J. T. (2005). Mathematics, science and technology in early childhood. In A. Taly-Ongan & E. A. Ap (Eds.), Child development and teaching young children. Southbank VIC: Thomson.

 Papic, M., & Mulligan, J. (2005). Pre-schoolers' mathematical patterning. 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. 609-616). Sydney: MERGA.

 Bragg, P., & Outhred, N. L. (2004). A measure of rulers - The importance of units in a measure. 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. 2, pp. 159-166). Bergen, Norway: Program Committee.

 Curry, M., Mitchelmore, M. C., & Outhred, L. N. (2004). Conceptual understanding of spatial measurement. Paper presented to the Topic Study Group on "New developments and trends in mathematics education at pre-school and primary level" at the International Congress on Mathematical Education, Copenhagen.

Doig, B., Groves, S. & Mulligan, J. T. (2004). Research on children's number learning in the primary school years. In B. Perry, C. Diezmann & G. Anthony (Eds.), Mathematics Education Research in Australasia 1999-2003. Sydney: Mathematics Education Research Group of Australasia.

Howell, S., & Kemp, C. (2004). The role of number sense in the identification and prevention of mathematics disability: A consideration of the phonemic awareness/number sense analogy. Australasian Journal of Special Education, 28(2), 65-79.

Mitchelmore, M. C. (2004). Teaching angle measurement without turning. In L. Sparrow & P. Swan (Eds.), APMC selected writings (pp. 119-123). Adelaide: Australian Association of Mathematics Teachers.

Mulligan, J. T., & Busatto, S. (2004). The Numeracy Research in NSW Primary Schools’ Project. In I. Putt, R. Farragher, & 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, Vol.2, pp.382-390). Sydney: MERGA.

 Mulligan, J. T., Prescott, A., & Mitchelmore, M. C. (2004). Children's development of structure in early mathematics. 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. 393-400). Bergen, Norway: Program Committee.

Outhred, L. N., & Mitchelmore, M. C. (2004). Students' structuring of rectangular arrays. 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. 465-472). Bergen, Norway: Program Committee.

Stewart, K. (2004). Gondwana connection: Partnerships for learning. Roots, 1(2): 24-26.

Stewart, K. (2004). Immersions, infusions and imitations: Case study of research-based practice in sustainability education. In Effective Sustainability Education (Proceedings of NSW Council on Environmental Education’s National Conference), University of NSW.

White, P., & Mitchelmore, M. C. (2004). Sharpening up on angles. In L. Sparrow & P. Swan (Eds.), APMC selected writings (pp. 115-118). Adelaide: Australian Association of Mathematics Teachers.

Mitchelmore, M. C., & White, P. (2003). Count Me Into Space: 2002 Evaluation. Unpublished report, New South Wales Department of Education and Training, Sydney.

Mitchelmore, M. C., & White, P. (2003). Teaching angles by abstraction: A second professional development experiment. Sydney: New South Wales Department of Education and Training, Sydney. See
http://www.curriculumsupport.nsw.edu.au/Maths/index.cfm?u=5&i=10

 Mulligan, J. T. & Prescott, A. (2003). First graders' use of structure in visual memory and unitising area tasks. In L. Bragg, C. Campbell, G. Herbert, & J. Mousley (Eds.), Mathematics Education Research: Innovation, Networking, Opportunity (Proceedings of the 26th annual conference of the Mathematics Education Research Group of Australasia, Geelong (pp. 539-546). Sydney: MERGA.

Mulligan, J. T. (2003). Developing mathematical patterns through structured activities. Paper presented at the annual conference of the Mathematical Association of New South Wales, Brighton-le-Sands.

 Mulligan, J. T., Mitchelmore, M. C., & Prescott, A. (2003). Developing a framework for pattern and structure in early numeracy. Reflections, 28(1), 7-12.

 Mulligan, J. T., Prescott, A., & Mitchelmore, M. C. (2003). Taking a closer look at young students' visual imagery. Australian Primary Mathematics Classroom, 8(4), 23-27.

 Outhred, L. N., Mitchelmore, M. C., McPhail, D., & Gould, P. (2003). Count Me Into Measurement: A program for the early elementary school. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement (2003 Yearbook, pp. 81-99). Reston, VA: National Council of Teachers of Mathematics

 White, P., & Mitchelmore, M. C. (2003). Teaching angles by abstraction from physical activities with concrete materials. In Pateman, N. A., Dougherty, B. J., & Zilliox, J. T. (Eds.), Proceedings of the 27th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 403-410). Hawaii: Program Committee.

Mitchelmore, M. C., & White, P. (2002). Teaching angles by abstraction: A professional development experiment in Year 3. Sydney: New South Wales Department of Education and Training. See http://www.curriculumsupport.nsw.edu.au/Maths/index.cfm?u=5&i=10

Mitchelmore, M. C., & White, P. (2002). Teaching angles by abstraction: A professional development experiment in Year 3. 2001 report. Sydney: New South Wales Department of Education and Training. Available on the Internet at http://www.curriculumsupport.nsw.edu.au/Maths/index.cfm?u=5&i=10

Mitchelmore, M. C., & White, P. (2002). Teaching angles by abstraction: A second professional development experiment. Unpublished report, New South Wales Department of Education and Training, Sydney. Available on the Internet at http://www.curriculumsupport.nsw.edu.au/Maths/index.cfm?u=5&i=10

 Mulligan, J. T. (2002). The role of structure in children's development of multiplicative reasoning. In B. Barton, K.C. Irwin. M. Pfannkuch, & M. O. J. Thomas (Eds.), Mathematics Education in the South Pacific (Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia, Auckland, NZ, pp. 497-503). Sydney: MERGA.

Outhred, L. N. (2002). Teaching and learning about measurement: Responses to the "Count Me into Measurement" programs. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 17-24). Norwich, UK: Program Committee.

Outhred, L. N. (2002). The implementation of Count Me Into Measurement K-6: An evaluation. Unpublished report, New South Wales Department of Education and Training, Sydney.

 Prescott, A., Mitchelmore, M. C., & White, P. (2002). Student difficulties in abstracting angle concepts from physical activities with concrete materials. In B. Barton, K. C. Irwin, M. Pfannkuch, & M. O. Thomas (Eds.), Mathematics education in the South Pacific (Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia, Auckland, NZ, pp. 583-591). Sydney: MERGA.

Prescott, A., Mitchelmore, M. C., & White, P. (2002). Student difficulties in abstracting angle concepts form physical activities with concrete materials. In B. Barton, K. C. Irwin, M. Pfannkuch, & M. O. Thomas (Eds.), Mathematics education in the South Pacific (Proceedings of the 25th annual conference of the Mathematics Education Research Group of Australasia, Auckland, NZ, pp. 583-591). Sydney: MERGA.

Thomas, N., Mulligan, J. T. & Goldin, G. A. (2002). Children's representations and cognitive structural development of the counting sequence 1-100. Journal of Mathematical Behavior, 21, 117-133

White, P., & Mitchelmore, M. C. (2002). The impact of Count Me In Too on Year 3 Basic Skills Test numeracy scores. Sydney: New South Wales Department of Education and Training.