# Reconceptualizing Early Mathematics Learning: The Fundamental Role of Pattern and Structure

## Abstract

The *Pattern and Structure Mathematics Awareness Program* (PASMAP) was developed concurrently with the studies of AMPS and the development of the Pattern and Structure Assessment (PASA) interview. We summarize some early classroom-based teaching studies and describe the PASMAP that resulted. A large-scale two-year longitudinal study, *Reconceptualizing Early Mathematics Learning* (REML) resulted. We provide an overview of the REML study and discuss the consequences for our view of early mathematics learning.

A purposive sample of four large primary schools, two in Sydney and two in Brisbane, representing 316 students from diverse socio-economic and cultural contexts, participated in an evaluation of the PASMAP intervention throughout the 2009 school year and a follow-up assessment in 2010. Two different mathematics programs were implemented: in each school, two Kindergarten teachers implemented the PASMAP and another two implemented their regular program. The study shows that both groups of students made substantial gains on the ‘I Can Do Maths’ standardized assessment and the PASA interview, but highly significant differences were found on the latter with PASMAP students outperforming the regular group on PASA scores. Qualitative analysis of students’ responses for structural development showed increased levels for the PASMAP students. Implications for pedagogy and curriculum are discussed.

### Keywords

Early childhood Mathematics Pre-algebra Patterns Structure Relationships Structural development Spatial structuring Awareness of mathematical pattern and structure (AMPS)### References

- Australian Curriculum, Assessment and Reporting Authority [ACARA] (2012). The Australian Curriculum: Mathematics (Version 3.0). Retrieved 30 March 2012 from http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10.
- Andrich, D., Lyne, A., Sheridan, B., & Luo, H. (2001).
*RUMM2010: a windows program for analyzing item response data according to Rasch unidimensional measurement models (version 3.3) [computer program]*. Perth: RUMM Laboratory. Google Scholar - Battista, M. C. (1999). Spatial structuring in geometric reasoning.
*Teaching Children Mathematics*,*6*, 171–177. Google Scholar - Blanton, M., & Kaput, J. (2005). Characterizing a classroom practice that promotes algebraic reasoning.
*Journal for Research in Mathematics Education*,*36*, 412–446. Google Scholar - Bobis, J. (1996). Visualization and the development of number sense with kindergarten children. In J. T. Mulligan & M. C. Mitchelmore (Eds.),
*Children’s number learning*(pp. 17–33). Adelaide: AAMT-MERGA. Google Scholar - Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and algebra in early mathematics education.
*Journal for Research in Mathematics Education*,*37*, 87–115. Google Scholar - Clements, D., & Sarama, J. (2009).
*Learning and teaching early maths: the learning trajectories approach*. New York: Routledge. Google Scholar - Doig, B., & de Lemos, M. (2000).
*I can do maths*. Melbourne: ACER. Google Scholar - English, L. D. (2012). Data modelling with first-grade students.
*Educational Studies in Mathematics Education*,*81*, 15–30. CrossRefGoogle Scholar - Goodwin, K. (2009).
*The impact and affordances of interactive multimedia on young students’ concept images of fractions*. Unpublished doctoral dissertation, Faculty of Human Sciences, Macquarie University, Sydney, Australia. Google Scholar - Highfield, K., & Mulligan, J. T. (2007). The role of dynamic interactive technological tools in preschooler’s mathematical patterning. 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. 372–381). Adelaide: MERGA. Google Scholar - Highfield, K., & Mulligan, J. T. (2009). Young children’s embodied action in problem-solving tasks using robotic toys. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.),
*Proceedings of the 33rd conference of the International Group for the Psychology of Mathematics Education*(Vol. 3, pp. 169–176). Thessaloniki: PME. Google Scholar - Hunting, R. (2003). Part-whole number knowledge in preschool children.
*The Journal of Mathematical Behavior*,*22*, 217–235. CrossRefGoogle Scholar - Lamon, S. (1996). The development of unitizing: its role in children’s partitioning strategies.
*Journal for Research in Mathematics Education*,*27*, 170–194. CrossRefGoogle Scholar - Mulligan, J. T. (2011). Towards understanding of the origins of children’s difficulties in mathematics learning.
*Australian Journal of Learning Difficulties*,*16*(1), 19–39. CrossRefGoogle Scholar - Mulligan, J. T., & Mitchelmore, M. C. (2009). Awareness of pattern and structure in early mathematical development.
*Mathematics Education Research Journal*,*21*(2), 33–49. CrossRefGoogle Scholar - 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*(Vol. 2, pp. 376–383). Canberra: MERGA. Google Scholar - Mulligan, J. T., 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. 1–8). México: Cinvestav-UMSNH. Google Scholar - Mulligan, J. T., English, L. D., Mitchelmore, M. C., Welsby, S., & Crevensten, N. (2011). An evaluation of the pattern and structure mathematics awareness program in the early years of schooling. In J. Clark, B. Kissane, J. Mousley, T. Spencer, & S. Thornton (Eds.),
*Mathematics: traditions and [new] practices. Proceedings of the joint conference of the Australian Association of Mathematics Teachers and the Mathematics Education Research Group of Australasia*(pp. 548–556). Alice Springs: AAMT-MERGA. Google Scholar - NSW Department of Education and Training (2002).
*Count me in too: a professional development package*. Sydney: NSW Department of Education and Training. Google Scholar - Papic, M., Mulligan, J. T., & Mitchelmore, M. C. (2011). Assessing the development of preschoolers’ mathematical patterning.
*Journal for Research in Mathematics Education*,*42*, 237–268. Google Scholar - van Nes, F., & de Lange, J. (2007). Mathematics education and neurosciences: relating spatial structures to the development of spatial sense and number sense.
*The Montana Mathematics Enthusiast*,*2*, 210–229. Google Scholar - Warren, E., & Cooper, T. J. (2008). Generalising the pattern rule for visual growth patterns: actions that support 8 year olds thinking.
*Educational Studies in Mathematics*,*67*, 171–185. CrossRefGoogle Scholar - Woodcock, R. W., McGrew, K. S., & Mather, N. (2001).
*Woodcock-Johnson III tests of achievement*. Itasca: Riverside Publishing. Google Scholar