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Evaluating the impact of a Spatial Reasoning Mathematics Program (SRMP) intervention in the primary school

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Abstract

As part of the Connecting Mathematics Learning through Spatial Reasoning project, a Spatial Reasoning Mathematics Program (SRMP) intervention was implemented with one cohort of 30 students in grades 3 through 4. The SRMP embedded transformation skills in learning sequences comprising repeating and growing patterns, 2D and 3D relationships, structuring area and perimeter, directionality and perspective-taking. Analysis indicated a significantly better gain by the experimental group on the PASA-2 measure of awareness of pattern and structure and on the PASA-Sp assessment of spatial ability at the post-SRMP period. However, there were no significant differences found between groups on the PATMaths4 test of mathematics achievement. Qualitative analyses indicated that students demonstrated the development of complex spatial concepts well beyond curriculum expectations. The SRMP highlighted the important role of patterning and spatial structuring in the formation and representation of spatial concepts.

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References

  • Australian Curriculum, Assessment and Reporting Authority [ACARA] (2015). Australian F-10 Curriculum: Mathematics. Retrieved from http://www.australiancurriculum. edu.au/mathematics/curriculum/f-10.

  • Australian Curriculum, Assessment and Reporting Authority [ACARA] (2019). National assessment plan–literacy and numeracy (NAPLAN) Retrieved from https://www.nap.edu.au/.

  • Battista, M. T. (1999). The importance of spatial structuring in geometric reasoning. Teaching Children Mathematics, 6, 170–177.

    Google Scholar 

  • Board of Studies NSW (2012). Mathematics K-10 Syllabus. Retrieved from https://syllabus.nesa.nsw.edu.au/mathematics/.

  • Bruce, C. D., & Hawes, Z. (2015). The role of 2D and 3D mental rotation in mathematics for young children: what is it? Why does it matter? And what can we do about it? ZDM–International Journal on Mathematics Education, 47, 331–343.

    Article  Google Scholar 

  • Bruce, C., Sinclair, N., Moss, J., Hawes, Z., & Caswell, B. (2015). Spatializing the curriculum. In B. Davis & the Spatial Reasoning Study Group (Eds.), Spatial reasoning in the early years: principles, assertions, and speculations (pp. 85–106). New York, NY: Routledge.

    Google Scholar 

  • Bruce, C., Davis, B., Sinclair, N., McGarvey, L., Hallowell, D., Drefs, M., Francis, K., Hawes, Z., Moss, J., Mulligan, J., Okamoto, Y., Whitely, W., & Woolcott, G. (2017). Understanding gaps in research networks: using spatial reasoning as a window into the importance of networked educational research. Educational Studies in Mathematics, 95, 143–161.

    Article  Google Scholar 

  • Buckley, J., Seery, N., & Canty, D. (2018). A heuristic framework of spatial ability: a review and synthesis of spatial factor literature to support its translation into STEM education. Educational Psychology Review, 30(3), 947–972.

    Article  Google Scholar 

  • Carr, M., Alexeev, N., Wang, L., Barned, N., Horan, E., & Reed, A. (2018). The development of spatial skills in elementary school students. Child Development, 89(2), 446–460.

    Article  Google Scholar 

  • Casey, B. M., Andrews, N., Schincler, H., Kersh, J. E., Samper, A., & Copley, J. (2008). The development of spatial skills through interventions involving block building activities. Cognition and Instruction, 26(3), 269–309.

    Article  Google Scholar 

  • Cheng, Y. L., & Mix, K. S. (2014). Spatial training improves children’s mathematics ability. Journal of Cognition and Development, 15(1), 2–11.

    Article  Google Scholar 

  • Clements, D. H., & Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the building blocks project. Journal for Research in Mathematics Education, 38(2), 136–163.

    Article  Google Scholar 

  • Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, D. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.

    Article  Google Scholar 

  • Davis, B., & the Spatial Reasoning Study Group (Eds.). (2015). Spatial reasoning in the early years: principles, assertions, and speculations. New York, NY: Routledge.

    Google Scholar 

  • Doig, B., & de Lemos, M. (2000). I can do maths. Camberwell VIC: Australian Council for Educational Research (ACER) press.

  • Hawes, Z., Moss, J., Caswell, B., Naqvi, S., & MacKinnon, S. (2017). Enhancing children’s spatial and numerical skills through a dynamic spatial approach to early geometry instruction: effects of a 32-week intervention. Cognition and Instruction, 35(3), 236–264.

    Article  Google Scholar 

  • Kidd, J. K., Pasnak, R., Gadzichowski, K. M., Gallington, D. A., Mcknight, P., Boyer, C. E., & Carlson, C. (2014). Instructing first-grade children on patterning improves reading and mathematics. Early Education and Development, 25(1), 134–151.

    Article  Google Scholar 

  • Lowrie, T., Logan, T., & Ramful, A. (2017). Visuospatial training improves elementary students’ mathematics performance. British Journal of Educational Psychology, 87, 170–186.

    Article  Google Scholar 

  • Lowrie, T., Logan, T., Harris, D., & Hegarty, M. (2018). The impact of an intervention program on students’ spatial reasoning: Student engagement through mathematics-enhanced learning activities. Cognitive Research: Principles and Implications, 3(50), 1–10.

    Google Scholar 

  • Mix, K. S. (2019). Why are spatial skill and mathematics related? Child Development Perspectives, 13(2), 121–126.

    Article  Google 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.

    Article  Google Scholar 

  • Mulligan, J. T., & Mitchelmore, M. C. (2013). Early awareness of mathematical pattern and structure. In L. English & J. Mulligan (Eds.), Reconceptualizing early mathematics learning (pp. 29–45). New York: Springer.

    Chapter  Google Scholar 

  • Mulligan, J., & Mitchelmore, M. (2016). PASMAP: pattern and structure mathematics awareness program. Books 1 and 2. Camberwell, VIC: Australian Council for Educational Research (ACER) Press.

  • Mulligan, J., & Mitchelmore, M. (2018). Promoting early mathematical structural development through an integrated assessment and pedagogical program. In I. Elia, J. Mulligan, A. Anderson, A. Baccaglini-Frank, & C. Benz (Eds.), ICME-13 monographs: contemporary research and perspectives on early childhood mathematics education (pp. 17–33). Cham: Springer.

    Chapter  Google Scholar 

  • Mulligan, J. T., & Woolcott, G. (2015). What lies beneath? The conceptual connectivity underpinning whole number arithmetic. In X. Sun, B. Kaur, & J. Novotná (Eds.), Proceedings of the twenty-third ICMI study: primary mathematics study on whole numbers (pp. 220–228). Macau: University of Macau.

    Google Scholar 

  • Mulligan, J. T., Mitchelmore, M. C., & Stephanou, A. (2015). Pattern and structure assessment: an assessment program for early mathematics (F-2) teacher guide. Camberwell, VIC, Australian Council for Educational Research (ACER) press.

  • Mulligan, J. T., Oslington, G., & English, L. D. (2020). Supporting early mathematical development through a ‘pattern and structure’ intervention program. ZDM—Mathematics Education, online first Doi, 1–14. https://doi.org/10.1007/s11858-020-01147-9.

  • Mulligan, J. T., Woolcott, G., Mitchelmore, M., & Davis, B. (2018). Connecting mathematics learning through spatial reasoning. Mathematics Education Research Journal, 30(1), 77–87.

    Article  Google Scholar 

  • Newcombe, N. S. (2017). Harnessing spatial thinking to support STEM learning. In OECD Education Working Paper, No. 161. OECD Publishing, Paris.

  • Papic, M. M., Mulligan, J. T., & Mitchelmore, M. C. (2011). Assessing the development of preschoolers’ mathematical patterning. Journal for Research in Mathematics Education, 42(3), 237–269.

    Article  Google Scholar 

  • Ramful, A., Ho, S. Y., & Lowrie, T. (2015). Visual and analytical strategies in spatial visualisation: perspectives from bilateral symmetry and reflection. Mathematics Education Research Journal, 27(4), 443–470.

    Article  Google Scholar 

  • Raven, J. C. (2004). Coloured progressive matrices and Crichton vocabulary scale—Manual. London: Pearson.

    Google Scholar 

  • Rittle-Johnson, B., Zippert, E. L., & Boice, K. L. (2019). The roles of patterning and spatial skills in early mathematics development. Early Childhood Research Quarterly, 46, 166–178.

    Article  Google Scholar 

  • Stephanou, A., & Lindsey, J. (2013). Progressive achievement tests in mathematics (PATMaths) (4th ed.). Camberwell VIC: Australian Council for Educational Research (ACER) Press.

    Google Scholar 

  • Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: a meta-analysis of training studies. Psychological Bulletin, 139, 352.

    Article  Google Scholar 

  • van den Heuvel-Panhuizen, M., Elia, I., & Robitzch, A. (2014). Effects of reading picture books on kindergartners’ mathematics performance. Educational Psychology: An International Journal of Experimental Educational Psychology, 36(2), 323–346.

    Article  Google Scholar 

  • Verdine, B., Golinkoff, R., Hirsh-Pasek, K., & Newcombe, N. (2017). Links between spatial and mathematical skills across the preschool years. Monographs of the Society for Research in Child Development, 82(1), 7–30.

    Article  Google Scholar 

  • Verdine, B. N., Golinkoff, R., Hirsh-Pasek, K., Newcombe, N., Filipowocz, A. T., & Chang, A. (2013). Deconstructing building blocks: preschoolers’ spatial assembly performance relates to early mathematics skills. Child Development, 85(3), 1062–1076.

    Article  Google Scholar 

  • Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817–835.

    Article  Google Scholar 

  • Warren, E., & Cooper, T. J. (2008). Generalising the pattern rule for visual growth patterns: actions that support 8-year olds’ thinking. Education Studies in Mathematics, 67, 171–185.

    Article  Google Scholar 

  • Woolcott, G., Logan, T., Marshman, M., Ramful, A., Whannell, R., & Lowrie, T. (2020a). The re-emergence of spatial reasoning within primary years mathematics education. In J. Way, J. Anderson, J. Bobis, H. McMaster, K. Cartwright, & C. Attard (Eds.), Research in mathematics education in Australasia (pp. 2016–2019). New York, NY: Springer.

  • Woolcott, G., Tran, T.-L., Mulligan, J. T., Davis, B., & Mitchelmore, M. C. (2020b). Towards a framework for spatial reasoning and primary mathematics learning: an analytical synthesis of intervention studies. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-020-00318-x

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Acknowledgements

We are very grateful to the students and teachers who participated.

Funding

This research was supported by an Australian Research Council Discovery project award (DP170101588) Connecting mathematics learning through spatial reasoning.

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Correspondence to Joanne Mulligan.

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Mulligan, J., Woolcott, G., Mitchelmore, M. et al. Evaluating the impact of a Spatial Reasoning Mathematics Program (SRMP) intervention in the primary school. Math Ed Res J 32, 285–305 (2020). https://doi.org/10.1007/s13394-020-00324-z

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  • DOI: https://doi.org/10.1007/s13394-020-00324-z

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