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The Re-emergence of Spatial Reasoning Within Primary Years Mathematics Education

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Research in Mathematics Education in Australasia 2016–2019

Abstract

This chapter presents a review of the re-emergence of spatial reasoning in Australasia as a potentially powerful but under-utilised bridging mechanism between real-world experiences and mathematics teaching and learning. This is the first time a chapter has been dedicated solely to spatial reasoning in the Mathematics Education Research Group of Australasia’s (MERGA’s) four yearly review and hence the chapter outlines preliminary studies that have formed the basis for the research profiled in the 2016–2019 period. The focus on primary years (Foundation to Year six) mathematics reflects a resurgence of insights from the 1980s amplified as a research focus on the interaction of spatial reasoning and mathematics development during childhood. Because mathematical concept formation is connected to interaction with the three-dimensional world in both a mathematical and non-mathematical way it will be important to spatialise the primary curriculum. The review includes coverage of the work of established Australasian research projects, along with smaller studies and literature emanating from intervention programs that are not nominally spatial, but have spatial underpinnings or spatial reasoning components. While further research is needed to explore teacher knowledge and practice, this chapter acknowledges the valuable contributions and global influence of re-emerging Australasian research.

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References

  • Atweh, B., Goos, M., Jorgensen, R. L., & Siemon, D. (Eds.). (2012). Engaging the Australian national curriculum mathematics: Perspectives from the field. Adelaide: MERGA.

    Google Scholar 

  • Axelsen, T., Galligan, L., & Woolcott, G. (2017). The modelling process and pre-service teacher confidence. In A. Downton, S. Livy, & J. Hall (Eds.), Proceedings of the 40th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 93–100). Melbourne: MERGA.

    Google Scholar 

  • Bishop, A. J. (1980). Spatial abilities and mathematics education: A review. Educational Studies in Mathematics, 11, 257–269. https://doi.org/10.1007/BF00697739.

    Article  Google Scholar 

  • Blom, S., Pentland, P., & Woolcott, G. (2018, November). Water in the 21st century: Experiencing modules for student-centred STEM practices from the iSME project (STELR). Paper presented at the 5th International STEM in Education Conference, Queensland University of Technology, Brisbane, Australia.

    Google Scholar 

  • Boger, J. H. (1952). An experimental study of the effects of perceptual training on group IQ test scores of elementary pupils in rural ungraded schools. The Journal of Educational Research, 46, 43–52. https://doi.org/10.1080/00220671.1952.10881998.

    Article  Google Scholar 

  • Bruce, C., Davis, B., Sinclair, N., McGarvey, L., Hallowell, D., Drefs, M., et al. (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. https://doi.org/10.1007/s10649-016-9743-2.

    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, 947–972. https://doi.org/10.1007/s10648-018-9432-z.

    Article  Google Scholar 

  • Chao, J. Y., & Liu, C. H. (2017). A case study on the spatial conceptualization abilities for sixth grade elementary students from urban, suburban and remote schools. Eurasia Journal of Mathematics, Science and Technology Education, 13, 1675–1686.https://doi.org/10.12973/eurasia.2017.00691a.

  • Cheng, Y. L., & Mix, K. S. (2014). Spatial training improves children’s mathematics ability. Journal of Cognition and Development, 15, 2–11. https://doi.org/10.1080/15248372.2012.725186.

    Article  Google Scholar 

  • Clements, D. H., & Battista, M. T. (1986). Geometry and geometric measurement. Arithmetic Teacher, 33, 29–32. Retrieved June 10, 2019 from http://www.jstor.org/stable/41192838.

  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420–464). New York, NY: Macmillan.

    Google Scholar 

  • Cohrssen, C., de Quadros-Wander, B., Page, J., & Klarin, S. (2017). Between the big trees: A project-based approach to investigating shape and spatial thinking in kindergarten program. Australasian Journal of Early Childhood, 42, 94–104. https://doi.org/10.23965/AJEC.42.1.01.

  • Cunningham, L. (2019). Pāsifika students’ perspectives and understandings of mathematics embedded within their lives beyond the classroom. In G. Hine, S. Blackley, & A. Cooke (Eds.), Proceedings of the 42nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 196–203). Perth: MERGA.

    Google Scholar 

  • Cutting, C. (2019). Re-thinking fraction instruction in primary school: The case for an alternative approach in the early years. In G. Hine, S. Blackley, & A. Cooke (Eds.), Proceedings of the 42nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 204–211). Perth: MERGA.

    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 

  • de Freitas, E., & Sinclair, N. (2013). New materialist ontologies in mathematics education: The body in/of mathematics. Educational Studies in Mathematics, 83, 453–470. https://doi.org/10.1007/s10649-012-9465-z.

    Article  Google Scholar 

  • Elkind, D., Barocas, R., & Rosenthal, B. (1968). Combinatorial thinking in adolescents from graded and ungraded classrooms. Perceptual and Motor Skills, 27, 1015–1018. https://doi.org/10.2466/pms.1968.27.3.1015.

    Article  Google Scholar 

  • Forndran, A., Lowrie, T., & Harris, D. (2019). Strategy use in mathematics assessment: Does spatial reasoning matter? In G. Hine, S. Blackley, & A. Cooke (Eds.), Proceedings of the 42nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 276–283). Perth: MERGA.

    Google Scholar 

  • Fowler, S., O’Keefe, L., Cutting, C., & Leonard, S. (2019). The mathematics proficiencies: A doorway into spatial thinking. Australian Primary Mathematics Classroom, 24(1), 36–40.

    Google Scholar 

  • Francis, K., Khan, S., & Davis, B. (2016). Enactivism, spatial reasoning and coding. Digital Experiences in Mathematics Education, 2, 1–20. https://doi.org/10.1007/s40751-015-0010-4.

    Article  Google Scholar 

  • Galligan, L., Axelsen, T., Pennicott, T., Addie, R., Galbraith, P., & Woolcott, G. (2019). It’s part of my life and the modelling process. Journal of Mathematics Teacher Education, 22, 355–378. https://doi.org/10.1007/s10857-019-09426-3.

    Article  Google Scholar 

  • Geiger, V., Goos, M., & Dole, S. (2014). Students’ perspectives on their numeracy development across the learning areas. In Y. Li & G. Lappan (Eds.), Mathematics curriculum in school education (pp. 473–492). New York, NY: Springer. https://doi.org/10.1007/978-94-007-7560-2_22.

  • Gronow, M., Cavanagh, M., & Mulligan, J. (2019). Primary pre-service teachers noticing of structural thinking in mathematics. In G. Hine, S. Blackley, & A. Cooke (Eds.), Proceedings of the 42nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 324–332). Perth: MERGA.

    Google Scholar 

  • Hamdan, N., & Gunderson, E. A. (2017). The number line is a critical spatial-numerical representation: Evidence from a fraction intervention. Developmental Psychology, 53, 587–596. https://doi.org/10.1037/dev0000252.

    Article  Google Scholar 

  • Hamid, H. A., & Idris, N. (2017). Enhancing Malaysia’s human capital: A study of students’ preference and usage level of graphs in solving applied derivative problems. Geografia-Malaysian Journal of Society and Space, 12, 12–23.

    Google Scholar 

  • 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, 1–29. https://doi.org/10.1080/07370008.2017.1323902.

    Article  Google Scholar 

  • Hegarty, M., Goodchild, M., Janelle, D., & Doehner, K. (2013). Report on the Center for Spatial Studies. Santa Barbara, CA: The Center for Spatial Studies University of California, Santa Barbara.

    Google Scholar 

  • Highfield, K., & Mulligan, J. (2008). Young children’s engagement with technological tools: The impact on mathematics learning. In M. Santos & S. Yoshi (Eds.), Proceedings of the International Congress in Mathematics Education (Vol. 11, pp. 6–13). Monterrey: ICME.

    Google Scholar 

  • Highfield, K., Mulligan, J., & Hedberg, J. (2008). Early mathematics learning through exploration with programmable toys. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepúlveda (Eds.), Proceedings of the Joint Meeting of PME and PME-NA (Vol. 3, pp. 169–176). Morelia: Cinvestav-UMSNH.

    Google Scholar 

  • Hilbert, D., & Cohn-Vossen, S. (1952). Geometry and the imagination. New York, NY: Chelsea.

    Google Scholar 

  • Ho, A., & McMaster, H. (2019). Is ‘capacity’ volume? Understandings of 11–12-year-old children. In G. Hine, S. Blackley, & A. Cooke (Eds.), Proceedings of the 42nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 356–363). Perth: MERGA.

    Google Scholar 

  • Ho, S. Y., & Lowrie, T. (2014). The model method: Students’ performance and its effectiveness. The Journal of Mathematical Behavior, 35, 87–100. https://doi.org/10.1016/j.jmathb.2014.06.002.

    Article  Google Scholar 

  • Höffler, T. N. (2010). Spatial ability: Its influence on learning with visualizations—a meta-analytic review. Educational Psychology Review, 22, 245–269. https://doi.org/10.1007/s10648-010-9126-7.

    Article  Google Scholar 

  • Hsieh, S. S., Lin, C. C., Chang, Y. K., Huang, C. J., & Hung, T. M. (2017). Effects of childhood gymnastics program on spatial working memory. Medicine and Science in Sports and Exercise, 49, 2537–2547. https://doi.org/10.1249/MSS.0000000000001399.

    Article  Google Scholar 

  • Hung, P. H., Hwang, G. J., Lee, Y. H., & Su, I. H. (2012). A cognitive component analysis approach for developing game-based spatial learning tools. Computers & Education, 59, 762–773. https://doi.org/10.1016/j.compedu.2012.03.018.

    Article  Google Scholar 

  • Inskeep, J. E. (1968). Primary-grade instruction in geometry. The Arithmetic Teacher, 15, 422–426.

    Google Scholar 

  • Janelle, D. G., Grossner, K., & Lenaburg, L. (2012). TeachSpatial: A portal to instructional resources on spatial concepts for STEM education, final report. Santa Barbara, CA: The Center for Spatial Studies University of California, Santa Barbara.

    Google Scholar 

  • Jorgensen, R., & Lowrie, T. (2013). Both ways strong: Using digital games to engage Aboriginal learners. International Journal of Inclusive Education, 17(2), 130–142.

    Article  Google Scholar 

  • Jorgensen, R., & Lowrie, T. (2017). Pedagogical and mathematical capital: Does teacher education make a difference. In A. Chronaki (Ed.), Proceedings of the 9th Mathematics Education and Society conference (MES9) (Vol. 2, pp. 580–591). Volos: MES9.

    Google Scholar 

  • Jorgensen, R., & Lowrie, T. (2018). Speaking spatially: Implications for remote Indigenous learners. In J. Hunter, P. Perger, & L. Darragh (Eds.), Proceedings of the 41st Annual Conference of the Mathematics Education Research Group of Australasia (pp. 439–446). Auckland: MERGA.

    Google Scholar 

  • Jorgensen, R., Grootenboer, P., Niesche, R., & Lerman, S. (2010). Challenges for teacher education: The mismatch between beliefs and practice in remote Indigenous contexts. Asia-Pacific Journal of Teacher Education, 38, 161–175. https://doi.org/10.1080/13598661003677580.

    Article  Google Scholar 

  • Kearins, J. (1986). Visual spatial memory in aboriginal and white Australian children. Australian Journal of Psychology, 38, 203–214.

    Article  Google Scholar 

  • Khairunnisak, C., Elizar, E., Johar, R., & Utami, T. P. (2018). Teachers’ use of learning resources in spatial learning. In Proceedings of the 6th South East Asia Design Research International Conference (6th SEA-DR IC) 27–28 June 2018, Banda Aceh, Indonesia. Journal of Physics: Conference Series (Vol. 1088, No. 1, p. 012035). Washington, DC: IOP Publishing.

    Google Scholar 

  • Khan, S., Francis, K., & Davis, B. (2015). Accumulation of experience in a vast number of cases: Enactivism as a fit framework for the study of spatial reasoning in mathematics education. ZDM Mathematics Education, 47, 269–279. https://doi.org/10.1007/s11858-014-0623-x.

    Article  Google Scholar 

  • Khine, M. S. (Ed.). (2016). Visual-spatial ability in STEM education: Transforming research into practice. New York, NY: Springer.

    Google Scholar 

  • Krintz, C., Wolski, R., Golubovic, N., Lampel, B., Kulkarni, V., Roberts, B., et al. (2016). SmartFarm: Improving agriculture sustainability using modern information technology. In Workshop Report, ACM Knowledge Discovery and Data Mining (KDD) Workshop on Data Science for Food, Energy, and Water, San Francisco, CA. http://dx.doi.org/10.1145/1235.

  • Kuhn, W., Hegarty, M., Ballatore, A., Doehner, K., Medrano, A., & Janelle, D. (2016). Report on the center for spatial studies. Santa Barbara, CA: The Center for Spatial Studies University of California, Santa Barbara.

    Google Scholar 

  • Kurniadi, E., Putri, I., Ilma, R., Hartono, Y., & Abels, M. J. (2013). Map as a tool to support the development of spatial ability. In Zulkardi (Ed.), Proceeding of the 1st South East Asia Design/Development Research (SEA-DR) International Conference (pp. 95–103). Palembang: Sriwijaya University.

    Google Scholar 

  • Lake, W., Wallin, M., Boyd, W. E., Woolcott, G., Boyd, W., Foster, A., et al. (2018). Optimising the efficacy of hybrid academic teams: Lessons from a systematic review process. Australian Universities’ Review, 60, 16–24.

    Google Scholar 

  • Lake, W., Wallin, M., Woolcott, G., Boyd, W. E., Foster, A., Markopoulos, C., et al. (2017). Applying an alternative mathematics pedagogy for students with weak mathematics: Meta-analysis of alternative pedagogies. International Journal of Mathematical Education in Science and Technology, 48, 215–228. https://doi.org/10.1080/0020739X.2016.1245876.

    Article  Google Scholar 

  • Lakoff, G., & Núñez, R. (2000). Where mathematics comes from. New York, NY: Basic Books.

    Google Scholar 

  • Lean, G. (1984). The conquest of space: A review of the research literatures pertaining to the development of spatial abilities underlying an understanding of 3-D geometry. Paper presented at the 5th International Congress on Mathematical Education, Adelaide, Australia.

    Google Scholar 

  • Lean, G., & Clements, M. K. (1981). Spatial ability, visual imagery, and mathematical performance. Educational Studies in Mathematics, 12, 267–299. https://doi.org/10.1007/BF00311060.

    Article  Google Scholar 

  • Lee, J., Jo, I., Xuan, X., & Zhou, W. (2018). Geography preservice teachers’ disposition toward teaching spatial thinking through geography: A comparison between China and Korea. International Research in Geographical and Environmental Education, 27, 135–148. https://doi.org/10.1080/10382046.2017.1320898.

    Article  Google Scholar 

  • Livy, S., Downton, A., Reinhold, S., & Wöller, S. (2018). Insights into a year 4 student’s spatial reasoning and conceptual knowledge of rectangular prisms. In J. Hunter, P. Perger, & L. Darragh (Eds.), Proceedings of the 41st Annual Conference of the Mathematics Education Research Group of Australasia (pp. 487–494). Auckland: MERGA.

    Google Scholar 

  • Logan, T., & Lowrie, T. (2017). Gender perspectives on spatial tasks in a national assessment: A secondary data analysis. Research in Mathematics Education, 19, 199–216. https://doi.org/10.1080/14794802.2017.1334577.

    Article  Google Scholar 

  • Logan, T., Lowrie, T., & Diezmann, C. M. (2014). Co-thought gestures: Supporting students to successfully navigate map tasks. Educational Studies in Mathematics, 87, 87–102. https://doi.org/10.1007/s10649-014-9546-2.

    Article  Google Scholar 

  • Logan, T., Lowrie, T., & Ramful, A. (2017). Decoding map items through spatial orientation: Performance differences across grade and gender. In B. Kaur, W. K. Ho, T. L. Toh, & B. H. Choy (Eds.), Proceedings of 41st Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 193–200). Singapore: PME.

    Google Scholar 

  • Lowrie, T. (1994). Developing talented children’s mathematical ability through visual and spatial learning tasks. Geelong: Australian Association for Research. in Education.

    Google Scholar 

  • Lowrie, T. (2012). Visual and spatial reasoning: The changing form of mathematics representation and communication. In B. Kaur & T. T. Lam (Eds.), Reasoning, communication and connections in mathematics: Yearbook 2012, Association of Mathematics Educators (pp. 149–168). Singapore: World Scientific. https://doi.org/10.1142/9789814405430_0008.

  • Lowrie, T. (2014). An educational practices framework: The potential for empowerment of the teaching profession. Journal of Education for Teaching, 40, 34–46.

    Article  Google Scholar 

  • Lowrie, T., & Jorgensen, R. (2018). Equity and spatial reasoning: reducing the mathematical achievement gap in gender and social disadvantage. Mathematics Education Research Journal, 30, 65–75. https://doi.org/10.1007/s13394-017-0213-7.

    Article  Google Scholar 

  • Lowrie, T., & Logan, T. (2017). The influence of students’ spatial reasoning on mathematics performance across different test mode formats. In B. Kaur, W. K. Ho, T. L. Toh, & B. H. Choy (Eds.), Proceedings of 41st annual conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 201–208). Singapore: PME.

    Google Scholar 

  • Lowrie, T., & Logan, T. (2019). Early learning STEM Australia (ELSA): The policy and practice(s) of engagement in the early years. In G. Hine, S. Blackley, & A. Cooke (Eds.), Proceedings of the 42nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 73–76). Perth: MERGA.

    Google Scholar 

  • Lowrie, T., & Owens, K. (2000). Making connections with space and measurement. In K. Owens & J. Mousley (Eds.), Research in mathematics education in Australasia, 1996–1999 (pp. 181–214). Sydney: MERGA.

    Google Scholar 

  • Lowrie, T., Diezmann, C. M., & Logan, T. (2012). A framework for mathematics graphical tasks: The influence of the graphic element on student sense making. Mathematics Education Research Journal, 24, 169–187. https://doi.org/10.1007/s13394-012-0036-5.

    Article  Google Scholar 

  • Lowrie, T., Harris, D., Logan, T., & Hegarty, M. (2019). The impact of a spatial intervention program on students’ spatial reasoning and mathematics performance. The Journal of Experimental Education, 1–19. https://doi.org/10.1080/00220973.2019.1684869

  • Lowrie, T., Leonard, S., & Fitzgerald, R. (2018). STEM Practices: A translational framework for large-scale STEM education design. EDeR—Educational Design Research, 2, 1–20. http://dx.doi.org/10.15460/eder.2.1.1243.

  • Lowrie, T., Logan, T., & Hegarty, M. (2019b). The influence of spatial visualization training on students’ spatial reasoning and mathematics performance. Journal of Cognition and Development, 20, 729–751. https://doi.org/10.1080/15248372.2019.1653298.

    Article  Google Scholar 

  • Lowrie, T., Logan, T., & Larkin, K. (2017). The “math” in STEM practices: The role of spatial reasoning in the early years. In A. Downton, S. Livy & J. Hall (Eds.), Proceedings of the 40th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 625–628). Melbourne. MERGA.

    Google Scholar 

  • Lowrie, T., Logan, T., & Ramful, A. (2016a). Cross cultural comparison of grade 6 students’ performance and strategy use on graphic and non-graphic tasks. Learning and Individual Differences, 52, 97–108. https://doi.org/10.1016/j.lindif.2016.10.005.

    Article  Google Scholar 

  • Lowrie, T., Logan, T., & Ramful, A. (2016b). Spatial reasoning influences students’ performance on mathematics tasks. In B. White, M. Chinnappan, & S. Trenholm (Eds.), Proceedings of the 39th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 405–412). Adelaide: MERGA.

    Google Scholar 

  • Lowrie, T., Logan, T., Harris, D., & Hegarty, M. (2018b). The impact of an intervention program on students’ spatial reasoning: Student engagement through mathematics-enhanced learning activities. Cognitive Research: Principles and Implications, 3, 50–60. https://doi.org/10.1186/s41235-018-0147-y.

    Article  Google Scholar 

  • Lowrie, T., Logan, T., & Ramful, A. (2017b). Visuospatial training improves elementary students’ mathematics performance. British Journal of Educational Psychology, 87, 170–186. https://doi.org/10.1111/bjep.12142.

    Article  Google Scholar 

  • Lubinski, D. (2010). Spatial ability and STEM: A sleeping giant for talent identification and development. Personality and Individual Differences, 49, 344–351.

    Article  Google Scholar 

  • Ma’rifatin, S., Amin, S. M., & Siswono, T. Y.E. (2018). Students’ mathematical ability and spatial reasoning in solving geometric problem. Journal of Physics: Conference series, 1157. https://doi.org/10.1088/1742-6596/1157/4/042062.

  • Marshman, M., Woolcott, G., & Dole, S. (2017). Engaging pre-service mathematics teachers in creating spatially-based problems in a 3D virtual environment: A CAVE2TM experience. In A. Downton, S. Livy, & J. Hall (Eds.), Proceedings of the 40th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 365–372). Melbourne: MERGA.

    Google Scholar 

  • Maturana, H. R., & Varela, F. J. (1991). Autopoiesis and cognition: The realization of the living. Dordrecht, The Netherlands: D. Reidel Publishing Company.

    Google Scholar 

  • McGee, M. G. (1979). Human spatial abilities: Psychometric studies and environmental, genetic, hormonal, and neurological influences. Psychological Bulletin, 86(5), 889–918. https://doi.org/10.1037/0033-2909.86.5.889.

    Article  Google Scholar 

  • Mitchelmore, M. C. (1976). Cross-cultural research on concepts of space and geometry. In J. L. Martin (Ed.), space and geometry (pp. 143–184). Columbus, Ohio: SEMAC.

    Google Scholar 

  • Mitchelmore, M. C. (1980a). Prediction of developmental stages in the representation of regular space figures. Journal for Research in Mathematics Education, 11(2), 83–93. https://www.jstor.org/stable/748901.

  • Mitchelmore, M. C. (1980b). Three-dimensional geometrical drawing in three cultures. Educational Studies in Mathematics, 11, 205–216. https://doi.org/10.1007/BF00304356.

    Article  Google Scholar 

  • Mitchelmore, M. (1984). Spatial abilities and geometry teaching. UNESCO Studies in Mathematics Education, 3, 135–143.

    Google Scholar 

  • Mowat, E., & Davis, B. (2010). Interpreting embodied mathematics using network theory: Implications for mathematics education. Complicity: An International Journal of Complexity and Education, 7, 1–31.

    Google Scholar 

  • Mulligan, J. T. (1985). The place of geometry in the primary school. Square One, 5, 2–7.

    Google Scholar 

  • Mulligan, J. (1992). Children’s solutions to partition problems. In B. Southwell, R. Perry, & K. Owens (Eds.), Proceedings of the 15th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 410–420). Sydney: MERGA.

    Google Scholar 

  • Mulligan, J. (2015). Looking within and beyond the geometry curriculum: Connecting spatial reasoning to mathematics learning. ZDM Mathematics Education, 47, 511–517. https://doi.org/10.1007/s11858-015-0696-1.

    Article  Google Scholar 

  • Mulligan, J. (2016). Connecting young children’s mathematics learning: Early years (P-3). In W. Widjaja, E. Yook-Kin Loong, & L. A. Bragg (Eds.), Proceedings of the 53rd Annual Conference of the Mathematical Association of Victoria (pp. 65–70). Brunswick: Mathematical Association of Victoria.

    Google Scholar 

  • Mulligan, J. T., English, L. D., Mitchelmore, M. C., & Crevensten, N. (2013). Reconceptualising early mathematics learning: The fundamental role of pattern and structure. In L. D. English & J. T. Mulligan (Eds.), Reconceptualizing early mathematics learning (pp. 47–66). New York, NY: Springer. https://doi.org/10.1007/978-94-007-6440-8_4.

  • Mulligan, J. T., Mitchelmore, M. C., & Stephanou, A. (2015). Pattern and structure assessment (PASA): An assessment program for early mathematics (F-2) teacher guide. Melbourne: ACER Press.

    Google Scholar 

  • Mulligan, J., & Woolcott, G. (2015). What lies beneath? The conceptual connectivity underpinning whole number arithmetic. In X. Sun, B. Kaur, & J. Novotná (Eds.), Proceedings of the International Commission on Mathematical Instruction: The twenty-third ICMI study—Primary Mathematics Study on Whole Numbers (pp. 220–229). Macao: ICMI23 IOC.

    Google Scholar 

  • Mulligan, J., Woolcott, G., Mitchelmore, M., & Davis, B. (2018). Connecting mathematics learning through spatial reasoning. Mathematics Education Research Journal, 30, 77–87. https://doi.org/10.1007/s13394-017-0210-x.

    Article  Google Scholar 

  • Murphy, C. (2019). Exploring the role of visual imagery in learning mathematics. In G. Hine, S. Blackley, & A. Cooke (Eds.), Proceedings of the 42nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 508–515). Perth: MERGA.

    Google Scholar 

  • National Research Council. (2006). Learning to think spatially–GIS as a support system in the K-12 curriculum. Washington, DC: The National Academies Press.

    Google Scholar 

  • Newcombe, N. S. (2013). Seeing relationships: Using spatial thinking to teach science, mathematics, and social studies. American Educator, 37, 26.

    Google Scholar 

  • Ogena, E. B., Ubiña-Balagtas, M., & Diaz, R. V. (2018). Philippines: Mathematics and its teaching in the Philippines. In J. Mack & D. Vogeli (Eds.), Mathematics and its teaching in the Asia-Pacific region (pp. 157–190). Singapore: World Scientific.

    Chapter  Google Scholar 

  • Oldham, H. W. (1937). A psychological study of mathematical ability with special reference to school mathematics. British Journal of Educational Psychology, 7, 269–286. https://doi.org/10.1111/j.2044-8279.1938.tb03180.x.

    Article  Google Scholar 

  • Owens, K. (1992). Spatial thinking takes shape through primary school experiences. In W. Geeslin & K. Graham (Eds.), Proceedings of the 16th PME International Conference (pp. 202–209). Durham, NC: IGPME.

    Google Scholar 

  • Owens, K. (2015a). Changing the teaching of mathematics for improved Indigenous education in a rural Australian city. Journal of Mathematics Teacher Education, 18, 53–78. https://doi.org/10.1007/s10857-014-9271-x.

    Article  Google Scholar 

  • Owens, K. (2015b). Visuospatial reasoning: An ecocultural perspective for space, geometry and measurement education. Cham: Springer.

    Book  Google Scholar 

  • Owens, K. D., & Clements, M. K. (1998). Representations in spatial problem solving in the classroom. The Journal of Mathematical Behavior, 17, 197–218. https://doi.org/10.1016/S0364-0213(99)80059-7.

    Article  Google Scholar 

  • Owens, K., Mitchelmore, M., Outhred, L., & Pegg, J. (1996). Space, geometry, measurement, and visualisation. In B. Atweh, K. Owens, & P. Sullivan (Eds.), Research in mathematics education in Australasia, 1992–1995 (pp. 331–343). Sydney: MERGA.

    Google Scholar 

  • Owens, K., & Outhred, L. (1997). Early representations of tiling areas. In E. Pehkonen (Ed.), Proceedings of the 21st PME International Conference (Vol. 3, pp. 312–319). Lanti: PME.

    Google Scholar 

  • Patahuddin, S. M., Logan, T., & Ramful, A. (2018). Characteristics of spatial visualisation: Perspectives from area of composite shapes. In J. Hunter, P. Perger, & L. Darragh (Eds.), Proceedings of the 41st Annual Conference of the Mathematics Education Research Group of Australasia (pp. 623–630). Auckland: MERGA.

    Google Scholar 

  • Patahuddin, S. M., Suwarsono, S., & Johar, R. (2018b). Indonesia: History and perspective on mathematics education. In J. Mack & D. Vogeli (Eds.), Mathematics and its teaching in the Asia-Pacific region (pp. 191–230). Singapore: World Scientific.

    Chapter  Google Scholar 

  • Pegg, J. (1992). Students’ understanding of geometry: Theoretical perspectives. In B. Southwell, B. Perry, & K. Owens (Eds.), Proceedings of the 15th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 18–36). Sydney: MERGA.

    Google Scholar 

  • Pegg, J., & Davey, G. (1991). Levels of geometric understanding. Australian Mathematics Teacher, 47, 10–13.

    Google Scholar 

  • Pegg, J., & Woolley, S. (1994). An investigation of strategies used to solve a simple deductive exercise in geometry. In G. Bell, B. Wright, N. Leeson, & J. Geake (Eds.), Proceedings of the 17th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 471–479). Lismore: MERGA.

    Google Scholar 

  • Piaget, J., & Inhelder, B. (1948). La représentation de l’espace chez l’enfant [Representation of space by the child]. Paris: Presses Universitaires de France.

    Google Scholar 

  • Presmeg, N. C. (1989). Visualization in multicultural mathematics classrooms. Focus on Learning Problems in Mathematics, 11, 17–24.

    Google Scholar 

  • Ramful, A., Lowrie, T., & Logan, T. (2017). Measurement of spatial ability: Construction and validation of the spatial reasoning instrument for middle school students. Journal of Psychoeducational Assessment, 35, 709–727. https://doi.org/10.1177/0734282916659207.

    Article  Google Scholar 

  • Reilly, D., Neumann, D. L., & Andrews, G. (2017). Gender differences in spatial ability: Implications for STEM education and approaches to reducing the gender gap for parents and educators. In M. Khine (Ed.), Visual-spatial ability in STEM education (pp. 195–224). Cham: Springer.

    Chapter  Google Scholar 

  • Revina, S., Zulkardi, Z., Darmawijoyo, D., & Galen, F. V. (2014). Spatial visualization tasks to support students’ spatial structuring in learning volume measurement. Journal on Mathematics Education, 2, 127–146. http://dx.doi.org/10.22342/jme.2.2.745.127-146.

  • Saha, R. A., Ayub, A. F. M., & Tarmizi, R. A. (2010). The effects of GeoGebra on mathematics achievement: Enlightening coordinate geometry learning. Procedia-Social and Behavioral Sciences, 8, 686–693. https://doi.org/10.1016/j.sbspro.2010.12.095.

    Article  Google Scholar 

  • Seah, R., & Horne, M. (2019). An exploratory study on students’ reasoning about symmetry. In G. Hine, S. Blackley, & A. Cooke (Eds.), Proceedings of the 42nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 628–635). Perth: MERGA.

    Google Scholar 

  • Septia, T., Prahmana, R. C. I., Pebrianto, & Wahyu, R. (2018). Improving students spatial reasoning with course lab. Journal on Mathematics Education, 9, 327–336. https://doi.org/10.22342/jme.9.2.3462.327-336

  • Sethuramasamyraja, B., Sachidhanantham, S., & Wample, R. (2010). Geospatial modeling of wine grape quality indicators (anthocyanin) for development of differential wine grape harvesting technology. International Journal of Geomatics and Geosciences, 1, 372–385.

    Google Scholar 

  • Shanty, N. O., & Wijaya, S. (2012). Rectangular array model supporting students’ spatial structuring in learning multiplication. Indonesian Mathematical Society Journal on Mathematics Education, 3, 175–186.

    Google Scholar 

  • Sharma, S. (2019). Developing an understanding of shapes and their representations in multilingual primary school classes: A systematic literature review. In G. Hine, S. Blackley, & A. Cooke (Eds.), Proceedings of the 42nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 676–683). Perth: MERGA.

    Google Scholar 

  • Shin, E. E., Milson, A. J., & Smith, T. J. (2016). Future teachers’ spatial thinking skills and attitudes. Journal of Geography, 115, 139–146. https://doi.org/10.1080/00221341.2015.1100654.

    Article  Google Scholar 

  • Sinclair, N., Bussi, M. G. B., de Villiers, M., Jones, K., Kortenkamp, U., Leung, A., et al. (2016). Recent research on geometry education: An ICME-13 survey team report. ZDM Mathematics Education, 48, 691–719. https://doi.org/10.1007/s11858-016-0796-6.

    Article  Google Scholar 

  • Sinton, D. S. (2014). Spatial learning in higher education. In D. R. Montello, K. Grossner, & D. G. Janelle (Eds.), Space in mind: Concepts for spatial learning and education (pp. 219–238). Cambridge, MA: MIT Press.

    Google Scholar 

  • Taylor, H. A., & Hutton, A. (2013). Think3d!: Training spatial thinking fundamental to STEM education. Cognition and Instruction, 31, 434–455. https://doi.org/10.1080/07370008.2013.828727.

    Article  Google Scholar 

  • Thomson, S., De Bortoli, L., & Buckley, S. (2013). PISA 2012: How Australia measures up: The PISA 2012 assessment of students’ mathematical, scientific and reading literacy. Retrieved June 10, 2019 from https://research.acer.edu.au/ozpisa/15.

  • Tosto, M. G., Hanscombe, K. B., Haworth, C., Davis, O. S., Petrill, S. A., Dale, P. S., et al. (2014). Why do spatial abilities predict mathematical performance? Developmental Science, 17, 462–470. https://doi.org/10.1111/desc.12138.

    Article  Google Scholar 

  • Tronco, T. R. (2010). A brief history of the internet. In T. R. Tronco (Ed.), New network architectures (pp. 1–11). Berlin: Springer. https://doi.org/10.1007/978-3-642-13247-6_1.

  • Trump, P. (1946). Utilizing pupil experiences in their discovery of mathematics. School Science and Mathematics, 46, 521–527. https://doi.org/10.1111/j.1949-8594.1946.tb05875.x.

    Article  Google Scholar 

  • Uttal, D. H., & Cohen, C.A. (2012). Spatial thinking and STEM education: When, why, and how? In B. H. Ross (Ed.), Psychology of learning and motivation (Vol. 57, pp. 147–181). San Diego, CA: Academic Press. https://doi.org/10.1016/B978-0-12-394293-7.00004-2.

  • Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., et al. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139, 352–402. https://doi.org/10.1037/a0028446.

    Article  Google Scholar 

  • Uttal, D. H., Miller, D. I., & Newcombe, N. S. (2013). Exploring and enhancing spatial thinking: Links to achievement in science, technology, engineering, and mathematics? Current Directions in Psychological Science, 22, 367–373. https://doi.org/10.1177/0963721413484756.

    Article  Google Scholar 

  • van Hiele, P. (1986). Structure and insight: A theory of mathematics education. London: Academic Press.

    Google Scholar 

  • Verdine, B., Golinkoff, R. M., Hirsh-Pasek, K., & Newcombe, N. (2017). Links between spatial and mathematical skills across the preschool years. Society for Research in Child Development Monograph, 82, 1–150.

    Article  Google Scholar 

  • Verner, I., & Merksamer, A. (2015). Digital design and 3D printing in technology teacher education. Procedia CIRP, 36, 182–186. https://doi.org/10.1016/j.procir.2015.08.041.

    Article  Google Scholar 

  • Wahab, R. A., Abdullah, A. H., Mokhtar, M., Atan, N. A., & Abu, M. S. (2017). Evaluation by experts and designated users on the learning strategy using sketchup make for elevating visual spatial skills and geometry thinking. Bolema: Boletim de Educação Matemática, 31, 819–840. http://dx.doi.org/10.1590/1980-4415v31n58a15.

  • 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, 817–835. https://doi.org/10.1037/a0016127.

    Article  Google Scholar 

  • Wai, J., Lubinski, D., Benbow, C. P., & Steiger, J. H. (2010). Accomplishment in science, technology, engineering, and mathematics (STEM) and its relation to STEM educational dose: A 25-year longitudinal study. Journal of Educational Psychology, 102, 860. https://doi.org/10.1037/a0019454.

    Article  Google Scholar 

  • Watson, H., & Chambers, D. W. (1989). Singing the land, signing the land: A portfolio of exhibits. Geelong: Deakin University.

    Google Scholar 

  • Winarti, D. W. (2018). Developing spatial reasoning activities within geometry learning. Journal of Physics: Conference series, 1088. http://dx.doi.org/10.1088/1742-6596/1088/1/012004.

  • Winarti, D. W., & Pathuddin, S. M. (2019). Students’ ability to solving mental rotation items: Gender perspective within disadvantaged community. In G. Hine, S. Blackley, & A. Cooke (Eds.), Proceedings of the 42nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 556–563). Perth: MERGA.

    Google Scholar 

  • Woolcott, G. (2018). The tail of a whale: A real-world problem for the maths classroom. Australian Mathematics Teacher, 74, 3–13.

    Google Scholar 

  • Woolcott, G., Chamberlain, D., & Mulligan, J. (2015). Using network analysis to connect structural relationships in early mathematics assessment. In K. Beswick, T. Muir, & J. Wells (Eds.). Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 321–328). Hobart: PME.

    Google Scholar 

  • Woolcott, G., Scott, A., Norton, M., Whannell, R., Galligan, L., Marshman, M., et al. (2017). The Enhancement-Lesson-Reflection process: A resource manual for science and mathematics learning and teaching. Companion Report to the Final report: It’s part of my life: Engaging university and community to enhance science and mathematics education. Canberra: Department of Education and Training.

    Google Scholar 

  • Wright, V. (2016). Visualisation and analytic strategies for anticipating the folding of nets. In B. White, M. Chinnappan, & S. Trenholm (Eds.), Proceedings of the 39th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 632–639). Adelaide: MERGA.

    Google Scholar 

  • Wright, V., & Smith, K. (2017). Children’s schemes for anticipating the validity of nets for solids. Mathematics Education Research Journal, 29, 369–394. https://doi.org/10.1007/s13394-017-0219-1.

    Article  Google Scholar 

  • Yeigh, T., Woolcott, G., Donnelly, J., Whannell, R., Snow, M., & Scott, A. (2016). Emotional literacy and pedagogical confidence in pre-service science and mathematics teachers. Australian Journal of Teacher Education, 41, 107–121. http://dx.doi.org/10.14221/ajte.2016v41n6.7.

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Authors and Affiliations

  1. Southern Cross University, Lismore, Australia

    Geoff Woolcott

  2. University of Canberra, Canberra, Australia

    Tracy Logan & Tom Lowrie

  3. University of the Sunshine Coast, Sippy Downs, Australia

    Margaret Marshman

  4. Mauritius Institute of Education, Moka, Mauritius

    Ajay Ramful

  5. University of New England, Armidale, Australia

    Robert Whannell

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  6. Tom Lowrie
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  1. University of Sydney, Sydney, NSW, Australia

    Jennifer Way

  2. Western Sydney University, Penrith, NSW, Australia

    Catherine Attard

  3. University of Sydney, Sydney, NSW, Australia

    Judy Anderson

  4. University of Sydney, Sydney, NSW, Australia

    Janette Bobis

  5. University of Sydney, Sydney, NSW, Australia

    Heather McMaster

  6. University of Sydney, Sydney, NSW, Australia

    Katherin Cartwright

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Woolcott, G., Logan, T., Marshman, M., Ramful, A., Whannell, R., Lowrie, T. (2020). The Re-emergence of Spatial Reasoning Within Primary Years Mathematics Education. In: Way, J., Attard, C., Anderson, J., Bobis, J., McMaster, H., Cartwright, K. (eds) Research in Mathematics Education in Australasia 2016–2019. Springer, Singapore. https://doi.org/10.1007/978-981-15-4269-5_10

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