Visualizing Mathematics pp 253-276 | Cite as

# The Interaction Between Spatial Reasoning Constructs and Mathematics Understandings in Elementary Classrooms

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## Abstract

Numerous studies from cognitive and educational psychology research have highlighted the strong association between spatial reasoning and mathematics performance. This chapter examines this relationship from a mathematics education perspective, with a focus on elementary classrooms. Three spatial constructs critical to mathematics instruction and learning are identified: namely, spatial visualization; mental rotation; and spatial orientation. These constructs are described in relation to student’s encoding and decoding of mathematics information and the increasing influence these constructs have on mathematics assessment. The extent to which spatial training can enhance student’s math performance is also considered in relation to these three constructs. Implications highlight the potential of explicitly focusing on spatial reasoning in math classrooms, given the malleability of instruction and ongoing affordances of technology.

## Keywords

Spatial reasoning Mathematics Space Spatial visualization Mental rotation Spatial orientation Encoding Decoding Curriculum Classroom Elementary Geometry Graphics Graphical languages STEM Assessment Digital Technology Spatial training Australia## References

- Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2009a).
*National assessment program literacy and numeracy: Numeracy year 3 2009*. Sydney: Author.Google Scholar - Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2009b).
*National assessment program literacy and numeracy: Numeracy year 5 2009*. Sydney: Author.Google Scholar - Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2010a).
*National assessment program literacy and numeracy: Numeracy year 3 2010*. Sydney: Author.Google Scholar - Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2010b).
*National assessment program literacy and numeracy: Numeracy year 5 2010*. Sydney: Author.Google Scholar - Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2010c).
*National assessment program literacy and numeracy: Numeracy year 7 2010*. Sydney: Author.Google Scholar - Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2011).
*Australian Curriculum v7.5: General capabilities: Overview*. Australian Curriculum, Assessment and Reporting Authority, Commonwealth Government. Retrieved on February 29, 2017, from: http://v7-5.australiancurriculum.edu.au/generalcapabilities/numeracy/organising-elements/using-spatial-reasoning. - Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester Jr. (Ed.),
*Second handbook of research on mathematics teaching and learning*(pp. 843–908). Charlotte, NC: Information Age Publishing.Google Scholar - Battista, M. T., & Clements, D. H. (1988). A case for a logo-based elementary school geometry curriculum.
*Arithmetic Teacher, 36*, 11–17.Google Scholar - Battista, M. T., Clements, D. H., Arnoff, J., Battista, K., & Borrow, C. V. A. (1998). Students’ spatial structuring of 2D arrays of squares.
*Journal for Research in Mathematics Education, 29*(5), 503–532.CrossRefGoogle Scholar - Bertin, J. (1967).
*Semiology of graphics: Diagrams, networks, maps*. Wisconsin: University of Wisconsin Press. (first published in French in 1967 translated by William J. Berg in 1983).Google Scholar - Bishop, A. J. (2008). Spatial abilities and mathematics education–a review. In P. Clarkson & N. Presmeg (Eds.),
*Critical issues in mathematics education*(pp. 71–81). New York: Springer.CrossRefGoogle Scholar - Bowe, B., Nevin, E., Carthy, D., Seery N., & Sorby, S. (2016).
*National spatial skills report - phase 1 preliminary findings*. CREATE Dublin Institute of Technology (Contributions to Research in Engineering and Applied Technology Education) 2016.Google Scholar - Carroll, J. B. (1993).
*Human cognitive abilities: A survey of factor-analytic studies*. New York, NY: Cambridge University Press.CrossRefGoogle Scholar - Cheng, Y. L., & Mix, K. S. (2014). Spatial training improves children's mathematics ability.
*Journal of Cognition and Development, 15*(1), 2–11.CrossRefGoogle Scholar - Clements, D. H., Battista, M., Sarama, J., & Swaminathan, S. (1997). Development of students’ spatial thinking in a unit on geometric motions and area.
*The Elementary School Journal, 98*(2), 171–186.CrossRefGoogle Scholar - 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: Macmillan.Google Scholar - Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: The case of geometry.
*Journal of Mathematics Teacher Education, 14*(2), 133–148.CrossRefGoogle Scholar - Cleveland, W. S., & McGill, R. (1984). Graphical perception: Theory, experimentation, and application to the development of graphical methods.
*Journal of the American Statistical Association, 79*(387), 531–554.CrossRefGoogle Scholar - Curriculum Planning and Development Division. (2006).
*Mathematics syllabus primary*. Retrieved from the Singapore Ministry of Education: http://www.moe.edu.sg/education/syllabuses/sciences/files/maths-primary-2007.pdf. - Diezmann, C. M., & Lowrie, T. (2009). An instrument for assessing primary students’ knowledge of information graphics in mathematics.
*Assessment in Education: Principles, Policy and Practice, 16*(2), 131–147.CrossRefGoogle Scholar - Educational Testing Centre NSW. (2002).
*Primary school mathematics competition, year 4*. Sydney, Australia: University of New South Wales.Google Scholar - Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. A. Cuoco & F. R. Curcio (Eds.),
*The roles of representation in school mathematics*(pp. 1–23). Reston, VA: National Council of Teachers of Mathematics.Google Scholar - Hegarty, M., & Stull, A. (2012). Visuospatial thinking. In K. J. Holyoak & R. G. Morrison (Eds.),
*The Oxford handbook of thinking and reasoning*(pp. 606–630). London: Oxford University Press.Google Scholar - Ho, S. Y., & Lowrie, T. (2014). The model method: Students’ performance and its effectiveness.
*Journal of Mathematical Behavior, 35*, 87–100.CrossRefGoogle Scholar - Jones, K. (2000). Critical issues in the design of the geometry curriculum. In B. Barton (Ed.),
*Readings in mathematics education*(pp. 75–90). Auckland, New Zealand: University of Auckland.Google Scholar - Kell, H. J., Lubinski, D., Benbow, C. P., & Steiger, J. H. (2013). Creativity and technical innovation spatial ability’s unique role.
*Psychological Science, 24*(9), 1831–1836.CrossRefGoogle Scholar - Kosslyn, S., & Miller, G. W. (2013).
*Top brain, bottom brain: Surprising insights into how you think*. New York, NY: Simon & Schuster.Google Scholar - Kosslyn, S. M. (1983).
*Ghosts in the mind’s machine*. New York: Norton.Google Scholar - Kosslyn, S. M. (2006).
*Graph design for the eye and mind*. New York: Oxford University Press.CrossRefGoogle Scholar - Kozhevnikov, M., & Hegarty, M. (2001). A dissociation between object manipulation spatial ability and spatial orientation ability.
*Memory & Cognition, 29*(5), 745–756.CrossRefGoogle Scholar - Kozhevnikov, M., Hegarty, M., & Mayer, R. (1999).
*Students’ use of imagery in solving qualitative problems in kinematics*. Washington DC: US Department of Education (ERIC Document Reproduction, 433 239).Google Scholar - Linn, M., & Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta-analysis.
*Child Development, 56*(6), 1479–1498.CrossRefGoogle 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.CrossRefGoogle Scholar - Lowrie, T., & Diezmann, C. M. (2007). Solving graphics problems: Student performance in the junior grades.
*Journal of Educational Research, 100*(6), 369–377.CrossRefGoogle Scholar - Lowrie, T., & Diezmann, C. M. (2009). National numeracy tests: A graphic tells a thousand words.
*Australian Journal of Education, 53*(2), 141–158.CrossRefGoogle 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*(2), 169–187.CrossRefGoogle Scholar - Lowrie, T., & Logan, T. (2007). Using spatial skills to interpret maps: Problem solving in realistic contexts.
*Australian Primary Mathematics Classroom, 12*(4), 14–19.Google Scholar - Lowrie, T., & Logan, T. (2015). The role of test-mode effect: Implications for assessment practices and item design. In C. Vistro-Yu (Ed.),
*In pursuit of quality mathematics for all, Proceedings of the 7th ICMI-East Asia Regional Conference on Mathematics Education*(pp. 649–655). Cebu, Philippines: Philippine Council of Mathematics Teacher Educators (MATHTED), Inc..Google Scholar - Lowrie, T., Logan, T., & Ramful, A. (2016). Cross cultural comparison of grade 6 students’ performance and strategy use on graphic and non-graphic tasks.
*Learning and Individual Differences, 52*, 97–108.CrossRefGoogle Scholar - Lowrie, T., Logan, T., & Ramful, A. (2017). Visuospatial training improves elementary students’ mathematics performance.
*British Journal of Educational Psychology, 87*(2), 170–186.CrossRefGoogle Scholar - Lowrie, T., Ramful, A., Logan, T., & Ho, S. Y. (2014). Do students solve graphic tasks with spatial demands differently in digital form? In J. Anderson, M. Cavanagh, & A. Prescott (Eds.),
*Curriculum in focus: Research guided practice, Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia*(Vol. 2, pp. 429–436). Sydney: MERGA.Google Scholar - Mackinlay, J. (1999). Automating the design of graphical presentations of relational information. In S. K. Card, J. D. Mackinlay, & B. Schneiderman (Eds.),
*Readings in information visualization: Using vision to think*(pp. 66–81). San Francisco, CA: Morgan Kaufmann.Google Scholar - Ministry of Education, Curriculum Planning and Development Division. (2006).
*Mathematics syllabus primary*. Retrieved from the Singapore Ministry of Education website: http://www.moe.edu.sg/education/syllabuses/sciences/files/maths-primary-2007.pdf. - Nath, S., & Szücs, D. (2014). Construction play and cognitive skills associated with the development of mathematical abilities in 7-year-old children.
*Learning and Instruction, 32*, 73–80.CrossRefGoogle Scholar - National Research Council. (2006).
*Learning to think spatially: GIS as a support system in the K—12 curriculum*. Washington, DC: National Academy Press.Google Scholar - Newcombe, N. S. (2013). Seeing relationships: Using spatial thinking to teach science, mathematics, and social studies.
*American Educator, 37*(1), 26–40.Google Scholar - Newcombe, N. S., & Frick, A. (2010). Early education for spatial intelligence: Why, what, and how.
*Mind, Brain, and Education, 4*(3), 102–111.CrossRefGoogle Scholar - Ng, O., & Sinclair, N. (2015). Young children reasoning about symmetry in a dynamic geometry environment.
*ZDM Mathematics Education, 47*(3), 421–434.CrossRefGoogle Scholar - Ontario Ministry of Education [OME]. (2008).
*Geometry and spatial sense, grades 4 to 6: A guide to effective instruction in mathematics, kindergarten to grade 6*. Ontario: Queen’s Printer for Ontario.Google Scholar - Ontario Ministry of Education [OME]. (2014).
*Paying attention to spatial reasoning: Support document for paying attention to mathematics education*. Ontario: Queen’s Printer for Ontario.Google Scholar - Pape, S. J., & Tchoshanov, M. A. (2001). The role of representation(s) in developing mathematical understanding.
*Theory Into Practice, 4*(2), 118–127.CrossRefGoogle Scholar - Polya, G. (1965).
*Mathematical discovery; on understanding and teaching problem solving*. Hoboken: Wiley.Google Scholar - Porter, A. (1989). A curriculum out of balance: The case of elementary school mathematics.
*Educational Researcher, 18*(5), 9–15.Google Scholar - Postigo, Y., & Pozo, J. I. (2004). On the road to graphicacy: The learning of graphical representational systems.
*Educational Psychology, 24*(5), 623–644.CrossRefGoogle Scholar - Queensland Studies Authority. (2001).
*Aspects of numeracy test, year 3*. Camberwell, Australia: Australian Council for Educational Research.Google Scholar - Queensland Studies Authority. (2009).
*3579 Test reporting handbook: 2009 national assessment program—Literacy and numeracy*. Brisbane, Australia: Author.Google Scholar - Queensland Studies Authority. (2010).
*3579 Test reporting handbook: 2010 national assessment program—Literacy and numeracy*. Brisbane, Australia: Author.Google Scholar - Ramful, A., Lowrie, T., & Logan, T. (2016). Measurement of spatial ability: Construction and validation of the spatial reasoning instrument for middle school students.
*Journal of Psychoeducational Assessment., 35*, 709. https://doi.org/10.1177/0734282916659207CrossRefGoogle Scholar - Sarfaty, Y., & Patkin, D. (2013). The ability of second graders to identify solids in different positions and to justify their answer: Original research.
*Pythagoras, 34*(1), 1–10.CrossRefGoogle Scholar - ServiceOntario Publications. (2014).
*Paying attention to spatial reasoning, K-12: Support document for paying attention to mathematics education*. Retrieved from http://www.edu.gov.on.ca/eng/literacynumeracy/LNSPayingAttention.pdf. - Shah, P., & Miyake, A. (2005).
*The Cambridge handbook of visuospatial thinking*. New York: Cambridge University Press.CrossRefGoogle Scholar - Shea, D. L., Lubinski, D., & Benbow, C. P. (2001). Importance of assessing spatial ability in intellectually talented young adolescents: A 20-year longitudinal study.
*Journal of Educational Psychology, 93*, 604.CrossRefGoogle Scholar - Sinclair, N., & Bruce, C. (2015). New opportunities in geometry education at the primary school.
*ZDM – The International Journal on Mathematics Education, 47*(3), 319.CrossRefGoogle Scholar - Singapore Examinations and Assessment Board. (2009).
*PSLE Examination Questions Mathematics 2005–2009*(Part A, Item 21, p.6). Singapore, SEAB.Google Scholar - Slotnick, S. D., Thompson, W. L., & Kosslyn, S. M. (2005). Visual mental imagery induces retinotopically organized activation of early visual areas.
*Cerebral Cortex, 15*(10), 1570–1583.CrossRefGoogle Scholar - Taylor, H. A., & Hutton, A. (2013). Think3d!: Training spatial thinking fundamental to STEM education.
*Cognition and Instruction, 31*(4), 434–455.CrossRefGoogle 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*(5), 367–373.CrossRefGoogle Scholar