Abstract
What difficulties do seventh grade students have in constructing internal representations and in their mathematizing processes while considering external representations from various viewpoints ? Students received a photograph and were asked to mark where on a map they think the photograph was taken. The results reveal seven types of places where students mark a point and six specific perspective cues they use. Different kinds of difficulty students had in each category are found by examining the relational terms, such as in front of, or right side, used by the students. The study suggests that a possible cause of difficulty in constructing internal representations is a lack of connection between the objects in terms of their position and direction from several perspectives. Finally our data indicates that crating positional relation with information of real world is a significant ability in mathematizing process .
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Notes
- 1.
Author’s translation from the original in Japanese.
References
Bishop, A. J. (1986). What are some obstacles to learning geometry? In Studies in mathematics education (Vol. 5, pp. 141–159). UNESCO.
Bishop, A. J. (2008). Spatial abilities and mathematics education—A review. In Critical issues in mathematics education (pp. 71–81). Springer US.
Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420–464). New York: Macmillan.
Eliot, J. (1987). Models of psychological space. New York, NY: Springer.
Flavell, J. H. (1974). The development of inferences about others. In T. Mischel (Ed.), Understanding other persons (pp. 66–116). Oxford: Basil Blackwell.
Hazama, S. (2004). Research initiative of geometry curriculum development from the perspective of fostering spatial thinking. In Bulletin of Osaka Kyoiku University (pp. 67–70).
Krutetskii, V. A. (1969). An analysis of the individual structure of mathematical abilities in schoolchildren. Soviet Studies in the Psychology of Learning and Teaching Mathematics, 2, 59–104.
Liben, L. S. (1997). Children’s understanding of spatial representations of place: Mapping the methodological landscape. In N. Foreman & R. Gillet (Eds.), Handbook of spatial research paradigms and methodologies, Vol 1: Spatial cognition in the child and adult. Psychology Press.
McGee, M. G. (1979). Human spatial abilities: Psychometric studies and environmental, genetic, hormonal, and neurological influences. Psychological Bulletin, 86(5), 889.
Ministry of Education, Science, Sports and Technology. (2014). Report of national assessment of academic ability (pp. 98–102). http://www.nier.go.jp/14chousakekkahoukoku/report/data/mmath.pdf.
Murakoshi, S. (2012). The process and characteristics of spatial thinking while solving spatial problems. Shizuoka University Research Report, 43, 71–83.
National Research Council Committee on Geography. (2006). Learning to think spatially: GIS as a support system in the K–12 curriculum. Washington, DC: National Academies Press.
Saeki, Y. (1978). Learning and knowledge by building imagery. Tokyo: Toyokan Press.
Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York: Routledge.
Taylor, H. A., & Tversky, B. (1996). Perspective in spatial descriptions. Journal of Memory and Language, 35, 371–391.
Watanabe, M., & Takamatsu, M. (2014). Developmental change from childhood to adulthood of imaginary body movement in spatial perspective taking. The Japanese Journal of Developmental Psychology, 25(2), 111–120.
Yamamoto, H. (2013). The state of mathematics education based on the development of spatial representation ability. The Journal of the Department of Social Welfare, Kansai University of Social Welfare, 16(2), 93–102.
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Arai, M. (2018). Aspects of Spatial Thinking in Problem Solving: Focusing on Viewpoints in Constructing Internal Representations. In: Herbst, P., Cheah, U., Richard, P., Jones, K. (eds) International Perspectives on the Teaching and Learning of Geometry in Secondary Schools. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-77476-3_17
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