Hypothetical learning trajectory in student’s spatial abilities to learn geometric transformation

Ricki Yuliardi(1*), Rizky Rosjanuardi(2)

(1) Department of Mathematics Education, Universitas Pendidikan Indonesia, Indonesia & Department of Mathematics Education, STKIP Muhammadiyah Kuningan, Indonesia
(2) Department of Mathematics Education, Universitas Pendidikan Indonesia, Indonesia
(*) Corresponding Author

Abstract

The relationship between spatial conceptions and students' spatial abilities is still rarely studied specifically, even though this is the basis for students to think in learning geometry. This paper aims to explore spatial abilities and the development of spatial ability theory, discusses the relationship between spatial conceptions in students' understanding, and how to develop HLT (Hypothetical Learning Trajectory)in transformation geometry learning. HLT design consists of three stages: initial design, experimental, and retrospective analysis. The results of HLT are then refined into LIT (Local Instructional Trajectory). Then this paper present the empirical results of the perceptions of twenty  9th grade students in one of Islamic private school in Kabupaten Kuningan, West Java, Indonesia, towards the corresponding geometric and math questions. Literature review analysis was used to analyze the retrieved articles. At the end of the paper, we explain and discuss how to apply mathematical conceptions in learning geometry. This research is expected to be a guidance for teachers to develop learning in accordance with the students' spatial thinking process in studying geometry.

Keywords

Spatial abilities, spatial conception, geometric transformations, hypothetical learning trajectory

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References

Bakker, A., & van Eerde, D. (2015). An Introduction to Design-Based Research with an Example From Statistics Education (pp. 429–466). https://doi.org/10.1007/978-94-017-9181-6_16

Borst, G., & Kosslyn, S. M. (2008). Visual mental imagery and visual perception: Structural equivalence revealed by scanning processes. Memory and Cognition, 36(4), 849–862. https://doi.org/10.3758/MC.36.4.849

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. In Educational Psychology Review (Vol. 30, Issue 3, pp. 947–972). Educational Psychology Review. https://doi.org/10.1007/s10648-018-9432-z

Burte, H., Gardony, A. L., Hutton, A., & Taylor, H. A. (2017). Think3d!: Improving mathematics learning through embodied spatial training. Cognitive Research: Principles and Implications, 2(1), 1–18. https://doi.org/10.1186/s41235-017-0052-9

Bustang, Zulkardi, Darmawijoyo, Dolk, M., & van Eerde, D. (2013). Developing a local instruction theory for learning the concept of angle through visual field activities and spatial representations. International Education Studies, 6(8), 58–70. https://doi.org/10.5539/ies.v6n8p58

Clements, D. H., & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333(6045), 968–970. https://doi.org/10.1126/science.1204537

Confrey, J., Toutkoushian, E., & Shah, M. (2020). Working at scale to initiate ongoing validation of learning trajectory-based classroom assessments for middle grade mathematics. Journal of Mathematical Behavior, 60(September), 100818. https://doi.org/10.1016/j.jmathb.2020.100818

Daro, P., Mosher, F., & Corcoran, T. (2011). Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction. CPRE Research Report. Consortium for Policy Research in Education, 86. Retrieved from http://proxy-remote.galib.uga.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=ED519792&site=ehost-live

Diane F, H. (2003). Sex differences in cognitive abilities (3rd edition). In Applied Cognitive Psychology (Vol. 17, Issue 3). https://doi.org/10.1002/acp.883

Frick, A. (2019). Spatial transformation abilities and their relation to later mathematics performance. Psychological Research, 83(7), 1465–1484. https://doi.org/10.1007/s00426-018-1008-5

Gardner, H. (1999). Frames of Mind, Intelligence Reframed: Multiple Intelligences for The 21st Century. In New York : Basic Book.

Gutiérrez, Á. (1996). Visualization in 3-Dimensional Geometry: In Search of a Framework. Proceedings of the 20th PME Conference, 1(July 1996), 3–19.

Harris, J., Hirsh-Pasek, K., & Newcombe, N. S. (2013). Understanding spatial transformations: Similarities and differences between mental rotation and mental folding. Cognitive Processing, 14(2), 105–115. https://doi.org/10.1007/s10339-013-0544-6

Hegarty, M. & Kozhevnikov, M. (1999). Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), 684–689. https://doi.org/10.1037//0022-0663.91.4.684

Kartianom, K & Retnawari, H. (2018). Why are Their Mathematical Learning Achievements Different? Re-Analysis TIMSS 2015 Data in Indonesia, Japan and Turkey. International Journal on New Trends in Education and Their Implications, 9(2), 33–46.

Kragten, M., Admiraal, W., & Rijlaarsdam, G. (2015). Students’ Learning Activities While Studying Biological Process Diagrams. International Journal of Science Education, 37(12), 1915–1937. https://doi.org/10.1080/09500693.2015.1057775

Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: a meta-analysis. Child Development, 56(6), 1479–1498. https://doi.org/10.1111/j.1467-8624.1985.tb00213.x

Lubinski, D. (2010). Spatial ability and STEM: A sleeping giant for talent identification and development. Elsevier Personality and Individual Differences, 49(4), 344–351. https://doi.org/10.1016/j.paid.2010.03.022

Maeda, Y., & Yoon, S. Y. (2013). A Meta-Analysis on Gender Differences in Mental Rotation Ability Measured by the Purdue Spatial Visualization Tests: Visualization of Rotations (PSVT:R). Educational Psychology Review, 25(1), 69–94. https://doi.org/10.1007/s10648-012-9215-x

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

Mix, K. S., Levine, S. C., Cheng, Y. L., Young, C., Hambrick, D. Z., Ping, R., & Konstantopoulos, S. (2016). Separate but correlated: The latent structure of space and mathematics across development. Journal of Experimental Psychology: General, 145(9), 1206–1227. https://doi.org/10.1037/xge0000182

Moreno, R., & Mayer, R. E. (1999). Cognitive principles of multimedia learning: The role of modality and contiguity. Journal of Educational Psychology, 91(2), 358–368. https://doi.org/10.1037//0022-0663.91.2.358

National Council of Teacher Mathematics. (2000). Principles Standards and for School Mathematics. Reston VA: NCTM.

Newcombe, N. S. (2013). Seeing Relationships. American Educator, 26–32.

Ningsih, Y. L., & Paradesa, R. (2018). Improving students’ understanding of mathematical concept using maple. Journal of Physics: Conference Series, 948(1). https://doi.org/10.1088/1742-6596/948/1/012034

Nuraida, I., & Amam, A. (2019). Hypothetical Learning Trajectory in Realistic Mathematics Education To Improve the Mathematical Communication of Junior High School Students. Infinity Journal, 8(2), 247. https://doi.org/10.22460/infinity.v8i2.p247-258

Nurjanah, Latif, B., Yuliardi, R., & Tamur, M. (2020). Computer-assisted learning using the Cabri 3D for improving spatial ability and self- regulated learning. Heliyon, 6(July), e05536. https://doi.org/10.1016/j.heliyon.2020.e05536

Nurjanah, Yuliardi, R., & Luthfi, A. F. (2020). Learning mathematics assisted by adobe flash software to improve mathematical reasoning ability students ongeometry concepts. Journal of Physics: Conference Series, 1567(3). https://doi.org/10.1088/1742-6596/1567/3/032011

Parsons, T. D., Rizzo, A. R., Van Der Zaag, C., McGee, J. S., & Buckwalter, J. G. (2005). Gender differences and cognition among older adults. Aging, Neuropsychology, and Cognition, 12(1), 78–88. https://doi.org/10.1080/13825580590925125

Philip, Clarkson; Presmeg, N. (2004). Critical issues in maths edcation. In Springer. Retrieved from http://onlinelibrary.wiley.com/doi/10.1002/cbdv.200490137/ abstract

Pirrone, C., Nicolosi, A., Passanisi, A., & Di Nuovo, S. (2015). Learning potential in mathematics through imagination and manipulation of building blocks. Mediterranean Journal of Social Sciences, 6(4S3), 152–159. https://doi.org/10.5901/mjss.2015.v6n4s3p152

Pöhler, B., & Prediger, S. (2015). Intertwining lexical and conceptual learning trajectories - A design research study on dual macro-scaffolding towards percentages. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1697–1722. https://doi.org/10.12973/eurasia.2015.1497a

Poltrock, S. E., & Brown, P. (1984). Individual Differences in visual imagery and spatial ability. Intelligence, 8(2), 93–138. https://doi.org/10.1016/0160-2896(84)90019-9

Reilly, D., & Neumann, D. L. (2013). Gender-Role Differences in Spatial Ability: A Meta-Analytic Review. In Sex Roles (Vol. 68, Issues 9–10). https://doi.org/10.1007/s11199-013-0269-0

Retnawati, H., Djidu, H., Kartianom, Apino, E., & Anazifa, R. D. (2018). Teachers’ knowledge about higher-order thinking skills and its learning strategy. Problems of Education in the 21st Century, 76(2), 215–230.

Rezky, R. (2019). Hypothetical Learning Trajectory (HLT) dalam Perspektif Psikologi Belajar Matematika. Ekspose: Jurnal Penelitian Hukum Dan Pendidikan, 18(1), 762–769. https://doi.org/10.30863/ekspose.v18i1.364

Sack, J. & Vazquez, I. (2011). Development of a Learning Trajectory to Conceptualize. Conference: 35th Annual Conference of The, 1, 89–96.

Simon, M. A. (2017). Explicating mathematical concept and mathematicalconception as theoretical constructs for mathematics education research. Educational Studies in Mathematics, 94(2), 117–137. https://doi.org/10.1007/s10649-016-9728-1

Simon, M. A. (2020). Reconstructing Mathematics Pedagogy from a Constructivist Perspective. Journal for Research in Mathematics Education, 26(2), 114–145. https://doi.org/10.5951/jresematheduc.26.2.0114

Simon, M. A., Kara, M., Placa, N., & Avitzur, A. (2018). Towards an integrated theory of mathematics conceptual learning and instructional design: The Learning Through Activity theoretical framework. Journal of Mathematical Behavior, 52(April), 95–112. https://doi.org/10.1016/j.jmathb.2018.04.002

Sorby, S., Veurink, N., & Streiner, S. (2018). Does spatial skills instruction improve STEM outcomes? The answer is ‘yes.’ Learning and Individual Differences, 67(August), 209–222. https://doi.org/10.1016/j.lindif.2018.09.001

Supriatna, T. (2017). Local Intruction Theory dalam Pendidikan Matematika Realistik untuk Menumbuhkan Kemampuan Berpikir Logis. Mimbar Pendidikan, 2(2), 173–184. https://doi.org/10.17509/mimbardik.v2i2.8627

Turgut, M., & Nagy-kondor, R. (2013). Spatial Visualization Skills of Hungarian and Turkish Spatial Visualization Skills of Hungarian and Turkish. International Journal for Studies in Mathematics Education 6(1), 168–183.

Ulfa, C., & Wijaya, A. (2019). Expanding hypothetical learning trajectory in mathematics instructional. Journal of Physics: Conference Series, 1320(1). https://doi.org/10.1088/1742-6596/1320/1/012091

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(2), 352–402. https://doi.org/10.1037/a0028446

Yüksel, N. S., & Bülbül, A. (2015). Test development study on the mental rotation ability. Anthropologist, 20(1–2), 128–139. https://doi.org/10.1080/09720073.2015. 11891732

Yuliardi, R. N. (2017). Mathematics Learning Assisted Geogebra using Technologically Aligned Classroom ( TAC ) to Improve Communication Skills of Vocational High School Student Mathematics Learning Assisted Geogebra using Technologically Aligned Classroom ( TAC ) to Improve Comm. IOP Conf. Series: Journal of Physics:, 895 012156. https://doi.org/10.1088/1742-6596/895/1/012156

Yurt, E., & Sunbul, A. M. (2014). A Structural Equation Model Explaining 8th Grade Students’ Mathematics Achievements. Educational Sciences: Theory & Practice, August. https://doi.org/10.12738/estp.2014.4.2193

DOI: 10.23917/jramathedu.v6i3.13338

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