An investigation of geometric knowledge in pupils with mild educational needs


Published: Mar 24, 2021
Keywords:
Geometric shapes Geometry Mild educational needs Pictorial and tactile material Solid bodies
Maria Papadam
https://orcid.org/0000-0003-3021-2330
Ioannis Agaliotis
https://orcid.org/0000-0002-3870-8077
Abstract
Geometry is a structural component of mathematics, with increased spatial and design requirements that cannot be easily met by students with mild disabilities. Systematic investigation of the difficulties encountered by students with mild disabilities in their effort to learn Geometry is a prerequisite for the implementation of effective intervention programs. However, research on this issue is relatively scarce. The aim of the present study was to assess the geometric knowledge of 54 students with mild disabilities (learning disabilities or ADHD) who attended the two last classes of elementary school. Participants were asked to recognize, describe and categorize geometric shapes and solid bodies that were presented in tactile mode and through pictorial representations. Semi-structured clinical interviews were used for gathering the data in the context of Curriculum Based Assessment and the Van Hiele’s model of geometrical thinking. Participants of both categories of mild disabilities presented difficulties in distinguishing shapes and bodies, properly using the terminology, and formatting inductive geometrical reasoning. Participants with learning disabilities had higher achievement when dealing with haptic relative to pictorial representations of geometric shapes and bodies. Sixth graders performed better than fifth graders. Results are discussed in terms of the differences between the two categories of mild disabilities as well as with regard to the implementation of intervention programs.
Article Details
  • Section
  • SPECIAL SECTION
Downloads
Author Biographies
Maria Papadam, University of Macedonia

Department of Educational and Social Policy

Ioannis Agaliotis, University of Macedonia

Department of Educational and Social Policy

References
Αγαλιώτης, Ι. (2012). Εκπαιδευτική αξιολόγηση μαθητών με δυσκολίες μάθησης και προσαρμογής: Το αξιολογικό σύστημα μαθησιακών αναγκών. Γρηγόρης.
Αγαλιώτης, Ι. (2013). Διδασκαλία μαθηματικών στην ειδική αγωγή και εκπαίδευση: Φύση και εκπαιδευτική διαχείριση μαθηματικών δυσκολιών. Γρηγόρης.
Αγαλιώτης, Ι., Κόιου, Ε., & Χρυσικού, Β. (2011). Διδάσκοντας Γεωμετρία σε μαθητές με ήπιες εκπαιδευτικές ανάγκες: Γνωστική ανάλυση και διδακτική διαχείριση συστηματικών λαθών. Στο Δ. Γουδήρας (Επιμ.), ΙΔ΄ Διεθνές Συνέδριο Παιδαγωγικής Εταιρείας Ελλάδος «Εκπαίδευση ατόμων με ειδικές ανάγκες: Μια πρόκληση για το σχολείο και την κοινωνία» (σελ. 504–520). Πανεπιστήμιο Μακεδονίας.
Aguiar, A., Eubig, P. A., & Schantz, S. L. (2010). Attention deficit/hyperactiveity disorder: A focused overview for children’s environmental health researchers. Environmental Health Perspectives, 118(12), 1646–1653. https://doi.org/10.1289/ehp.1002326
Barkley, R. A. (Ed.). (2014). Attention-deficit hyperactivity disorder: A handbook for diagnosis and treatment. Guilford Press.
Battista, M. (2011). Conceptualizations and issues related to learning progressions, learning trajectories, and levels of sophistication. The Mathematics Enthusiast, 8(3), 507–569.
Bergstrom, C., & Zhang, D. (2016). Geometry interventions for K-12 students with and without disabilities: A research synthesis. International Journal of Educational Research, 80, 134–154. https://doi.org/10.1016/j.ijer.2016.04.004
Boada, R., Willcutt, E. G., & Pennington, B. F. (2012). Understanding the comorbidity between dyslexia and attention-deficit/hyperactivity disorder. Topics in Language Disorders, 32(3), 264–284. https://doi.org/10.1097/TLD.0b013e31826203ac
Butterworth, B. (2010). Foundational numerical capacities and the origins of dyscalculia. Trends in Cognitive Sciences, 14(12), 534–541. https://doi.org/10.1016/j.tics.2010.09.007
Cass, M., Cates, D., Smith, M., & Jackson, C. (2003). Effects of manipulative instruction on solving area and perimeter problems by students with learning disabilities. Learning Disabilities Research and Practice, 18(2), 112–120. https://doi.org/10.1111/1540-5826.00067
Cawley, J. F., Foley, T. E., & Hayes, A. M. (2009). Geometry and measurement: A discussion of status and content options for elementary school students with learning disabilities. Learning Disabilities: A Contemporary Journal, 7(1),21–42.
Clements, D. H. (2003). Teaching and learning geometry. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 151–178). National Council of Teachers of Mathematics.
Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: The case of geometry. Journal of Mathematics Teacher Education, 14(2), 133–148. https://doi.org/10.1007/s10857-11-9173-0
Clements, D. H., Swaminathan, S., Hannibal, M. A. Z., & Sarama, J. (1999). Young children’s concept of shape. Journal for Research in Mathematics Education, 30(2), 192–212. https://doi.org/10.2307/749610
Cohen, L., Manion, L., & Morrison, K. (2008). Μεθοδολογία εκπαιδευτικής έρευνας (Χ. Μητσοπούλου & Μ. Φιλοπούλου, Μτφρ.). Έκφραση. (Έτος έκδοσης πρωτοτύπου 1997).
Dobbins, A., Gagnon, J. C., & Ulrich, T. (2013). Teaching geometry to students with math difficulties using graduated and peer-mediated instruction in a response-to-intervention model. Preventing School Failure: Alternative Education for Children and Youth, 58(1), 17–25. https://doi.org/10.1080/1045988X.2012.743454
Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century: An ICMI study (pp. 37–52). Kluwer.
Edmond, V., Joyal, C. & Poissant, H. (2008). Structural and functional neuroanatomy of attention-deficit hyperactivity disorder (ADHD). L’ Encephale, 35, 107–114. https://doi.org/10.1016/j.encep.2008.01.005
Fuys, D. (1985). Van Hiele levels of thinking in geometry. Education and Urban Society, 17(4), 447–462. https://doi.org/10.1177/0013124585017004008
Gal, H., & Linchevski, L. (2010). To see or not to see: Analyzing difficulties in geometry from the perspective of visual perception. Educational Studies in Mathematics, 74(2), 163–183. https://doi.org/10.1007/s10649-010-9232-y
Galletta, A. (2013). Mastering the semi-structured interview and beyond: From research design to analysis and publication. New York University Press.
Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4–15. https://doi.org/10.1177/00222194040370010201
Geary, D. C., & Hoard, M. K. (2005). Learning disabilities in arithmetic and mathematics. In J. I. D. Campbell (Ed.), The handbook of mathematical cognition (pp. 253−267). Psychology Press.
Germanò, E., Gagliano, A., & Curatolo, P. (2010). Comorbidity of ADHD and dyslexia. Developmental Neuropsychology, 35(5), 475–493. https://doi.org/10.1080/87565641.2010.494748
Grobecker, B., & De Lisi, R. (2000). An investigation of spatial-geometrical understanding in students with learning disabilities. Learning Disability Quarterly, 23(1), 7–22. https://doi.org/10.2307/1511096
Hart, S. A., Petrill, S. A., Willcutt, E., Thompson, L. A., Schatschneider, C., Deater-Deckard, K., & Cutting, L. E. (2010). Exploring how symptoms of attention-deficit/hyperactivity disorder are related to reading and mathematics performance: General genes, general environments. Psychology Science, 21(11),1708–1715. https://doi.org/10.1177/0956797610386617
Hock, T. T., Tarmizi, R. A., Yunus, A. S. M., & Ayub, A. F. (2015). Understanding the primary school students’ Van Hiele levels of geometry thinking in learning shapes and spaces: A Q-methodology. Eurasia Journal of Mathematics, Science and Technology Education, 11(4), 793–802. https://doi.org/10.12973/eurasia.2015.1439a
Kang, H. W., & Zentall, S. S. (2011). Computer-generated geometry instruction: A preliminary study. Educational Technology Research and Development, 59(6), 783–797. http://doi.org/10.1007/s11423-011-9186-5
Maier, S., & Benz, C. (2013). Selecting shapes–how to children identify familiar shapes in two different educational settings. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), Proceedings of the 8th Congress of European Research in Mathematics Education (CERME8) (pp. 1–10).
Mammarella, I. C., Giofrè, D., & Caviola, S. (2017). Learning geometry: The development of geometrical concepts and the role of cognitive processes. In D. Geary, D. Berch, R. J. Ochsendorf, & K. Mann Koeple (Eds.), Acquisition of complex arithmetic skills and higher-order mathematics concepts (pp. 221–246). Elsevier. https://doi.org/10.1016/B978-0-12-805086-6.00010-2
Miller, A. C., Keenan, J. M., Betjemann, R. S., Willcutt, E. G., Pennington, B. F., & Olson, R. K. (2013). Reading comprehension in children with ADHD: Cognitive underpinnings of the centrality deficit. Journal of Abnormal Child Psychology, 41(3), 473–483. https://doi.org/10.1007/s10802-012-9686-8
Montague, M. (2008). Self-regulation strategies to improve mathematical problem solving for students with learning disabilities. Learning Disability Quarterly, 31(1), 37–44. https://doi.org/10.2307/30035524
Ramlan, A. M. (2016). The effect of Van Hiele learning model toward geometric reasoning ability based on self-efficacy of senior high school students. Journal of Mathematics Education, 1(2), 62–71. https://doi.org/10.31327/jomedu.v1i2%20July.54
Siew, N. M., & Abdullah, S. (2013). Learning geometry in a large-enrollment class: Do tangrams help in developing students’ geometric thinking. British Journal of Education, Society and Behavioural Science, 2(3), 239–259. https://doi.org/10.9734/BJESBS/2012/1612
Siew, N. M., Chang, C. L., & Abdullah, M. R. (2013). Facilitating students’ geometric thinking through Van Hiele’s phase-based learning using tangram. Journal of Social Science, 9(3), 101–111. https://doi.org/10.3844/jssp.2013.101.111
Skounti, M., Giannoukas, S., Dimitriou, E., Nikolopoulou, S., Linardakis, E., & Philalithis, A. (2010). Prevalence of attention deficit hyperactivity disorder in schoolchildren in Athens, Greece. Association of ADHD subtypes with social and academic impairment. ADHD Attention Deficit and Hyperactivity Disorders, 2(3), 127–132. https://doi.org/10.1007/s12402-010-0029-8
Sowerby, P., Seal, S., & Tripp, G. (2011). Working memory deficits in ADHD: The contribution of age, learning/language difficulties, and task parameters. Journal of Attention Disorders, 15(6), 461–472. https://doi.org/10.1177/1087054710370674
Tsamir, P., Tirosh, D., & Levenson, E. (2008). Intuitive non-examples: The case of triangles. Education Studies in Mathematics, 69(2), 81–95. https://doi.org/10.1007/s10649-008-9133-5
Van de Walle, A. J. (2005). Μαθηματικά για το δημοτικό και το γυμνάσιο: Μια εξελικτική διδασκαλία (Τ. Α. Τριανταφυλλίδης, Επιμ., Α. Αλεξανδροπούλου & Β. Κομπορόζος, Μτφρ.). Τυπωθήτω-Δαρδανός. (Έτος έκδοσης πρωτοτύπου 1998).
Wang, S., & Kinzel, M. (2014). How do they know it is a parallelogram?: Analysing geometric discourse at Van Hiele Level 3. Research in Mathematics Education, 16(3), 288–305. https://doi.org/10.1080/14794802.2014.933711
Wheatley, J. (2011). An investigation of three-dimensional problem solving and levels of thinking among high school geometry students. [Master’s thesis, Central Washington University]. https://pdfs.semanticscholar.org/994a/d70f32b0dd2b38342da230b6275e08f9032e.pdf
Wu, D. B., & Ma, H. L. (2006). The distributions of Van Hiele levels of geometric thinking among 1st through 6th graders. In J. Novotna, M. Kratka & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 409–416). PME.
Yang, J. C., & Chen, S. Y. (2010). Effects of gender differences and spatial abilities within a digital pentominoes game. Computers and Education, 55(3), 1220–1233. https://doi.org/10.1016/j.compedu.2010.05.019
Zhang, D., Ding, Y., Stegall, J., & Mo, L. (2012). The effect of visual‐chunking‐representation accommodation on geometry testing for students with math disabilities. Learning Disabilities Research and Practice, 27(4), 167–177. https://doi.org/10.1111/j.1540-5826.2012.00364.x
Zhang, D., Wang, Q., Ding, Y., & Liu, J. (2014). Testing accommodation or modification?: The effects of integrated object representation on enhancing geometry performance in children with and without geometry difficulties. Journal of Learning Disabilities, 47(6), 569–583. https://doi.org/10.1177/0022219413507602
Most read articles by the same author(s)