Skip to main content
SpringerLink
Log in

Facilitating the development of Preservice teachers’ proportional reasoning in geometric similarity problems using augmented reality activities

  • Published:
Education and Information Technologies Aims and scope Submit manuscript

Abstract

The literature reports preservice teachers’ overuse of proportionality when solving geometric similarity problems with nonproportional relationships. Changing this type of error is reported as difficult even after applying certain interventions. As a solution to this type of error, this study used augmented reality activities to facilitate the development of preservice mathematics teachers’ proportional reasoning. The data of this qualitative study included 17 preservice teachers’ written responses to a paper-and-pencil test with five problems, which had been applied before and after the implementation of the augment reality activities, and video recordings collected during the augment reality implementation process. A case study methodology was used in designing the study in which the collected data were analyzed using a content analysis method. The preservice teachers’ first test responses showed that although they were good at solving problems with regular figures, they had difficulty solving the problem with irregular figures. In this specific problem, the preservice teachers expected a proportional relationship between the areas of the two irregular figures. Their difficulties appeared to be a result of not being able to calculate the areas of these two figures by tiling or multiplying length and width that they used for regular figures. After the implementation of the augmented reality activities, which provided a dynamic representation of similar figures, the preservice teachers’ overuse of proportionality drastically decreased. This finding suggested the contribution of the augmented reality technology on the development of the preservice teachers’ proportional reasoning.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Alcañiz, M., Contero, M., Pérez-López, D. C., & Ortega, M. (2010). Augmented reality technology for education. In S. Soomro (Ed.), New achievements in technology education and development (pp. 247–256). Rijeka: IntechOpen. https://doi.org/10.5772/9228.

    Chapter  Google Scholar 

  • Arican, M. (2019). Preservice mathematics teachers’ understanding of and abilities to differentiate proportional relationships from nonproportional relationships. International Journal of Science and Mathematics Education, 17(7), 1423–1443. https://doi.org/10.1007/s10763-018-9931-x.

    Article  Google Scholar 

  • Arican, M., Koklu, O., Olmez, I. B., & Baltaci, S. (2018). Preservice middle grades mathematics teachers’ strategies for solving geometric similarity problems. International Journal of Research in Education and Science, 4(2), 502–516. https://doi.org/10.21890/ijres.428297.

    Article  Google Scholar 

  • Ayan, R., & Isiksal-Bostan, M. (2019). Middle school students’ proportional reasoning in real life contexts in the domain of geometry and measurement. International Journal of Mathematical Education in Science and Technology, 50(1), 65–81. https://doi.org/10.1080/0020739x.2018.1468042.

    Article  Google Scholar 

  • Beckmann, S. (2013). Mathematics for elementary teachers. Boston: Pearson.

    Google Scholar 

  • Ben-Chaim, D., Keret, Y., & Ilany, B. (2007). Designing and implementing authentic investigative proportional reasoning tasks: The impact on preservice mathematics teachers’ content and pedagogical knowledge and attitudes. Journal of Mathematics Teacher Education, 10, 333–340. https://doi.org/10.1007/s10857-007-9052-x.

    Article  Google Scholar 

  • Brown, R, E., Orrill, C, H., & Park, J. (2020). Exploring differences in practicing teachers’ knowledge use in a dynamic and static proportional task. Mathematics Education Research Journal, 1–18. https://doi.org/10.1007/s13394-020-00350-x.

  • Cerqueira, C., & Kirner, C. (2012). Developing educational applications with a non-programming augmented reality authoring tool. Proceedings of World Conference on Educational Multimedia, Hypermedia, and Telecommunications (pp. 2816–2825).

  • Chen, C. J. (2006). Are spatial visualization abilities relevant to virtual reality? E-Journal of Instructional Science and Technology, 9(2), 1–16.

    Google Scholar 

  • Coimbra, M. T., Cardoso, T., & Mateus, A. (2015). Augmented reality: An enhancer for higher education students in math’s learning. Procedia Computer Science, 67, 332–339. https://doi.org/10.1016/j.procs.2015.09.277.

    Article  Google Scholar 

  • Common Core Standards Writing Team (2011). Progressions for the Common Core State Standards for Mathematics (draft), 6–7, ratios and proportional relationships. Retrieved from http://math.arizona.edu/~ime/progressions/.

  • Cox, D. C. (2013). Similarity in middle school mathematics: At the crossroads of geometry and number. Mathematical Thinking and Learning, 15(1), 3–23. https://doi.org/10.1080/10986065.2013.738377.

    Article  Google Scholar 

  • Cox, D. C., & Lo, J. J. (2014). Detecting distortion: Bridging visual and quantitative reasoning on similarity tasks. Mathematics Education Research Journal, 26(1), 1–23.

    Article  Google Scholar 

  • Cunningham, R. F., & Rappa, A. (2016). Survey of mathematics teachers’ static and transformational performance and perspectives for teaching similarity. European Journal of Science and Mathematics Education, 4(4), 440–446.

    Article  Google Scholar 

  • De Bock, D., Verschaffel, L., & Janssens, D. (1998). The predominance of the linear model in secondary school students’ solutions of word problems involving length and area of similar plane figures. Educational Studies in Mathematics, 35(1), 65–83.

    Article  Google Scholar 

  • De Bock, D., Van Dooren, W., Janssens, D., & Verschaffel, L. (2002). Improper use of linear reasoning: An in-depth study of the nature and the irresistibility of secondary school students’ errors. Educational Studies in Mathematics, 50(3), 311–334.

    Article  Google Scholar 

  • Denton, J. (2017). Transforming mathematics: Using dynamic geometry software to strengthen understanding of enlargement and similarity. Warwick Journal of Education, 1(1), 69–84.

    Google Scholar 

  • Ekawati, R., Lin, F. L., & Yang, K. L. (2015). Developing an instrument for measuring teachers’ mathematics content knowledge on ratio and proportion: A case of Indonesian primary teachers. International Journal of Science and Mathematics Education, 13(1), 1–24.

    Article  Google Scholar 

  • Estapa, A., & Nadolny, L. (2015). The effect of an augmented reality enhanced mathematics lesson on student achievement and motivation. Journal of STEM Education, 16(3), 40–48.

  • Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education, Monograph, 3, 1–196. https://doi.org/10.2307/749957.

    Article  Google Scholar 

  • Gerretson, H. (2004). Pre-service elementary teachers’ understanding of geometric similarity: The effect of dynamic geometry software. Focus on Learning Problems in Mathematics, 26(3), 12–23.

    Google Scholar 

  • Haniff, D, J., & Baber, C. (2003). User evaluation of augmented reality systems. In Proceedings of the Seventh International Conference on Information Visualization (pp. 505–511). London, UK. https://doi.org/10.1109/iv.2003.1218032.

  • Hohenwarter, M., & Jones, K. (2007). Ways of linking geometry and algebra: The case of Geogebra. Proceedings of the British Society for Research into Learning Mathematics, 27(3), 126–131.

  • Hsieh, H. F., & Shannon, S. E. (2005). Three approaches to qualitative content analysis. Qualitative Health Research, 15(9), 1277–1288.

    Article  Google Scholar 

  • Hull, L, S, H. (2000). Teachers’ mathematical understanding of proportionality: Links to curriculum, professional development, and support (Unpublished doctoral dissertation). The University of Texas at Austin, Austin, TX.

  • Jesionkowska, J., Wild, F., & Deval, Y. (2020). Active learning augmented reality for STEAM education—A case study. Education Sciences, 10(8), 198. https://doi.org/10.3390/educsci10080198.

    Article  Google Scholar 

  • Kaufmann, H. (2004). Geometry education with augmented reality (Unpublished doctoral dissertation). Vienna: Vienna University of Technology.

  • Kaufmann, H., & Dünser, A. (2007). Summary of usability evaluations of an educational augmented reality application. In Proceedings of the Second International Conference on Virtual Reality (pp. 660–669). Beijing, China. https://doi.org/10.1007/978-3-540-73335-5_71.

  • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics (p. 10.17226/9822). Washington, DC: National Academy Press.

    Google Scholar 

  • Lamon, S. (1993). Ratio and proportion: Connecting content and children’s thinking. Journal for Research in Mathematics Education, 24(1), 41–61. https://doi.org/10.2307/749385.

    Article  Google Scholar 

  • Lamon, S. (2007). Rational numbers and proportional reasoning: Toward a theoretical research method for research. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol 1, pp. 629–667). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Lee, H. S., & Yim, J. (2014). Pursuing coherence among proportionality, linearity, and similarity: Two pathways from preservice teachers’ geometric representations. The Mathematics Enthusiast, 11(3), 541–554.

    Google Scholar 

  • Lehrer, R., Strom, D., & Confrey, J. (2002). Grounding metaphors and inscriptional resonance: Children’s emerging understanding of mathematical similarity. Cognition and Instruction, 20(3), 359–398. https://doi.org/10.1207/s1532690xci2003_3.

    Article  Google Scholar 

  • Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 93–118). VA: Reston.

    Google Scholar 

  • Lindgren, R., & Moshell, J, M. (2011). Supporting children’s learning with body-based metaphors in a mixed reality environment. In Proceedings of the 10th International Conference on Interaction Design and Children (pp. 177–180). Association for Computing Machinery, NY, USA. https://doi.org/10.1145/1999030.1999055.

  • Lobato, J., & Ellis, A. (2010). Developing essential understanding of ratios, proportions, and proportional reasoning for teaching mathematics: Grades 6–8. National Council of teachers of mathematics. Reston, VA.

  • Milgram, P., Takemura, H., Utsumi, A., & Kishino, F. (1995). Augmented reality: A class of displays on the reality-virtuality continuum. In Telemanipulator and telepresence technologies (Vol. 2351, pp. 282–292). International Society for Optics and Photonics. https://doi.org/10.1117/12.197321.

  • Mitchell, R. (2011). Alien contact!: Exploring teacher implementation of an augmented reality curricular unit. Journal of Computers in Mathematics and Science Teaching, 30(3), 271–302.

    Google Scholar 

  • Mitchell, R., & DeBay, D. (2012). Get real: Augmented reality for the classroom. Learning & Leading with Technology, 40(2), 16–21.

    Google Scholar 

  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.

  • Özçakır, B. (2017). Fostering spatial abilities of seventh graders through augmented reality environment in mathematics education: A design study (Unpublished doctoral dissertation). Ankara: Middle East Technical University.

  • Özdemir, D., & Özçakır, B. (2019). Artırılmış gerçeklik destekli matematik eğitiminin 5.sınıf öğrencilerinin başarı ve tutumlarına etkisinin incelenmesi [An analysis of the effects of augmented reality activities in teaching fractions on 5th grade students’ mathematics achievement and attitudes]. Adıyaman Üniversitesi Eğitim Bilimleri Dergisi, 9(1), 21–41. https://doi.org/10.17984/adyuebd.495731.

  • Seago, N., Jacobs, J., Driscoll, M., Nikula, J., Matassa, M., & Callahan, P. (2013). Developing teachers' knowledge of a transformations-based approach to geometric similarity. Mathematics Teacher Educator, 2(1), 74–85.

    Article  Google Scholar 

  • Seago, N. M., Jacobs, J. K., Heck, D. J., Nelson, C. L., & Malzahn, K. A. (2014). Impacting teachers’ understanding of geometric similarity: Results from field testing of the learning and teaching geometry professional development materials. Professional Development in Education, 40(4), 627–653. https://doi.org/10.1080/19415257.2013.830144.

    Article  Google Scholar 

  • Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2004). Remedying secondary school students’ illusion of linearity: A teaching experiment aiming at conceptual change. Learning and Instruction, 14(5), 485–501. https://doi.org/10.1016/j.learninstruc.2004.06.019.

    Article  Google Scholar 

  • Vincenzi, D, A., Valimont, B., Macchiarella, N., Opalenik, C., Gangadharan, S, N., & Majoros, A, E. (2003). The effectiveness of cognitive elaboration using augmented reality as a training and learning paradigm. In Proceedings of the Human Factors and Ergonomics Society (pp. 2054–2058). Denver, CO, USA. https://doi.org/10.1037/e576882012-008.

  • Wang, X., & Dunston, P. S. (2006). Compatibility issues in augmented reality systems for AEC: An experimental prototype study. Automation in Construction, 15(3), 314–326. https://doi.org/10.1016/j.autcon.2005.06.002.

    Article  Google Scholar 

  • Yin, R, K. (2009). Case study research: Design and methods (Vol. 5). Sage.

Download references

Acknowledgements

We would like to thank to Dr. Wim Van Dooren and Dr. Lieven Verschaffel for their valuable feedbacks on earlier drafts of this manuscript. The first author also thanks to the Scientific and Technological Research Council of Turkey (TUBITAK) for providing a grant for a research stay at KU Leuven during when he was able to complete writing this manuscript.

Availability of data and materials

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Author information

Authors and Affiliations

  1. Department of Mathematics and Science Education, Kirsehir Ahi Evran University, Kırşehir, Turkey

    Muhammet Arican

  2. Department of Mathematics and Science Education, Alanya Alaaddin Keykubat University, Alanya, Turkey

    Bilal Özçakir

Authors
  1. Muhammet Arican
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bilal Özçakir
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

MA taught the course and designed geometric similarity test items. BO designed augmented reality activities. Both authors reviewed the test items and augmented reality activities, analyzed preservice teachers’ responses, and contributed to writing of the necessary sections of the manuscript. The authors read and approved the final manuscript.

Corresponding author

Correspondence to Muhammet Arican.

Ethics declarations

Competing interests

The authors declare no potential competing interests with respect to the research, authorship, and publication of this article.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

1.1 The Geometric Similarity Test

figure afigure a

1.2 The Augmented Reality Activities

figure cfigure cfigure cfigure c

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arican, M., Özçakir, B. Facilitating the development of Preservice teachers’ proportional reasoning in geometric similarity problems using augmented reality activities. Educ Inf Technol 26, 2327–2353 (2021). https://doi.org/10.1007/s10639-020-10359-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10639-020-10359-1

Keywords

Search

Navigation