A Teaching Experiment on the Construction of a Coordinate System with a Student with Visual Impairment

Year 2023, Volume: 18 Issue: 40, 1423 - 1459, 13.12.2023

Fatma Nur Aktaş Ziya Argün

https://doi.org/10.35675/befdergi.1343644

Abstract

This study aims to investigate the learning processes involved in constructing a coordinate system with a learning trajectory by a student with visual impairment. The study is a teaching experiment designed according to the concrete material-supported hypothetical learning trajectory. The teaching experiment was conducted through clinical interviews with a student with visual impairment for the determination of pre-knowledge, construction of the number line and construction of the coordinate system. The data obtained from the video recordings of the sessions were analysed through ongoing and retrospective analysis. Despite containing visual elements and having learning outcomes different from those in the curriculum, it was discovered at the end of the teaching sessions that a student with visual impairment was able to identify the origin, coordinate axes using a fixed reference unit, determine ordered pairs in the coordinate system, and represent them symbolically. Although the hypothetical learning trajectory's objectives varied in sequence, it was determined that the concrete materials used served the purpose of the activities and allowed students to develop strategies. Thus, the results were presented as a guide for designing curricula, individualized education plans, and educational support materials.

Keywords

Student with visual impairment, learning trajectory, number line, coordinate system, teaching experiment

Project Number

2211-A

Görme Yetersizliğinden Etkilenen Bir Öğrenciyle Koordinat Sisteminin İnşasına İlişkin Bir Öğretim Deneyi

Abstract

Bu araştırmada görme yetersizliğinden etkilenen bir öğrencinin koordinat sisteminin inşasına dair öğrenme süreçlerinin öğrenme yol haritasıyla incelenmesi amaçlanmaktadır. Araştırma somut materyal destekli tahmini öğrenme yol haritasına göre tasarlanan bir öğretim deneyidir. Öğretim deneyi, görme yetersizliğinden etkilenen bir öğrenciyle ön bilgilerin belirlenmesi, sayı doğrusunun inşası ve koordinat sisteminin inşası için yürütülen klinik görüşmelerle gerçekleştirilmiştir. Video kayıtlarından elde edilen veriler süregelen ve geriye dönük analiz yoluyla analiz edilmiştir. Görsel unsurlar içermesine ve öğretim programındaki kazanımlardan farklı hedefler üzerine inşa edilmesine rağmen, öğretim oturumları sonunda görme yetersizliğinden etkilenen öğrencinin orijini belirleyebildiği, başlangıç noktasını referans alarak sabit bir birimle eksenleri koordinatlandırabildiği, sıralı ikilileri koordinat sisteminde belirleyebildiği ve sembolik olarak temsil edebildiği ortaya konulmuştur. Tahmini öğrenme yol haritası hedeflerinin diziliminde farklılık olsa da yararlanılan somut materyallerin etkinliklerin amacına hizmet ettiği ve öğrencilerin stratejiler geliştirmesine fırsat verdiği tespit edilmiştir. Böylece, tasarlanacak olan öğretim programları, bireyselleştirilmiş eğitim programları ve destek eğitim materyalleri için kılavuz niteliğinde sonuçlar sunulmuştur.

Keywords

Görme yetersizliğine sahip öğrenci, öğrenme yol haritası, sayı doğrusu, koordinat sistemi, öğretim deneyi

Supporting Institution

TÜBİTAK

Project Number

2211-A

Thanks

Araştırmaya burs desteği sağlayan TUBİTAK’ a teşekkür ederiz

References

• Agrawal, S. (2004). Teaching mathematics to blind students through programmed learning strategies. Abhijeet Publications.
• Aktaş, F. N. (2020). Görme engelli öğrencilerin cebirsel düşünme süreçlerinin incelenmesi: Öğrenme yol haritaları (Tez Numarası: 611057) [Doktora tezi, Gazi Üniversitesi]. Yükseköğretim Kurulu Ulusal Tez Merkezi.
• Aktaş, F. N., & Argün, Z. (2021). The needs and problems of individuals with visual impairment in mathematics education: The context of algebraic concepts. Ankara University Faculty of Educational Sciences Journal of Special Education, 22(3), 699-723. https://doi.org/10.21565/ozelegitimdergisi.750682
• Arieli-Attali, M., Wylie, E. C., & Bauer, M. I. (2012). The use of three learning progressions in supporting formative assessment in middle school mathematics [Paper presentation]. In annual meeting of the American Educational Research Association, Vancouver, Canada.
• Argün, Z., Arıkan, A., Bulut, S., Halıcıoğlu, S. (2014). Temel matematik kavramların künyesi. Gazi Kitabevi.
• Aydın, P., & Akça-Bayar, S. (2017). Görme yetersizliği: Tanım, sınıflama, yaygınlık ve nedenler. In H. Gürgür, & P. Şafak (Eds.), İşitme ve görme yetersizliği [Hearing and visual impairment] (pp. 128-151). Pegem Akademi.
• Battista, M. T. (2004). Applying cognition-based assessment to elementary school students' development of understanding of area and volume measurement. Mathematical Thinking and Learning, 6(2), 185-204.
• Barrett, J. E., Sarama, J., Clements, D. H., Cullen, C., McCool, J., Witkowski-Rumsey, C., & Klanderman, D. (2012). Evaluating and improving a learning trajectory for linear measurement in elementary grades 2 and 3: A longitudinal study. Mathematical Thinking and Learning, 14(1), 28-54. https://doi.org/10.1080/10986065.2012.625075
• Beswick, K. (2011). Positive experiences with negative numbers. Australian Association of Math Teachers, 67(2), 31–41.
• Brawand, A., & Johnson, N. (2016). Effective methods for delivering mathematics instruction to students with visual impairments. Journal of Blindness Innovation and Research, 6(1). https://nfb.org/images/nfb/publications/jbir/jbir16/jbir060101.html
• Buhagiar, M. A., & Tanti, M. B. (2013). Working toward the inclusion of blind students in Malta: The case of mathematics classrooms. Eğitimde Kuram ve Uygulama, 7(1), 59-78.
• Bülbül, M. Ş. (2013). Görme engelli öğrenciler ile grafik çalışırken nasıl bir materyal kullanılmalıdır. Fen Eğitimi ve Araştırmaları Derneği Fen Bilimleri Öğretimi Dergisi, 1(1), 1-11.
• Bülbül, M. Ş., Garip, B., Cansu, Ü., & Demirtaş, D. (2012). Görme engelliler için matematik öğretim materyali tasarımı: İğneli sayfa. İlköğretim Online, 11(4), 1-9.
• Cahill, H., Linehan, C., McCarthy, J., Bormans, G., & Engelen, J. (1996). Blind and partially sighted students' access to mathematics and computer technology in Ireland and Belgium. Journal of Visual Impairment & Blindness, 90(4), 105-114. https://doi.org/10.1177/0145482X9609000206
• Cansu, Ü. (2014, 20-21 March). Perception of visually ımpaired students equal sign and equality [Paper presentation]. International Conference New Perspectives in Science Education, Italy. https://books.google.com.tr/books.
• Cansu Kurt, Ü. (2015). Görme engelliler ve matematik eğitimi. Sürdürülebilir ve Engelsiz Bilim Eğitimi, 1(1), 21-28. http://fizikli.com/journal/3.pdf.
• Capraro, M. M., Kulm, G., & Capraro, R. M. (2005). Middle grades: Misconceptions in statistical thinking. School Science and Mathematics, 105(4), 165-174. https://doi.org/10.1111/j.1949-8594.2005.tb18156.x
• Chew, Y. C., Tomlinson, B. J., & Walker, B. N. (2014). Graph and number line input and exploration (GNIE) tool technical report. Georgia Institute of Technology. https://smartech.gatech.edu/bitstream/handle/1853/51943/GNIETechnical Report.pdf?sequence=1&isAllowed=y on Agus 2019.
• Clements, D. H. & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81-89.
• Cobb, P. & Steffe L. P. (1983) The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14(2), 83–94.
• Confrey, J., Maloney, A., Nguyen, K., Wilson, P.H., & Mojica, G. (2008). Synthesizing research on rational number reasoning. Working Session at the Research Pre-session of the National Council of Teachers of Mathematics, Salt Lake City, UT.
• Cowan, H. (2011). Knowledge and understanding of function held by students with visual impairments [Thesis number 3493370]. [Doctoral dissertation, The Ohio State University]. ProQuest.
• Dick, T., & Kubiak, E. (1997). Issues and aids for teaching mathematics to the blind. The Mathematics Teacher, 90(5), 344-349. https://doi.org/10.5951/MT.90.5.0344
• Edwards, A. D., & Stevens, R. D. (1994). A multimodal interface for blind mathematics students. INSERM'94, 97-104.
• Edwards, A. D., Stevens, R. D., & Pitt, I. J. (1995). Non-visual representation of mathematical information. University of York.
• Enç, M. (2005). Görme özürlüler gelişim, uyum ve eğitimleri. Gündüz Eğitim ve Yayıncılık.
• Friedlander, A., & Tabach, M. (2001). Promoting multiple representations in algebra. In A. A. Cuoco (Ed.), The roles of representation in school mathematics (pp. 173-185). National Council of Teachers of Mathematics.
• Goldreich, D. & Kanics, I. M. (2003). Tactile acuity is enhanced in blindness. Journal of Neuroscience, 23(8), 3439-3445. https://doi.org/10.1523/JNEUROSCI.23-08-03439.2003
• Groenveld, M. (1993). Effects of visual disability on behaviour and the family. In A.R. Fielder, A.B., Best, & M.C. Bax, (Eds.), The management of visual impairment in childhood (pp. 64-77). Cambridge University Press.
• Gürel Selimoğlu, Ö. (2017). Görme yetersizliği olan bireylerin gelişim özellikleri. In H. Gürgür & P. Şafak (Eds.), İşitme ve görme yetersizliği (pp. 151-184). Pegem Akademi Yayıncılık.
• Haber, R. N., Haber, L. R., Levin, C. A., & Hollyfield, R. (1993). Properties of spatial representations: Data from sighted and blind subjects. Perception & Psychophysics, 54(1), 1-13. https://doi.org/10.3758/BF03206932
• Hacısalihoğlu-Karadeniz, M. (2017). Opinions of preservice teachers about special education course and mathematical applications in inclusive education. Kalem Uluslararası Eğitim ve İnsan Bilimleri Dergisi, 7(1), 119-158. https://doi.org/10.23863/kalem.2017.78
• Horzum, T. (2016). Total görme engelli öğrencilerin perspektifinden üçgen kavramı. Kırşehir Eğitim Fakültesi Dergisi, 17(2), 275-295.
• Horzum, T. & Arikan, A. (2019). Understanding the polygon with the eyes of blinds. International Journal of Progressive Education, 15(1), 116-134. https://doi.org/10.29329/ijpe.2019.184.8
• Horzum, T. & Bülbül, M. Ş. (2017). Görme engelliler için bir geometri öğretim materyali: Geometri kafesi. Sürdürülebilir ve Engelsiz Bilim Eğitimi, 3(1), 1-15. http://fizikli.com/journal.
• Karshmer, A. I., Gupta, G., & Pontelli, E. (2007, July 7-9). Mathematics and accessibility: A survey [Paper presentation]. In Proc. 9th International Conference on Computers Helping People with Special Needs (Vol. 3118, pp. 664-669). https://www.utdallas.edu/%E2%88%BCgupta/mathaccsurvey.pdf
• Kay, D. C. (2001). College geometry: A discovery approach (2nd Edit.). Adison Wesley.
• Klingenberg, O. G., (2007). Geometry: Educational implications for children with visual impairment. Philosophy of Mathematics Education (Special Issue on Social Justice, Part 1), 20, 1-15. http://people.exeter.ac.uk/PErnest/pome20/index. htm on 10 Now 2011.
• Milli Eğitim Bakanlığı (2014). Özel eğitim mesleki eğitim merkezi eğitim programı (görme engelli için). Milli Eğitim Bakanlığı Yayınları.
• Milli Eğitim Bakanlığı (2018a). İlköğretim matematik (5, 6, 7 ve 8. sınıflar) dersi öğretim programı. Milli Eğitim Bakanlığı Yayınları.
• Milli Eğitim Bakanlığı (2018b). Ortaöğretim matematik (9, 10, 11 ve 12. sınıflar) dersi öğretim programı. Milli Eğitim Bakanlığı Yayınları.
• Milli Eğitim Bakanlığı (2018c). Özel Eğitim Hizmetleri Yönetmeliği. https://orgm.meb.gov.tr/meb_iys_dosyalar/2018_07/09101900_ozel_egitim_hizmetleri_yonetmeligi_07072018.pdf adresinden edinilmiştir.
• Okcu, B., Yazıcı, F., & Sözbilir, M.(2016). Ortaokul düzeyindeki görme engelli öğrencilerin okuldaki öğrenim sürecine dair görüşleri. Amasya Üniversitesi Eğitim Fakültesi Dergisi, 5(1), 51-83. https://doi.org/10.17539/aej.57861
• Özel Eğitim Hizmetleri Yönetmeliği [Special Education Services Regulation]. (2018). T.C. Resmi Gazete, (30471), 7 Temmuz 2018, 22-77.
• Özyürek, M. (2004). Bireyselleştirilmiş eğitim programı: Temelleri ve geliştirilmesi. Kök Yayıncılık.
• Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri. (M. Bütün & S. Demir, Çev.). Pegem Akademi.
• Roth, W.M., & Lee, Y. J. (2004). Interpreting unfamiliar graphs: A generative, activitytheoretic model. Educational Studies in Mathematics, 57(2), 265-290. https://doi.org/10.1023/B:EDUC.0000049276.37088.e4
• Shanty, N. O. (2016). Investigating students’ development of learning integer concept and integer addition, Journal on Mathematics Education, 7(2), 57-72. https://doi.org/10.22342/jme.7.2.3538.57-72
• Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114-145. https://doi.org/10.5951/jresematheduc.26.2.0114
• Simon, M. A. (2000). Research on the development of mathematics teachers: the teacher development experiment. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp.335-359). Lawrence Erlbaum Associates Publishers.
• Simon, M. A. (2017). Learning through activity: a developing integrated theory of mathematics learning and teaching [Paper presentation]. The 10th Congress of the European Society for Research in Mathematics Education, Dublin, Ireland.
• Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91-104.
• Simmons, G. F. (1996). Calculus with analytic geomertry (Second edition). The McGraw-Hill Companies.
• Spindler, R. (2006). Teaching mathematics to a student who is blind. Teaching Mathematics and Its Applications, 25(3), 120-126. https://doi.org/10.1093/teamat/hri028
• Steffe, L. P. (1991). The constructivist teaching experiment: Illustrations and implications. In E. V., Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 177-194). Springer Netherlands.
• Steffe, L. P. (2004). On the construction of learning trajectories of children: The case of commensurate fractions. Mathematical Thinking and Learning, 6(2), 129-162.
• Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E., Kelly, & R. A., Lesh (Eds.), Handbook of research design in mathematics and science education, (pp. 267-306). Routledge.
• Stevens, R. D., Edwards, A. D., & Harling, P. A. (1997). Access to mathematics for visually disabled students through multimodal interaction. Human-Computer Interaction, 12(1), 47-92.
• Tall, D., & Bakar, M., (1991). Students’ mental prototypes for functions and graphs. In F. Furinghetti (Ed.), Proceedings of the 15th Conference of the International Group for the Psychology of Mathematics Education, (Vol. I, pp. 104-111). Assisi, Italy.
• Thinus-Blanc, C., & Gaunet, F. (1997). Representation of space in blind persons: Vision as a spatial sense?. Psychological Bulletin, 127(1), 20-42. https://doi.org/10.1037/0033-2909.121.1.20
• Tekay, T., & Doğan, M. (2015). İlköğretim 7. sınıf öğrencilerinin doğrusal denklemlerin grafikleri ile ilgili soruları çözme becerilerinin değerlendirilmesi. MATDER Matematik Eğitimi Dergisi, 2(1), 0-0.
• Toennies, J. L., Burgner, J., Withrow, T. J., & Webster, R. J. (2011). Toward haptic/aural touchscreen display of graphical mathematics for the education of blind students [Paper presentation]. In 2011 IEEE World Haptics Conference (pp. 373-378).
• Warren, D. (1994). Blindness and children: An individual differences approach. Cambridge University Press.
• Van Scoy, F., McLaughlin, D., & Fullmer, A. (2005). Auditory augmentation of haptic graphs: Developing a graphic tool for teaching precalculus skill to blind students [Paper presentation]. The 11th Meeting of the International Conference on Auditory Display (Vol. 5).
• Yu, W., & Brewster, S. (2003). Evaluation of multimodal graphs for blind people. Universal Access in the Information Society, 2(2), 105-124.
• Yu, P., Barrett, J., & Presmeg, N. (2009). Prototypes and categorical reasoning: a perspective to explain how children learn about interactive geometry. In Craine, T.V. (Ed.), Understanding geometry for a changing World (pp. 109–126). Seventy-first Yearbook, National Council of Teachers of Mathematics.
• Zebehazy, K. T., Zigmond, N., & Zimmerman, G. J. (2012). Performance measurement and accommodation: students with visual impairments on Pennsylvania's alternate assessment. Journal of Visual Impairment & Blindness, 106(1), 17-30. https://doi.org/10.1177/0145482X1210600103
• Zorluoğlu, S., & Sözbilir, M. (2017). Görme yetersizliği olan öğrencilerin öğrenmelerini destekleyici ihtiyaçlar. Trakya Üniversitesi Eğitim Fakültesi Dergisi, 7(2), 659-682. https://doi.org/10.24315/trkefd.279369