Research Article
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Describing Pre-Service Teachers’ Reasoning within Drawing Geometrical Shapes in Logo

Year 2017, Issue: 44, 37 - 65, 21.12.2017
https://doi.org/10.21764/maeuefd.331250

Abstract

In this study, it was
aimed to determine the mistakes and possible misconceptions of pre-service
mathematics teachers made about the Logo-based tasks involving the concepts of
angle and rotation when they drawing some geometrical shapes using Logo
commands. For this purpose, 37 pre-service mathematics teachers (37)
participated in a “Computer based Mathematics Teaching Lesson” lasting 10
hours, in which they could learn and interact with Logo programming language.
Then, a five performance tasks about the concept of angle and rotation were
utilized to gather required data. The data of the study were obtained from
qualitative data collection methods through document analysis and clinical
interview. As a result of this study, most of the made mistakes in pen-paper
environment were because of geometrical features rather than Logo commands. These
are focused on three aspects: rotation of angle, angle-edge relationship and
missing/incorrect command. The ability to draw geometrical shapes using Logo
primitives is limited for some participants but acceptable for others. It was
recommended that teaching Logo should be applied with a constructive approach
that gives limited feedback when certain geometrical concepts are being
learned.

References

  • Appalanayudu, S., & Ismail, Z. (2005). Students’ Problem Solving Processes in LOGO Programming Environment Pengaturcaran LOGO. Reform, Revolution and Paradigm Shifts in Mathematics Education. Johor Bahru, Malaysia.
  • Baki, A. (2002). Öğrenen ve Öğretenler için Bilgisayar Destekli Matematik. İstanbul: Ceren Yayınları.
  • Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi. Ankara: Harf Eğitim Yayıncılık.
  • Barry-Joyce, M. (2001). The effects of a Logo environment on the metacognitive functioning of Irish students. Ph.D. thesis, University of Hull.
  • Biber, Ç, Tuna, A., & Korkmaz, S. (2013). The mistakes and the misconceptions of the eighth grade students on the subject of angles. European Journal of Science and Mathematics Education, 1(2), 50–59.
  • Clement, J. (2000). Analysis of clinical interview: Foundations and model viability. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 547-589). London: Lawrence Erlbaum Associates Publishers.
  • Clements, D. H., & Meredith, J. S. (1992). Research on Logo: Effects and efficacy. National Science Foundation.
  • Clements, D. H. & Sarama, J. (1997). Research on Logo: A decade of progress. Computers in the Schools, 14(1/2), pp. 9-46.
  • Clements, D. H. & Burns, B. A.(2000). Students’ development of strategies for turn and angle measure. Educational Studies in Mathematics, 41:31–45.
  • Creswell, J. W. (2009). Research Design: Qualitative, quantitative and mixed methods approaches (3rd eds.). Thousand Oaks, CA: Sage.
  • Cope, P., Smith, H. & Simmons, M. (1992). Misconceptions Concerning Rotation and Angle in Logo. Journal for Computer Assisted Learning, 8, pp. 16-24.
  • Çepni, S. (2012). Araştırma ve Proje Çalışmalarına Giriş. Geliştirilmiş 6. Baskı. s 76. Ankara. Ekiz, D. (2003). Eğitimde araştırma yöntem ve metotlarına giriş: nitel, nicel ve eleştirel kuram metodolojileri. Ankara: Anı Yayıncılık.
  • Ersoy, A.& Yalçınoğlu, P.(2012). Nitel araştırmaya giriş. Ankara: Anı Yayıncılık.
  • Goos, M. (2010). Using technology to support effective mathematics teaching and learning: What counts? Make it count: What research tells us about effective teaching and learning of mathematics (pp. 21-26). Camberwell: ACER.
  • Henderson, D.W & Taimina D. (2005). Experiencing geometry: Euclidean and non-Euclidean with history. 3rd ed. New York (NY): Prentice Hall.
  • Higgins, S. (2003). Does ICT improve learning and teaching in schools?, Nottingham: British Educational Research Association.
  • Higgins, S., Z. Xiao, & M. Katsipataki. (2012). The Impact of Digital Technology on Learning: A Summary for the Education Endowment Foundation (Full Report).
  • Karakırık, E. (2016). LogoTürk Kaplumbağa Matematiği. Doğan, M ve Karakırık, E. (Ed.). Matematik Eğitiminde Teknoloji Kullanımı (2.Baskı) (s.47-77). Ankara. Nobel-Atlas Yayıncılık.
  • Karakırık, E., & Durmuş, S. (2005). A New Graphical Logo Design Called LogoTurk. Eurasia Journal of Mathematics, Science and Technology Education,1(1), 61-75.
  • Keiser, J,M. (2014). Struggles with developing the concept of angle: comparing sixth-grade students’ discourse to the history of the angle concept. Mathematical Thinking and Learning, 6, 285–306.
  • Khasawneh, A. A. (2009). Assessing Logo programming among Jordanian seventh grade students through turtle geometry. International journal of Mathematical Education in Science and Technology, 40(5), 619-639.
  • Kokol-Voljc, V. (2007). Use of mathematical software in pre-service teacher training: The case of DGS. Proceedings of The British Society For research into Learning Mathematics, 27(3), 126-131.
  • Lin, C-Y. (2008). Pre-service teachers’ beliefs about using technology in the mathematics classroom. The Journal of Computers in Mathematics and Science Teaching, 27(3), pp. 341 360. Littlefield, J., Delclos, V. R., Bransford, J. D., Clayton, K. N., & Franks, J. J. (1989). Some prerequisites for teaching thinking: Methodological issues in the study of LOGO programming. Cognition and Instruction, 6(4), 331-366.
  • Liu, L., & Cummings, R. (1997). Logo and Geometric Thinking. Computers in the Schools.14 (1-2), 95-110.
  • McMillan, J. H., & Schumacher, S. (2010). Research in Education: Evidence-Based Inquiry. (7th ed.). Boston, MA: Pearson.
  • Milli Eğitim Bakanlığı [MEB]. (2017). Ortaokul matematik dersi 1-8. sınıflar öğretim programı. Ankara: MEB Talim Terbiye Başkanlığı Yayınları.
  • Mitchelmore, M.C. & White, P. (1998). Development of angle concepts: A framework for research. Mathematics Education Research Journal, 10(3), 4–27.
  • National Council of the Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. Reston, VA: Author.
  • Oldknow, A., Taylor, R., & Tetlow, L.(2010). Teaching Mathematics Using ICT (3rd.ed), New York: Continuum International Publishing Group.
  • Palmer, D. H. (1998). Measuring contextual error in the diagnosis of alternative conceptions in science. Issues in Educational Research, 8(1), 65-76.
  • Papert, S. (1993). Mindstorms: children, computers, and powerful ideas. 2nd ed. New York; London: Harvester Wheatsheaf.
  • Simmons, M., & Cope, P. (1997). Working with a round turtle: the development of angle/rotation concepts under restricted feedback conditions. Computers and Education, 28 (1), p. 23-33.
  • Sinclair, N., & Jackiw, N. (2005). Understanding and projecting ICT trends in mathematics education. In S. Johnston-Wilder & D. Pimm (Eds.), Teaching secondary mathematics with ICT (pp. 235–251). Maidenhead, UK: Open University Press.
  • So H.-J., & Kim, B. (2009). Learning about problem based learning: Student teachers integrating technology, pedagogy and content knowledge. Australasian Journal of Educational Technology. 25(1), 101-116.
  • Sulaiman, N.A.J. (2011). Exploring Kuwaiti mathematics: student-teachers' beliefs toward using Logo and mathematics education. PhD, Nottingham Trent University.
  • Stevens, T., To, Y., Harris, G., & Dwyer, J. (2008).The LOGO project: designing an effective continuing education program for teachers. The Journal of Computers in Mathematics and Science Teaching, 27(2), pp. 195-219.
  • Yelland, N. (1995). Mindstorms or storm in a teacup? A review of research with LOGO. International Journal of Mathematical Education for Science and Technology, 26, 853–869.
  • Yıldırım, A., ve Şimşek, H. (2006). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. (6. baskı) Ankara: Seçkin Yayıncılık.
  • Wilson, M., & Cooney, T. (2002). Mathematics teacher change and development. The role of beliefs. In G. C. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 127-147). Dordrecht: Kluwer Academic Publishers.
  • Yin, R. K. (2009). Case study research: Design and methods (4th ed.). Thousand Oaks, CA: Sage.

Logo Programlama Sürecinde Öğretmen Adaylarının Yaptıkları Hatalar Üzerine Bir Nitel Çalışma

Year 2017, Issue: 44, 37 - 65, 21.12.2017
https://doi.org/10.21764/maeuefd.331250

Abstract

Bu çalışmada, ilköğretim matematik öğretmeni adaylarının bilgisayar
destekli matematik öğretimi (BDMÖ) dersi kapsamında temel Logo komutlarını
kullanarak geometrik şekilleri çizerken açı ve dönme kavramlarını içeren
problemlere yönelik yaptıkları hataları ve olası kavram yanılgılarını tespit
etmeyi amaçlanmıştır. Bu amaçla, 2016-2017 eğitim-öğretim yılı güz döneminde 37
ilköğretim matematik öğretmeni adayına 10 saatlik Logo programlama dili eğitimi
verilmiştir. Daha sonra adaylardan Logo komutlarını kullanarak açı ve dönme
kavramıyla ilgili performans gösterebilecekleri 8 sorudan oluşan açık uçlu bir
sınav yapılmıştır. Bu çalışmada 8 soru içinden seçilen 5 soru üzerinde
durulmaktadır. Çalışmanın verileri, nitel veri toplama yöntemlerinden doküman
analizi ve klinik mülakat ile elde edilmiştir. Elde edilen bulgular
neticesinde, öğretmen adayları kâğıt-kalem ortamında problemleri çözerken Logo
programlama komutlarından daha çok dönme açısı ve geometrik şekillerin
özellikleriyle ilgili hatalar yaptıkları tespit edilmiştir. Bu hatalar şu üç
noktada yoğunlaşmaktadır: Dönme açısı, açı-kenar bağıntısı ve eksik kodlama.
Logo ’da performans gösterebilecekleri problemleri çözerken bazı öğretmen
adaylarının programlama becerilerinin sınırlı; diğerlerinin kabul edilebilir seviyede
olduğu belirlenmiştir. Araştırma sonucunda elde edilen bulgular dâhilinde Logo
programlama dili belirli geometrik kavramların öğrenilmesinde kullanılırken
sınırlı geri bildirim veren yapılandırmacı yaklaşımla ile hayata
geçirilmelidir.

References

  • Appalanayudu, S., & Ismail, Z. (2005). Students’ Problem Solving Processes in LOGO Programming Environment Pengaturcaran LOGO. Reform, Revolution and Paradigm Shifts in Mathematics Education. Johor Bahru, Malaysia.
  • Baki, A. (2002). Öğrenen ve Öğretenler için Bilgisayar Destekli Matematik. İstanbul: Ceren Yayınları.
  • Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi. Ankara: Harf Eğitim Yayıncılık.
  • Barry-Joyce, M. (2001). The effects of a Logo environment on the metacognitive functioning of Irish students. Ph.D. thesis, University of Hull.
  • Biber, Ç, Tuna, A., & Korkmaz, S. (2013). The mistakes and the misconceptions of the eighth grade students on the subject of angles. European Journal of Science and Mathematics Education, 1(2), 50–59.
  • Clement, J. (2000). Analysis of clinical interview: Foundations and model viability. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 547-589). London: Lawrence Erlbaum Associates Publishers.
  • Clements, D. H., & Meredith, J. S. (1992). Research on Logo: Effects and efficacy. National Science Foundation.
  • Clements, D. H. & Sarama, J. (1997). Research on Logo: A decade of progress. Computers in the Schools, 14(1/2), pp. 9-46.
  • Clements, D. H. & Burns, B. A.(2000). Students’ development of strategies for turn and angle measure. Educational Studies in Mathematics, 41:31–45.
  • Creswell, J. W. (2009). Research Design: Qualitative, quantitative and mixed methods approaches (3rd eds.). Thousand Oaks, CA: Sage.
  • Cope, P., Smith, H. & Simmons, M. (1992). Misconceptions Concerning Rotation and Angle in Logo. Journal for Computer Assisted Learning, 8, pp. 16-24.
  • Çepni, S. (2012). Araştırma ve Proje Çalışmalarına Giriş. Geliştirilmiş 6. Baskı. s 76. Ankara. Ekiz, D. (2003). Eğitimde araştırma yöntem ve metotlarına giriş: nitel, nicel ve eleştirel kuram metodolojileri. Ankara: Anı Yayıncılık.
  • Ersoy, A.& Yalçınoğlu, P.(2012). Nitel araştırmaya giriş. Ankara: Anı Yayıncılık.
  • Goos, M. (2010). Using technology to support effective mathematics teaching and learning: What counts? Make it count: What research tells us about effective teaching and learning of mathematics (pp. 21-26). Camberwell: ACER.
  • Henderson, D.W & Taimina D. (2005). Experiencing geometry: Euclidean and non-Euclidean with history. 3rd ed. New York (NY): Prentice Hall.
  • Higgins, S. (2003). Does ICT improve learning and teaching in schools?, Nottingham: British Educational Research Association.
  • Higgins, S., Z. Xiao, & M. Katsipataki. (2012). The Impact of Digital Technology on Learning: A Summary for the Education Endowment Foundation (Full Report).
  • Karakırık, E. (2016). LogoTürk Kaplumbağa Matematiği. Doğan, M ve Karakırık, E. (Ed.). Matematik Eğitiminde Teknoloji Kullanımı (2.Baskı) (s.47-77). Ankara. Nobel-Atlas Yayıncılık.
  • Karakırık, E., & Durmuş, S. (2005). A New Graphical Logo Design Called LogoTurk. Eurasia Journal of Mathematics, Science and Technology Education,1(1), 61-75.
  • Keiser, J,M. (2014). Struggles with developing the concept of angle: comparing sixth-grade students’ discourse to the history of the angle concept. Mathematical Thinking and Learning, 6, 285–306.
  • Khasawneh, A. A. (2009). Assessing Logo programming among Jordanian seventh grade students through turtle geometry. International journal of Mathematical Education in Science and Technology, 40(5), 619-639.
  • Kokol-Voljc, V. (2007). Use of mathematical software in pre-service teacher training: The case of DGS. Proceedings of The British Society For research into Learning Mathematics, 27(3), 126-131.
  • Lin, C-Y. (2008). Pre-service teachers’ beliefs about using technology in the mathematics classroom. The Journal of Computers in Mathematics and Science Teaching, 27(3), pp. 341 360. Littlefield, J., Delclos, V. R., Bransford, J. D., Clayton, K. N., & Franks, J. J. (1989). Some prerequisites for teaching thinking: Methodological issues in the study of LOGO programming. Cognition and Instruction, 6(4), 331-366.
  • Liu, L., & Cummings, R. (1997). Logo and Geometric Thinking. Computers in the Schools.14 (1-2), 95-110.
  • McMillan, J. H., & Schumacher, S. (2010). Research in Education: Evidence-Based Inquiry. (7th ed.). Boston, MA: Pearson.
  • Milli Eğitim Bakanlığı [MEB]. (2017). Ortaokul matematik dersi 1-8. sınıflar öğretim programı. Ankara: MEB Talim Terbiye Başkanlığı Yayınları.
  • Mitchelmore, M.C. & White, P. (1998). Development of angle concepts: A framework for research. Mathematics Education Research Journal, 10(3), 4–27.
  • National Council of the Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. Reston, VA: Author.
  • Oldknow, A., Taylor, R., & Tetlow, L.(2010). Teaching Mathematics Using ICT (3rd.ed), New York: Continuum International Publishing Group.
  • Palmer, D. H. (1998). Measuring contextual error in the diagnosis of alternative conceptions in science. Issues in Educational Research, 8(1), 65-76.
  • Papert, S. (1993). Mindstorms: children, computers, and powerful ideas. 2nd ed. New York; London: Harvester Wheatsheaf.
  • Simmons, M., & Cope, P. (1997). Working with a round turtle: the development of angle/rotation concepts under restricted feedback conditions. Computers and Education, 28 (1), p. 23-33.
  • Sinclair, N., & Jackiw, N. (2005). Understanding and projecting ICT trends in mathematics education. In S. Johnston-Wilder & D. Pimm (Eds.), Teaching secondary mathematics with ICT (pp. 235–251). Maidenhead, UK: Open University Press.
  • So H.-J., & Kim, B. (2009). Learning about problem based learning: Student teachers integrating technology, pedagogy and content knowledge. Australasian Journal of Educational Technology. 25(1), 101-116.
  • Sulaiman, N.A.J. (2011). Exploring Kuwaiti mathematics: student-teachers' beliefs toward using Logo and mathematics education. PhD, Nottingham Trent University.
  • Stevens, T., To, Y., Harris, G., & Dwyer, J. (2008).The LOGO project: designing an effective continuing education program for teachers. The Journal of Computers in Mathematics and Science Teaching, 27(2), pp. 195-219.
  • Yelland, N. (1995). Mindstorms or storm in a teacup? A review of research with LOGO. International Journal of Mathematical Education for Science and Technology, 26, 853–869.
  • Yıldırım, A., ve Şimşek, H. (2006). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. (6. baskı) Ankara: Seçkin Yayıncılık.
  • Wilson, M., & Cooney, T. (2002). Mathematics teacher change and development. The role of beliefs. In G. C. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 127-147). Dordrecht: Kluwer Academic Publishers.
  • Yin, R. K. (2009). Case study research: Design and methods (4th ed.). Thousand Oaks, CA: Sage.
There are 40 citations in total.

Details

Journal Section Makaleler
Authors

Ümit Kul 0000-0002-3651-4519

Salih Birişçi This is me

Publication Date December 21, 2017
Submission Date July 27, 2017
Published in Issue Year 2017 Issue: 44

Cite

APA Kul, Ü., & Birişçi, S. (2017). Logo Programlama Sürecinde Öğretmen Adaylarının Yaptıkları Hatalar Üzerine Bir Nitel Çalışma. Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi(44), 37-65. https://doi.org/10.21764/maeuefd.331250