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Virtual Or Physical: In-Service And Pre-Service Teacher’s Beliefs And Preferences On Manipulatives

Year 2012, Volume: 13 Issue: 4, 167 - 192, 01.12.2012

Abstract

Although the use of physical manipulatives, which have been emphasized to use in preschool education program and primary and secondary mathematics curriculum, in classroom environments is old, it is very new to use virtual manipulatives in classroom environments. The selection, preparation, and the integration to learning environments of both types of manipulatives are the most basic duties of teachers. However, the experiences, of using the physical and virtual manipulatives in course environments, of teachers and pre-service teachers are influenced by beliefs about the nature, teaching and learning of mathematics. The aim of this study is to determine and compare the beliefs of teachers and pre-service teachers in different branches for the use of virtual and physical manipulatives in mathematics education. For this purpose, 148 teachers, in the provinces of Trabzon, Kars and Gümüşhane, and 228 pre-service teachers, in the Education Faculties of Karadeniz Technical University and Kafkas University, have been applied two types of scales and interviews have been conducted with 40 teachers and pre-service teachers selected from that sample. Frequencies, percentages and arithmetic averages have been used to analyze the data. As a result, the majority of teachers and pre-service teachers have been identified to carry positive beliefs for the use of virtual and physical manipulatives in mathematics education and they have expressed that they desire to use both types of manipulatives more in the future.

References

  • Akkaya, Durmuş & Tunç (2012). İlköğretim matematik öğretmen adaylarının somut materyal ve sanal manipülatifleri eğitim süreçleri boyunca kullanabilme durumlarının belirlenmesi, X. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi (X. UFBMEK), Niğde.
  • Albirin, A. (2006). Teachers-attitudes toward information and communication technologies: The case of Syrian EFL teachers. Computers & Education, 47, 373–398.
  • Arı, M. & Bayhan, P. (2002). Okulöncesi dönemde bilgisayar destekli eğitim. İstanbul: Epsilon Yayıncılık.
  • Baki, A. (2000). Preparing student teachers to use computers in mathematics classrooms through a long –term pre-service course in Turkey. Journal of Information
  • Technology for Teacher Education, 9(3), 343-462. Baykal, A. (1994). Davranış ölçümünde yapısal geçerlik göstergesi. Türk Psikoloji Dergisi, 33, 45-50.
  • Bulut, S., Cömlekoğlu, G., Secil, S.O., Yıldırım, H. & Yıldız, B.T. (2002). Matematik öğretiminde somut materyallerin kullanılması. V. Ulusal Fen Bilimleri ve Matematik
  • Eğitimi Kongresi, Ankara. Clement, D. H. & McMillen, S. (1996). Rethinking concrete manipulatives. Teaching
  • Children Mathematics, 2(5), 270-279. Clement, D. H. (2002). Computers in early childhood mathematics. Contemporary
  • Issues in Early Childhood, 3(2), 160-181. Clements, D. (1999). Concrete' manipulatives, concrete ideas. Contemporary Issues in Early Childhood, 1(1), 45-60.
  • Crawford, C., & Brown, E. (2003). Integrating internet-based mathematical manipulatives within a learning environment. Journal of Computers in M athematics and Science Teaching, 22, 169–180.
  • Çakıroğlu, U, Güven, B. & Akkan,Y. (2008). Matematik öğretmenlerinin matematik eğitiminde bilgisayar kullanımına yönelik inançlarının incelenmesi, H. U. Journal of Education, 35, 38-52,.
  • Drickey, N.A. (2000). A comparison of virtual and physical manipulatives in teaching visualization andspatial reasoning to middle school mathematics students.
  • Unpublished doctoral dissertation, Utah State University. Durmus, S. & Karakirik, E. (2006). Virtual manipulatives in mathematics education: A theoretical framework. The Turkish Online Journal of Educational Technology, 5(1), 12.
  • Ernest, P. (1989). The impact of beliefs on the teaching of mathematics.(edit. Paul Ernest) Mathematics teaching: The stateof art (s. 249–254). London, Falmer Pres.
  • Ernest, P. (1991). The philosophy of mathematics education. Hampshire: The Falmer Press.
  • Fine, A. E. & Fleener, M. J. (1994). Calculators as instructional tools: Perceptions of three preservice teachers. Journal ofComputers in Mathematics and Science Teaching, (1), 83-100.
  • Forgasz, H. & Prince, N. (2001, Ağustos). Computers for secondary mathematics: Who uses them and how ? Makale Proceedings of the 2001 Annual Conference of the Australian Association for Research in Education konferansında bildiri olarak sunulmuştur, Fremantle, WA.
  • Forster, P. A. (2006). Assessing technology-based approaches for teaching and learning mathematics. International Journal of Mathematical Education in Science and Technology. 37(2), 145-164.
  • Gagnon, J.C. & Maccini, P. (2001). Preparing students with disabilities for algebra.
  • Teaching Exceptional Children, 34, 8–15. Hacıömeroğlu, G. & Apaydın, S. (2009). Tangram etkinliği ile çevre ve alan hesabı.
  • İlköğretim Online, 8 (2), 1-6. Heath, G. D. (2002) Using applets in teaching mathematics. Mathematics and Computer Education. 36(1), 43-52.
  • Inan, C. (2006). Matematik öğretiminde materyal geliştirme ve kullanma. Dicle
  • Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi. 7, 47-56. Kami, C. & Lewis, B.A. (1990). Constructivism and first grade arithmetics. Aritmetic Teacher, 38 (1), 34-35.
  • Kennedy, L. M. (1986). A rationale. Arithmetic Teacher, 33, 6–7, 32.
  • Manoucherhri, A. (1999). Computers and school mathematics reform: Implications for mathematics teacher education. Journal of Computers in Mathematics and Science Teaching, 18(1), 31-48.
  • Marzano, R.J. (1998). A theory-based meta-analysis of research on instruction. Aurora,
  • CO: Mid- continent Research for Education and Learning. McNeil, N. M., & Jarvin, L. (2007). When theories don’t add up: Disentangling the manipulative debate. Theory into Practice 46(4), 309-316.
  • Moyer P. S., & Bolyard, J. J. (2002). Exploring representation in the middle grades:
  • Investigations in geometry with virtual manipulatives. The Australian M athematics Teacher, 58(1), 19-25. Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47, 175-197.
  • Moyer, P. S., & Jones, M. G. (2004). Controlling choice: Teachers, students, and manipulatives in mathematics classrooms. School Science and Mathematics, 104, 16–31.
  • Moyer, P.S., Bolyard, J.J., & Spikell, M. A. (2002). What are virtual manipulatives?
  • Teaching ChildrenMatehematics, 8(6), 372-377. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics (2006). Curriculum focal points for prekindergarten throughgrade 8 mathematics: A guest for coherence, Reston,VA:NCTM.
  • Ozdemir, I. E. Y. (2008). Prospective elementary teachers’ cognitive skills on using manipulatives in teaching mathematics. H. U. Journal of Education,35, 362-373.
  • Seferoğlu, S. S., Akbıyık, C. & Bulut, M. (2008). İlköğretim öğretmenlerinin ve öğretmen adaylarının bilgisayarların öğrenme-öğretme sürecinde kullanımı ile ilgili algıları.
  • Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 35, 273-283. Semerci, A. (2006). İlköğretim birinci kademede görev yapan sınıf öğretmenlerinin, etkili materyal kullanma yeterlilikleri üzerine öğretmen ve yönetici görüşleri.
  • Yayımlanmamış yüksek lisans tezi, Fırat Üniversitesi, Elazığ, Türkiye. Sime, D. & Priestley, M. (2005). Student teachers’ first reflections on information and communications technology and classroom learning: Implications for initial teacher education. Journal of Computer AssistedLearning, 21(2), 130–142.
  • Simonsen, L. M. & Dick, T. P. (1997). Teachers’ perceptions of the impact of graphing calculators in the mathematics classroom. Journal of Computers in Mathematics and Science Teaching, 16(2/3), 239-268.
  • Sowell, E. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20(5),498-505.
  • Stein, M., & Bovalino, J. (2001). Manipulatives: One piece of the puzzle. Mathematics
  • Teaching in the Middle School,6(6), 356-359. Stipek, D., Givvin, K., Salmon, J. & MacGyvers, V. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 226.
  • Suh, J. & Moyer, P. S. (2005). Examining technology uses in the classroom: Developing fraction sense using virtual manipulative concept tutorials. Journal of Interactive Online Learning. 3(4), 1-22.
  • Suh, J. (2005). Third graders’ mathematics achievement and representation preference using virtual andphysical manipulatives for adding fractions and balancing equations.
  • Unpublished doctoral dissertation, George Mason University, Fairfax, VA. Thompson, A. (1984). The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15, 5-l27.
  • Van de Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Boston, MA: Pearson /Allyn and Bacon.
  • Veneziano L. & Hooper J. (1997). A method for quantifying content validity of health- related questionnaires. AmericanJournal of Health Behavior, 21(1):67-70.
  • Walen, S., Williams, S. & Garner, B. (2003). Pre-service teachers learning mathematics using calculators: A failure to connect current and future practice. Teaching and Teacher Education, 19(4), 445-462.
  • Williams, C.K. & Kamii, C. (1986). How do children learn by handling objects? Young Children, 42 (1) 23-46.
  • Wu, H.-K., Hsu,Y.-S. & Hwang, F.K. (2008). Factors affecting teachers’ adoption of techonology in classrooms: Does school size matter? International Journal of Science and Mathematics Education, 6(1),63-85.
  • Yurdugül, H. (2005). Ölçek geliştirme çalısmalarında kapsam geçerligi için kapsam geçerlik indekslerinin kullanılması. XIV.Eğitim Bilimleri Kurultayı, 28-30 Eylül,
  • Pamukkale Üniversitesi, Denizli. http://yunus.hacettepe.edu.tr/~yurdugul/3/indir/PamukkaleBildiri.pdf Yolcu, B. & Kurtulus, A. (2010). A study on developing sixth-grade students’ spatial visualization ability, Elementary Education Online, 9(1), 256-274
Year 2012, Volume: 13 Issue: 4, 167 - 192, 01.12.2012

Abstract

References

  • Akkaya, Durmuş & Tunç (2012). İlköğretim matematik öğretmen adaylarının somut materyal ve sanal manipülatifleri eğitim süreçleri boyunca kullanabilme durumlarının belirlenmesi, X. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi (X. UFBMEK), Niğde.
  • Albirin, A. (2006). Teachers-attitudes toward information and communication technologies: The case of Syrian EFL teachers. Computers & Education, 47, 373–398.
  • Arı, M. & Bayhan, P. (2002). Okulöncesi dönemde bilgisayar destekli eğitim. İstanbul: Epsilon Yayıncılık.
  • Baki, A. (2000). Preparing student teachers to use computers in mathematics classrooms through a long –term pre-service course in Turkey. Journal of Information
  • Technology for Teacher Education, 9(3), 343-462. Baykal, A. (1994). Davranış ölçümünde yapısal geçerlik göstergesi. Türk Psikoloji Dergisi, 33, 45-50.
  • Bulut, S., Cömlekoğlu, G., Secil, S.O., Yıldırım, H. & Yıldız, B.T. (2002). Matematik öğretiminde somut materyallerin kullanılması. V. Ulusal Fen Bilimleri ve Matematik
  • Eğitimi Kongresi, Ankara. Clement, D. H. & McMillen, S. (1996). Rethinking concrete manipulatives. Teaching
  • Children Mathematics, 2(5), 270-279. Clement, D. H. (2002). Computers in early childhood mathematics. Contemporary
  • Issues in Early Childhood, 3(2), 160-181. Clements, D. (1999). Concrete' manipulatives, concrete ideas. Contemporary Issues in Early Childhood, 1(1), 45-60.
  • Crawford, C., & Brown, E. (2003). Integrating internet-based mathematical manipulatives within a learning environment. Journal of Computers in M athematics and Science Teaching, 22, 169–180.
  • Çakıroğlu, U, Güven, B. & Akkan,Y. (2008). Matematik öğretmenlerinin matematik eğitiminde bilgisayar kullanımına yönelik inançlarının incelenmesi, H. U. Journal of Education, 35, 38-52,.
  • Drickey, N.A. (2000). A comparison of virtual and physical manipulatives in teaching visualization andspatial reasoning to middle school mathematics students.
  • Unpublished doctoral dissertation, Utah State University. Durmus, S. & Karakirik, E. (2006). Virtual manipulatives in mathematics education: A theoretical framework. The Turkish Online Journal of Educational Technology, 5(1), 12.
  • Ernest, P. (1989). The impact of beliefs on the teaching of mathematics.(edit. Paul Ernest) Mathematics teaching: The stateof art (s. 249–254). London, Falmer Pres.
  • Ernest, P. (1991). The philosophy of mathematics education. Hampshire: The Falmer Press.
  • Fine, A. E. & Fleener, M. J. (1994). Calculators as instructional tools: Perceptions of three preservice teachers. Journal ofComputers in Mathematics and Science Teaching, (1), 83-100.
  • Forgasz, H. & Prince, N. (2001, Ağustos). Computers for secondary mathematics: Who uses them and how ? Makale Proceedings of the 2001 Annual Conference of the Australian Association for Research in Education konferansında bildiri olarak sunulmuştur, Fremantle, WA.
  • Forster, P. A. (2006). Assessing technology-based approaches for teaching and learning mathematics. International Journal of Mathematical Education in Science and Technology. 37(2), 145-164.
  • Gagnon, J.C. & Maccini, P. (2001). Preparing students with disabilities for algebra.
  • Teaching Exceptional Children, 34, 8–15. Hacıömeroğlu, G. & Apaydın, S. (2009). Tangram etkinliği ile çevre ve alan hesabı.
  • İlköğretim Online, 8 (2), 1-6. Heath, G. D. (2002) Using applets in teaching mathematics. Mathematics and Computer Education. 36(1), 43-52.
  • Inan, C. (2006). Matematik öğretiminde materyal geliştirme ve kullanma. Dicle
  • Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi. 7, 47-56. Kami, C. & Lewis, B.A. (1990). Constructivism and first grade arithmetics. Aritmetic Teacher, 38 (1), 34-35.
  • Kennedy, L. M. (1986). A rationale. Arithmetic Teacher, 33, 6–7, 32.
  • Manoucherhri, A. (1999). Computers and school mathematics reform: Implications for mathematics teacher education. Journal of Computers in Mathematics and Science Teaching, 18(1), 31-48.
  • Marzano, R.J. (1998). A theory-based meta-analysis of research on instruction. Aurora,
  • CO: Mid- continent Research for Education and Learning. McNeil, N. M., & Jarvin, L. (2007). When theories don’t add up: Disentangling the manipulative debate. Theory into Practice 46(4), 309-316.
  • Moyer P. S., & Bolyard, J. J. (2002). Exploring representation in the middle grades:
  • Investigations in geometry with virtual manipulatives. The Australian M athematics Teacher, 58(1), 19-25. Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47, 175-197.
  • Moyer, P. S., & Jones, M. G. (2004). Controlling choice: Teachers, students, and manipulatives in mathematics classrooms. School Science and Mathematics, 104, 16–31.
  • Moyer, P.S., Bolyard, J.J., & Spikell, M. A. (2002). What are virtual manipulatives?
  • Teaching ChildrenMatehematics, 8(6), 372-377. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
  • National Council of Teachers of Mathematics (2006). Curriculum focal points for prekindergarten throughgrade 8 mathematics: A guest for coherence, Reston,VA:NCTM.
  • Ozdemir, I. E. Y. (2008). Prospective elementary teachers’ cognitive skills on using manipulatives in teaching mathematics. H. U. Journal of Education,35, 362-373.
  • Seferoğlu, S. S., Akbıyık, C. & Bulut, M. (2008). İlköğretim öğretmenlerinin ve öğretmen adaylarının bilgisayarların öğrenme-öğretme sürecinde kullanımı ile ilgili algıları.
  • Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 35, 273-283. Semerci, A. (2006). İlköğretim birinci kademede görev yapan sınıf öğretmenlerinin, etkili materyal kullanma yeterlilikleri üzerine öğretmen ve yönetici görüşleri.
  • Yayımlanmamış yüksek lisans tezi, Fırat Üniversitesi, Elazığ, Türkiye. Sime, D. & Priestley, M. (2005). Student teachers’ first reflections on information and communications technology and classroom learning: Implications for initial teacher education. Journal of Computer AssistedLearning, 21(2), 130–142.
  • Simonsen, L. M. & Dick, T. P. (1997). Teachers’ perceptions of the impact of graphing calculators in the mathematics classroom. Journal of Computers in Mathematics and Science Teaching, 16(2/3), 239-268.
  • Sowell, E. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20(5),498-505.
  • Stein, M., & Bovalino, J. (2001). Manipulatives: One piece of the puzzle. Mathematics
  • Teaching in the Middle School,6(6), 356-359. Stipek, D., Givvin, K., Salmon, J. & MacGyvers, V. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 226.
  • Suh, J. & Moyer, P. S. (2005). Examining technology uses in the classroom: Developing fraction sense using virtual manipulative concept tutorials. Journal of Interactive Online Learning. 3(4), 1-22.
  • Suh, J. (2005). Third graders’ mathematics achievement and representation preference using virtual andphysical manipulatives for adding fractions and balancing equations.
  • Unpublished doctoral dissertation, George Mason University, Fairfax, VA. Thompson, A. (1984). The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15, 5-l27.
  • Van de Walle, J. A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Boston, MA: Pearson /Allyn and Bacon.
  • Veneziano L. & Hooper J. (1997). A method for quantifying content validity of health- related questionnaires. AmericanJournal of Health Behavior, 21(1):67-70.
  • Walen, S., Williams, S. & Garner, B. (2003). Pre-service teachers learning mathematics using calculators: A failure to connect current and future practice. Teaching and Teacher Education, 19(4), 445-462.
  • Williams, C.K. & Kamii, C. (1986). How do children learn by handling objects? Young Children, 42 (1) 23-46.
  • Wu, H.-K., Hsu,Y.-S. & Hwang, F.K. (2008). Factors affecting teachers’ adoption of techonology in classrooms: Does school size matter? International Journal of Science and Mathematics Education, 6(1),63-85.
  • Yurdugül, H. (2005). Ölçek geliştirme çalısmalarında kapsam geçerligi için kapsam geçerlik indekslerinin kullanılması. XIV.Eğitim Bilimleri Kurultayı, 28-30 Eylül,
  • Pamukkale Üniversitesi, Denizli. http://yunus.hacettepe.edu.tr/~yurdugul/3/indir/PamukkaleBildiri.pdf Yolcu, B. & Kurtulus, A. (2010). A study on developing sixth-grade students’ spatial visualization ability, Elementary Education Online, 9(1), 256-274
There are 51 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Yasar Akkan This is me

Publication Date December 1, 2012
Submission Date February 27, 2015
Published in Issue Year 2012 Volume: 13 Issue: 4

Cite

APA Akkan, Y. (2012). Virtual Or Physical: In-Service And Pre-Service Teacher’s Beliefs And Preferences On Manipulatives. Turkish Online Journal of Distance Education, 13(4), 167-192.