Skip to main content
SpringerLink
Log in

Developing Virtual Mathematics Manipulatives: The SAMAP Project

  • Chapter
  • First Online:
International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 7))

  • 1805 Accesses

Abstract

Online educational activities providing interactive environments where users can investigate the properties of abstract concepts and reflect on them are in great demand for all subjects in primary and secondary schools. However, the ubiquitous nature of these activities does not always guarantee students’ conceptual development if enough consideration was not given to the design and implementation of the system and an appropriate role was not defined for the technology used. A computer system could play a wide range of roles changing from a ‘tutor’ acting as “a decision-making” subject to a ‘tool’ acting as an “auxiliary” object. One can also interpret this classification of roles as a system having total control of flow or a system allowing free explorations. A computer system is regarded as suitable to be used in education when it provides facilities that promote the student’s conceptual development through engaging him/her in meaningful and authentic tasks. The new Turkish mathematics curriculum is based on constructivist educational approaches and advocates the wide usage of educational activities that help to make mathematical concepts and relations meaningful. The purpose of this chapter is to report the findings of a research project, SAMAP, funded by the Turkish National Science Foundation (TUBITAK), which aimed to develop virtual mathematics manipulatives in Turkish for the primary and secondary school curriculum.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16, 183–198.

    Article  Google Scholar 

  • Anderson-Pence, K. L., & Moyer-Packenham, P. S. (2015). Using virtual manipulatives to enhance collaborative discourse in mathematics instruction. Chicago, Illinois: Paper presented at the Annual Meeting of the American Educational Research Association (AERA).

    Google Scholar 

  • Bruner, J. (2003). The process of education: A landmark in educational theory. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Burns, B. A., & Hamm, E. M. (2011). A comparison of concrete and virtual manipulative use in third- and fourth-grade mathematics. School Science and Mathematics, 111(6), 256–261.

    Article  Google Scholar 

  • Butler, F. M., Miller, S. P., Crehan, K., Babbitt, B., & Pierce, T. (2003). Fraction instruction for students with mathematics disabilities: Comparing two teaching sequences. Learning Disabilities Research and Practice, 18(2), 99–111.

    Article  Google Scholar 

  • Cox, R., & Brna, P. (1995). Supporting the use of external representations in problem solving: The need for flexible learning environments. Journal of Artificial Intelligence in Education, 2(3), 239–302.

    Google Scholar 

  • Crook, C. (1994). Computers and the collaborative experience of learning. London and New York: Routledge.

    Google Scholar 

  • Dienes, Z. P. (1971). Building up mathematics (4th ed.). London: Hutchinson.

    Google Scholar 

  • Duffy, T. M., & Cunningham, D. J. (1996). Constructivism: Implications for the design and delivery of instruction. Handbook of Research for Educational Communications and Technology (pp. 170–198). New York: Simon and Schuster Macmillan.

    Google Scholar 

  • Durmuş, S., & Karakırık, E. (2006). Virtual manipulatives in mathematics education: A theoretical framework. The Turkish Journal of Educational Technology, 5(1), 117–123.

    Google Scholar 

  • Jonassen, D. H. (1996). Computers as cognitive tools: Learning with technology, not from technology. Journal of Computing in Higher Education, 6(2), 40–73.

    Article  Google Scholar 

  • Kaput, J. (1992). Technology and mathematics education. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 515–556). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Karakırık, E. (2008). SAMAP: A Turkish math virtual manipulatives site. Eskisehir, Turkey: 8th International Educational Technology Conference, Eskisehir, 6th–9th May 2008.

    Google Scholar 

  • Karakırık, E. (2010). SAMAP mathematics manipulatives. Malaysia: Fifteenth Asian Technology Conference in Mathematics (ATCM), 17th–22nd Dec 2010.

    Google Scholar 

  • Karakırık, E. (2011). Promoting investigative math classrooms through SAMAP manipulatives. Bolu, Turkey: Sixteenth Asian Technology Conference in Mathematics (ATCM), 19th–23rd Sept 2011.

    Google Scholar 

  • Karakırık, E. & Cakmak, B. (2009). SAMAP projesi raporu (The SAMAP Project Report). Unpublished manuscript submitted to Turkish National Science Foundation, TUBITAK. Available at http://uvt.ulakbim.gov.tr/uvt/index.php?cwid=9

  • Kuhn, D. (2007). Is direct instruction an answer to the right question? Educational Psychologist, 42(2), 109–113.

    Article  Google Scholar 

  • Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive Science, 11, 65–99.

    Article  Google Scholar 

  • McLeod, J., Vasinda, S., & Dondlinger, M. J. (2012). Conceptual visibility and virtual dynamics in technology-scaffolded learning environments for conceptual knowledge of mathematics. Journal of Computers in Mathematics and Science Teaching, 31(3), 283–310.

    Google Scholar 

  • MEB (Turkish Ministry of Education). (2005). Primary school mathematics curriculum grades 1 to 5 (İlköğretim okulu matematik dersi (1-5. sınıflar) öğretim program). Ankara, MEB-Talim Terbiye Kurulu Başkanlığı Yayınları.

    Google Scholar 

  • Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8(6), 372–377.

    Google Scholar 

  • Moyer-Packenham, P. S., Baker, J., Westenskow, A., Anderson-Pence, K., Shumway, J. F., & Jordan, K. E. (2014). Predictors of achievement when virtual manipulatives are used for mathematics instruction. Journal of Research in Mathematics Education, 3(2), 121–150.

    Google Scholar 

  • Moyer-Packenham, P., Baker, J., Westenskow, A., Anderson, K., Shumway, J., Rodzon, K., & Jordan, K. et al. (2013). A study comparing virtual manipulatives with other instructional treatments in third- and fourth-grade classrooms. Journal of Education, 193(2), 25–39.

    Google Scholar 

  • Moyer-Packenham, P., Shumway, J. F., Bullock, E., Tucker, S. I., Anderson-Pence, K., Westenskow, A., & Jordan, K. (2015). Young children’s learning performance and efficiency when using virtual manipulative mathematics iPad apps. The Journal of Computers in Mathematics and Science Teaching, 34(1), 41.

    Google Scholar 

  • Moyer-Packenham, P. S., & Suh, J. M. (2012). Learning mathematics with technology: The influence of virtual manipulatives on different achievement groups. Journal of Computers in Mathematics and Science Teaching, 31(1), 39–59.

    Google Scholar 

  • Moyer-Packenham, P. S., & Westenskow, A. (2013). Effects of virtual manipulatives on student achievement and mathematics learning. International Journal of Virtual and Personal Learning Environments, 4(3), 35–50.

    Article  Google Scholar 

  • Namukasa, I. K., Stanley, D., & Tuchtie, M. (2009). Virtual manipulative materials in secondary mathematics: A theoretical discussion. Journal of Computers in Mathematics and Science Teaching, 28(3), 277–307.

    Google Scholar 

  • Norman, D. (2013). Design of everyday things: Revised and expanded edition. Basic Books.

    Google Scholar 

  • O’Shea, T., & Self, J. (1983). Learning and Teaching with computers. Brighton: Harvester Press.

    Google Scholar 

  • Ozgun-Koca, S., & Edwards, T. (2011). Hands-on, minds-on or both? A discussion of the development of a mathematics activity by using virtual and physical manipulatives. Journal of Computers in Mathematics and Science Teaching, 30(4), 389–402.

    Google Scholar 

  • Özgün-Koca, S. A., Edwards, M. T., & Meagher, M. (2013). Spaghetti sine curves: Virtual environments for reasoning and sense making. The Mathematics Teacher, 107(3), 180–185.

    Article  Google Scholar 

  • Pea, R. D. (1985). Beyond amplification: Using the computer to reorganize mental functioning. Educational Psychologist, 20(4), 167–182.

    Article  Google Scholar 

  • Piaget, J. (1952). The child’s conception of number. New York: Humanities Press.

    Google Scholar 

  • Reimer, K., & Moyer, P. S. (2005). Third-graders learn about fractions using virtual manipulatives: A classroom study. Journal of Computers in Mathematics and Science Teaching, 24(1), 5–25.

    Google Scholar 

  • Satsangi, R., & Bouck, E. C. (2015). Using virtual manipulative instruction to teach the concepts of area and perimeter to secondary students with learning disabilities. Learning Disability Quarterly, 38(3), 174–186.

    Article  Google Scholar 

  • Sowell, E. J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20(5), 498–505.

    Article  Google Scholar 

  • Suh, J., & Moyer, P. S. (2007). Developing students’ representational fluency using virtual and physical algebra balances. Journal of Computers in Mathematics and Science Teaching, 26(2), 155–173.

    Google Scholar 

  • Vygotsky, L. S. (1978). Mind in society: The development of higher mental processes. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Wegerif, R., & Dawes, L. (2004). Thinking and learning with ICT: raising achievement in primary classrooms. London: Routledge.

    Google Scholar 

Download references

Acknowledgements

The SAMAP project is supported by the Turkish Science Foundation TUBİTAK by project number  SOBAG 106K140.

Author information

Authors and Affiliations

  1. Abant İzzet Baysal University, Bolu, Turkey

    Erol Karakırık

Authors
  1. Erol Karakırık
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Erol Karakırık .

Editor information

Editors and Affiliations

  1. Utah State University, Logan, Utah, USA

    Patricia S. Moyer-Packenham

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Karakırık, E. (2016). Developing Virtual Mathematics Manipulatives: The SAMAP Project. In: Moyer-Packenham, P. (eds) International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives. Mathematics Education in the Digital Era, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-32718-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-32718-1_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32716-7

  • Online ISBN: 978-3-319-32718-1

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation