Skip to main content
SpringerLink
Log in

Transformations of Teaching and Learning Through Digital Technologies

  • Chapter
  • First Online:
Research in Mathematics Education in Australasia 2012-2015

Abstract

This chapter is a critical synthesis of research related to the transformations that take place when digital technologies are incorporated into teaching and learning practices. In developing this synthesis, research from all levels of education was reviewed with a focus on the opportunities digital technologies offer for cognitive, pedagogical, affective and professional change. The chapter is structured in alignment with Pierce and Stacey’s (Pierce and Stacey, Int J Comput Math Learn 15(1):1–20 2010) map of pedagogical opportunities in which three dimensions for educational transformation were identified: tasks, classroom, and subject. A discussion of future directions for research into technology enhanced mathematics education concludes the review.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  • Allmond, S., & Makar, K. (2014). From hat plots to box plots in Tinkerplots: Supporting students to write conclusions which account for variability in data. In K. Makar, B. de Sousa, & R. Gould (Eds.), Proceedings of the Ninth International Conference on Teaching Statistics (pp. 1–6). International Association for Statistical Education. Retrieved from http://icots.info/9/proceedings/pdfs/ICOTS9_2E1_ALLMOND.pdf.

  • Attard, C., & Curry, C. (2012). Exploring the use of iPads to engage young students with mathematics. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Proceedings of the 35th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 75–82). Singapore: MERGA.

    Google Scholar 

  • Attard, C., & Orlando, J. (2014). Early career teachers, mathematics and technology: Device conflict and emerging mathematical knowledge. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 71–78). Sydney: MERGA.

    Google Scholar 

  • Aventi, B., Serow, P., & Tobias, S. (2014). Linking geogebra to explorations of linear relationships. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 79–86). Sydney: MERGA.

    Google Scholar 

  • Bardini, C., Oldenburg, R., Stacey, K., & Pierce, R. (2013). Technology prompts new understandings: The case of equality. In V. Steinle, L. Ball, & C. Bardini (Eds.), Proceedings of the 36th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 82–89). Melbourne: MERGA.

    Google Scholar 

  • Bate, F. G., Day, L., & Macnish, J. (2013). Conceptualising changes to pre-service teachers’ knowledge of how to best facilitate learning in mathematics: A TPACK inspired initiative. Australian Journal of Teacher Education, 38(5), 14–30.

    Article  Google Scholar 

  • Beswick, K., & Muir, T. (2013). Making connections: Lessons on the use of video in pre-service teacher education from the trial of particular protocol. Mathematics Teacher Education and Development, 15(2), 27–51.

    Google Scholar 

  • Brown, J. P. (2015a). Complexities of digital technology use and the teaching and learning of function. Computers & Education, 87, 112–122.

    Article  Google Scholar 

  • Brown, J. P. (2015b). Visualisation tactics for solving real world tasks. In G. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 431–442). Cham, Switzerland: Springer.

    Chapter  Google Scholar 

  • Brown, J. P. (2013). Teaching roles in technology-rich teaching and learning environments. In V. Steinle, L. Ball, & C. Bardini (Eds.), Proceedings of the 36th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 106–113). Melbourne: MERGA.

    Google Scholar 

  • Brown, J., & Stillman, G. (2014). Affordances: Ten years on. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 111–118). Sydney: MERGA.

    Google Scholar 

  • Calder, N. (2012). The Layering of mathematical interpretations through digital media. Educational Studies in Mathematics, 80(1), 269–285.

    Article  Google Scholar 

  • Calder, N. (2015). Apps: Appropriate, applicable and appealing? In T. Lowrie & R. Jorgensen (Eds.), Digital games and mathematics learning: Potential, promises and pitfalls (pp. 233–250). The Netherlands: Springer.

    Chapter  Google Scholar 

  • Calder, N. S., & Campbell, A. (2015). “You play on them. They’re active.” Enhancing the mathematics learning of reluctant teenage students. In M. Marshman, V. Geiger, & A. Bennison (Eds.), Proceedings of the 38th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 133–140). Sunshine Coast, QLD: MERGA.

    Google Scholar 

  • Cooper, T. E. (2012). Using virtual manipulatives with pre-service mathematics teachers to create representational models. The International Journal for Technology in Mathematics Education, 19(3), 105–115.

    Google Scholar 

  • Edens, K. M., & Potter, E. F. (2013). An exploratory look at the relationships among math skills, motivational factors and activity choice. Early Childhood Education Journal, 41(3), 235–243.

    Article  Google Scholar 

  • Engelbrecht, J., & Harding, A. (2005). Teaching undergraduate mathematics on the internet. Educational Studies in Mathematics, 58(2), 253–276.

    Article  Google Scholar 

  • Fitzallen, N., & Watson, J. (2014). Extending the curriculum with TinkerPlots: Opportunities for early development of informal inference. In K. Makar, B. de Sousa, & R. Gould (Eds.), Proceedings of the Ninth International Conference on Teaching Statistics (pp. 1–6). Voorburg: International Statistical Institute.

    Google Scholar 

  • Fun with Construction. (2011). Software. Singapore: Heulab Pte. Ltd.

    Google Scholar 

  • Galligan, L., & Hobohm, C. (2013). Students using digital technologies to produce screencasts that support learning in mathematics. In V. Steinle, L. Ball, & C. Bardini (Eds.), Proceedings of the 36th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 322–329). Melbourne: MERGA.

    Google Scholar 

  • Galligan, L., Hobohm, C., & Loch, B. (2012). Tablet technology to facilitate improved interaction and communication with students studying mathematics at a distance. Journal of Computers in Mathematics and Science Teaching, 31(4), 363–385.

    Google Scholar 

  • Geiger, V. (2009). The master, servant, partner, extension-of-self framework in individual, small group and whole class contexts. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 201–208). Wellington, NZ: MERGA.

    Google Scholar 

  • Geiger, V. (2013). Mathematical applications, modelling and technology as windows into industry based mathematical practice. In A. Damlamian, J. F. Rodrigues, & R. Straesser (Eds.), Educational interfaces between mathematics and industry: The 20th ICMI study (pp. 271–278). New York: Springer.

    Chapter  Google Scholar 

  • Geiger, V., Forgasz, H., Tan, H., Calder, N., & Hill, J. (2012). Technology in Mathematics education. In B. Perry, T. Lowrie, T. Logan, A. MacDonald, & J. Greenless (Eds.), Research in mathematics education in Australasia 2008–2011 (pp. 111–142). Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Geiger, V., Goos, M., & Dole, S. (2015). The role of digital technologies in numeracy teaching and learning. International Journal of Science and Mathematics Education, 13(5), 1115–1137.

    Article  Google Scholar 

  • Goodwin, K., & Gould, P. (2014). Race in the outback: Investigating technology designed to support number development in a preschool serving an under-resourced community. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 247–254). Sydney: MERGA.

    Google Scholar 

  • Goos, M. (2013). Technology integration in secondary school mathematics: The development of teachers’ professional identities. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era (pp. 139–161). Dordrecht, The Netherlands: Springer. doi:10.1007/978-94-007-4638-1_7.

    Google Scholar 

  • Goos, M. (2012). Digital technologies in the Australian Curriculum: Mathematics—A lost opportunity? In B. Atweh, M. Goos, R. Jorgensen, & D. Siemon (Eds.), Engaging the Australian Curriculum Mathematics—Perspectives from the field (pp. 135–152). Online publication: MERGA. Retrieved from http://www.merga.net.au/sites/default/files/editor/books/1/Chapter%207%20Goos.pdf.

  • Goos, M., & Cretchley, P. (2004). Computers, multimedia, and the internet in mathematics education. In B. Perry, G. Anthony, & C. Diezmann (Eds.), Research in mathematics education in Australasia 2000–2003 (pp. 151–174). Sydney: MERGA.

    Google Scholar 

  • Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2003). Perspectives on technology mediated learning in secondary school mathematics classrooms. Journal of Mathematical Behavior, 22, 73–89.

    Article  Google Scholar 

  • Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2000). Re-shaping teacher and student roles in technology enriched classrooms. Mathematics Education Research Journal, 12(3), 303–320

    Google Scholar 

  • Goos, M., & Geiger, V. (2012). Connecting social perspectives on mathematics teacher education in online environments. ZDM, 44(6), 705–715.

    Article  Google Scholar 

  • Handal, B., Campbell, C., Cavanagh, M., Petocz, P., & Kelly, N. (2013). Technological pedagogical content knowledge of secondary mathematics teachers. Contemporary Issues in Technology and Teacher Education, 13(1), 22–40.

    Google Scholar 

  • Heid, K. M., Thomas, M. O. T., & Zbiek, R. (2013). How might computer algebra systems change the role of algebra in the school curriculum? In K. Clements., A. Bishop., C. Keitel, J. Kilpatrick., & F. Leung. (Eds.), Third international handbook of mathematics education (pp. 597–641). New York: Springer.

    Google Scholar 

  • Konold, C., & Miller, C. (2005). Tinkerplots (Software v1.0). Emeryville, CA: KCP Technologies.

    Google Scholar 

  • Larkin, K. (2015). “An app! An app! My kingdom for an app”: An 18-month quest to determine whether apps support mathematical knowledge building. In T. Lowrie & R. Jorgensen (Eds.), Digital games and mathematics learning: Potential, promises and pitfalls (Vol. 4, pp. 251–276). Dordrecht, The Netherlands: Springer.

    Google Scholar 

  • Larkin, K., & Jamieson-Proctor, R. (2013). Transactional distance theory (TDT): An approach to enhancing knowledge and reducing anxiety of pre-service teachers studying a mathematics education course online. In V. Steinle, L. Ball, & C. Bardini (Eds.), Proceedings of the 36th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 434–441). Melbourne: MERGA.

    Google Scholar 

  • Larkin, K., & Jamieson-Proctor, R. (2015). Using transactional distance theory to redesign an online mathematics education course for pre-service primary teachers. Mathematics Teacher Education and Development, 17(1), 44–61.

    Google Scholar 

  • Larkin, K., Jamieson-Proctor, R., & Finger, G. (2012). TPACK and pre-service teacher mathematics education: Defining a signature pedagogy for mathematics education using ICT and based on the metaphor “mathematics is a language”. Computers in the Schools, 29(1), 207–226. doi:10.1080/07380569.2012.651424.

    Article  Google Scholar 

  • Larkin, K., & Jorgensen, R. (2014). Using video diaries to record student attitudes and emotions towards mathematics in year three and year six students. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia (pp. 373–380). Sydney: MERGA.

    Google Scholar 

  • Loong, E. Y. K., & Herbert, S. (2012). Student perspectives of web-based mathematics. International Journal of Educational Research, 53, 117–126.

    Article  Google Scholar 

  • Lowrie, T., & Jorgensen, R. L. (2012). The tyranny of remoteness: Changing and adapting pedagogical practices in distance education. International Journal of Pedagogies and Learning, 7(1), 1–8. doi:10.5172/ijpl.2012.7.1.1.

    Article  Google Scholar 

  • Lowrie, T., Jorgensen, R., & Logan, T. (2013). Navigating and decoding dynamic maps. Australian Journal of Educational Technology, 29(5), 626–639.

    Google Scholar 

  • Lowrie, T., Ramful, A., Logan, T., & Ho, S. Y. (2014). Do students solve graphic tasks with spatial demands differently in digital form? In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 429–436). Sydney: MERGA.

    Google Scholar 

  • Martin, D. (2012). Rich assessment in a first-year, teacher education (primary) mathematics education subject. International Journal of Pedagogies and Learning, 7(1), 62–72.

    Article  Google Scholar 

  • McDonald, S. (2012). The challenge to situate digital learning technologies in pre-service teacher mathematics education. Contemporary Issues in Technology and Teacher Education, 12(4), 355–368.

    Google Scholar 

  • Mojica-Casey, M., Dekkers, J., & Thrupp, R. (2014). Research guided practice: Student online experiences during mathematics class in the middle school. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 469–476). Sydney: MERGA.

    Google Scholar 

  • Muir, T. (2012). Virtual mathematics education: Using second life to model and reflect upon the teaching of mathematics. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Proceedings of the 35th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 521–528). Singapore: MERGA.

    Google Scholar 

  • Muir, T., & Chick, H. (2014). Flipping the classroom: A case study of mathematics methods class. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 485–492). Sydney: MERGA.

    Google Scholar 

  • Neumann, D. L., Hood, M. H., & Neumann, M. M. (2012). An evaluation of computer-based interactive simulations in the assessment of statistical concepts. The International Journal for Technology in Mathematics Education, 19(1), 17–23.

    Google Scholar 

  • O’Rourke, J., Main, S., & Ellis, M. (2013). “It doesn’t seem like work, it seems like good fun”: Perceptions of primary students on the use of handheld game consoles in mathematics classes. Technology, Pedagogy and Education, 22(1), 103–120. doi:10.1080/1475939X.2012.733537.

    Article  Google Scholar 

  • Pierce, R., & Bardini, C. (2015). Computer algebra systems: Permitted but are they used? Australian Senior Mathematics Journal, 29(1), 32–42.

    Google Scholar 

  • Pierce, R., & Stacey, K. (2010). Mapping pedagogical opportunities provided by mathematics analysis software. International Journal of Computers for Mathematics Learning, 15(1), 1–20.

    Article  Google Scholar 

  • Pierce, R., & Stacey, K. (2013). Teaching with new technology: Four “early majority” teachers. Journal of Mathematics Teacher Education, 16(5), 323–347. doi:10.1007/s10857-012-9227-y.

    Article  Google Scholar 

  • Prieto, E., & Holmes, K. (2014). Online Students’ perceptions of interactive tools to support postgraduate learning of mathematics. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 525–533). Sydney: MERGA.

    Google Scholar 

  • Prodromou, T. (2012). The classicist and the frequentist approach to probability within a Tinkerplots2 combinatorial problem. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Proceedings of the 35th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 610–617). Singapore: MERGA.

    Google Scholar 

  • Redmond, T., Brown, R., Sheehy, J., & Kanasa, H. (2012). Exploring student reflective practice during a mathematical modelling challenge. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Proceedings of the 35th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 641–647). Singapore: MERGA.

    Google Scholar 

  • Rogers, E. (1995). Diffusion of innovations. New York: The Free Press.

    Google Scholar 

  • Spencer, P. (2013). iPads: Improving numeracy learning in the early years. In V. Steinle, L. Ball, & C. Bardini (Eds.), Proceedings of the 36th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 610–617). Melbourne: MERGA.

    Google Scholar 

  • Stack, S., & Watson, J. (2013). Randomness, sample size, imagination and metacognition: Making judgments about differences in data sets. Australian Mathematics Teacher, 69(4), 23–30.

    Google Scholar 

  • Tan, H. (2012). Students’ ways of knowing and learning mathematics and their ways of interacting with advanced calculators. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Proceedings of the 35th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 704–711). Singapore: MERGA.

    Google Scholar 

  • Valsiner, J. (1997). Culture and the development of children’s action: A theory of human development (2nd ed.). New York: Wiley.

    Google Scholar 

  • Varsavsky, C. (2012). Use of CAS in secondary school: A factor influencing the transition to university-level mathematics? International Journal of Mathematical Education in Science and Technology, 43(1), 33–42.

    Article  Google Scholar 

  • Watson, J., & Chance, B. (2012). Building intuitions about statistical inference based on resampling. Australian Senior Mathematics Journal, 26(1), 6–18.

    Google Scholar 

  • Watson, J. M. (2013). Resampling with TinkerPlots. Teaching Statistics, 35(1), 32–36.

    Article  Google Scholar 

  • Watson, J. M. (2014). TinkerPlots as an interactive tool for learning about resampling. In T. Wassong, D. Frischemeier, P. R. Fischer, R. Hochmuth, & P. Bender (Eds.), Using tools for learning mathematics and statistics (pp. 421–436). Heidelberg, Germany: Springer Spektrum.

    Google Scholar 

  • Whyburn, L., & Way, J. (2012). Student perceptions of the influence of IWBs on their learning in mathematics. Australian Educational Computing, 27(1), 23–27.

    Google Scholar 

  • Yeh, A. (2013). Constructing a frame of a cube: Connecting 3D shapes with direction, location and movement. In V. Steinle, L. Ball, & C. Bardini (Eds.), Proceedings of the 36th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 690–697). Melbourne: MERGA.

    Google Scholar 

  • Yeh, A., & Chandra, V. (2015). Mathematics, programming, and STEM. In M. Marshman, V. Geiger, & A. Bennison (Eds.), Proceedings of the 38th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 659–666). Sunshine Coast, QLD: MERGA.

    Google Scholar 

  • Zuber, E. N., & Anderson, J. (2013). The initial response of secondary mathematics teachers to a one-to-one laptop program. Mathematics Education Research Journal, 25(4), 279–298.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Australian Catholic University, Virginia, Australia

    Vince Geiger

  2. The University of Waikato, Tauranga, New Zealand

    Nigel Calder

  3. Monash University, Clayton, Australia

    Hazel Tan

  4. Deakin University, Burwood, Australia

    Esther Loong

  5. Australian Catholic University, Virginia, Australia

    Jodie Miller

  6. Griffith University, Southport, Australia

    Kevin Larkin

Authors
  1. Vince Geiger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nigel Calder
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hazel Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Esther Loong
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jodie Miller
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Kevin Larkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vince Geiger .

Editor information

Editors and Affiliations

  1. School of Education, The University of Queensland, Brisbane, St Lucia, Queensland, Australia

    Katie Makar

  2. Fac of Sci, Health, Edu & Engineering, University of the Sunshine Coast, Sippy Downs, Queensland, Australia

    Shelley Dole

  3. School of Education, The University of Queensland, Brisbane, St Lucia, Queensland, Australia

    Jana Visnovska

  4. School of Education, The University of Queensland, Brisbane, St Lucia, Queensland, Australia

    Merrilyn Goos

  5. School of Education, The University of Queensland, Brisbane, St Lucia, Queensland, Australia

    Anne Bennison

  6. School of Education, The University of Queensland, Brisbane, St Lucia, Queensland, Australia

    Kym Fry

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media Singapore

About this chapter

Cite this chapter

Geiger, V., Calder, N., Tan, H., Loong, E., Miller, J., Larkin, K. (2016). Transformations of Teaching and Learning Through Digital Technologies. In: Makar, K., Dole, S., Visnovska, J., Goos, M., Bennison, A., Fry, K. (eds) Research in Mathematics Education in Australasia 2012-2015. Springer, Singapore. https://doi.org/10.1007/978-981-10-1419-2_13

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-1419-2_13

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-1417-8

  • Online ISBN: 978-981-10-1419-2

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation