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Conceptualising, Implementing and Evaluating the Use of Digital Technologies to Enhance Mathematical Understanding: Reflections on an Innovation-Development Cycle

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Educational Developments, Practices and Effectiveness

Abstract

This chapter first outlines the challenges related to teaching in quantitative disciplines (for example, mathematics, statistics, engineering, science and economics) in on-campus and online environments. It is followed by an analysis of the contribution that our decade of published and unpublished research has made to resolving these challenges. In so doing, we highlight a phased cycle of innovation (that is, conceptualising, implementing, evaluating and reconceptualising), and report the impact of the work on learning and teaching across different environments. Finally, the chapter provides an overview of developments that have worked and that are still successfully used, and others that did not proceed beyond trial status. Unsuccessful trials are rarely reported, but we make an exception here, as they are an integral part of this innovation cycle.

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References

  • Al-Zoubi, A. Y., Sammour, G., & Qasem, M. A. (2007). Utilization of tablet PCs in electromagnetics education. iJET: International Journal of Emerging Technologies in Learning, 2(2), 42–46.

    Google Scholar 

  • Anderson, T., Annand, D., & Wark, N. (2005). The search for learning community in learner paced distance education: Or, ‘Having your cake and eating it, too!’ Australasian Journal of Educational Technology, 21(2), 222–241.

    Google Scholar 

  • Barrington, F. (2012, February). 2011 Year 12 mathematics student numbers. Australian Mathematical Sciences Institute. Discipline profile of the mathematical sciences. Paper submitted as part of the ‘Maths for the Future: Keep Australia Competitive’ forum, Canberra, ACT, Australia.

    Google Scholar 

  • Bouhnik, D., & Marcus, T. (2006). Interaction in distance-learning courses. Journal of the American Society for Information Science and Technology, 57(3), 299–305. doi: 10.1002/asi.20277

    Article  Google Scholar 

  • Brodie, L., & Loch, B. (2009). Annotations with a tablet PC or typed feedback: Does it make a difference? In C. Kestell, S. Grainger, & J. Cheung (Eds.), Engineering the curriculum: 20th annual conference for the Australasian Association for Engineering Education (pp. 765–770). Adelaide, SA, Australia: Australasian Association for Engineering Education. Retrieved from https://eprints.usq.edu.au/6409/1/Brodie_Loch_AaeE_2009_PV.pdf.

    Google Scholar 

  • Cicchino, R. M., & Mirliss, D. S. (2004). Tablet PCs: A powerful teaching tool. Paper presented at the world conference on e-learning in corporate, government, healthcare and higher education, Washington, DC.

    Google Scholar 

  • Corcoles, C. (2012). The use of screencasts in mathematical and scientific education. eLC Research Paper Series: Time Factor in Online Teaching and Learning on Mathematics and Physics, 4, 6–10.

    Article  Google Scholar 

  • Croft, A., Duah, F., & Loch, B. (2013). ‘I’m worried about the correctness’: Undergraduate students as producers of mathematics screencasts for their peers – lecturer and student perceptions. International Journal of Mathematical Education in Science and Technology, 44(7), 1045–1055. doi: 10.1080/0020739X.2013.823252.

    Article  Google Scholar 

  • Croft, A., Harrison, M. C., & Robinson, C. L. (2009). Recruitment and retention of students – an integrated and holistic vision of mathematics support. International Journal of Mathematical Education in Science and Technology, 40(1), 109–125. doi: 10.1080/00207390802542395

    Article  Google Scholar 

  • Cromack, J. (2008, October 22–25). Technology and learning-centered education: Research-based support for how the tablet PC embodies the seven principles of good practice in undergraduate education. Paper presented at the 38th American Society for Engineering Education/Institute of Electrical and Electronics Engineers conference, Saratoga Springs, NY.

    Google Scholar 

  • Department of Industry, Innovation, Science, Research and Tertiary Education. (2012). Undergraduate applications, offers and acceptances. Canberra, ACT, Australia: Author.

    Google Scholar 

  • Donovan, D., & Loch, B. (2013). Closing the feedback loop: Engaging students in large first-year mathematics test revision sessions using pen-enabled screens. International Journal of Mathematical Education in Science and Technology, 44(1), 1–13. doi: 10.1080/0020739X.2012.678898

    Article  Google Scholar 

  • Freeman, M. (2010, February). Quantitative skills for historians (Historical insights: Focus on research). University of Warwick, Coventry, UK: History at the Higher Education Academy. Retrieved from https://www.heacademy.ac.uk/sites/default/files/rg_freeman_quantitativeskills_20100131_01.pdf.

    Google Scholar 

  • Galligan, L. (2008). Using Valsiner. In M. Goos, R. Brown, & K. Maker (Eds.), Navigating currents and charting directions: Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia Inc. (Vol. 1, pp. 211–218). Sydney, NSW, Australia: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Galligan, L. (2011). Developing a model of embedding academic numeracy in university programs: A case study from nursing. Unpublished Doctor of Philosophy dissertation, Queensland University of Technology, Brisbane, Qld, Australia.

    Google Scholar 

  • Galligan, L., & Hobohm, C. (2013). Investigating inking devices to support learning in mathematics. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow: Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 322–329). Melbourne, Vic, Australia: Mathematics Education Research Group of Australasia.

    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 

  • Galligan, L., Loch, B., McDonald, C., & Taylor, J. A. (2010). The use of tablet and related technologies in mathematics teaching. Australian Senior Mathematics Journal, 24(1), 38–51.

    Google Scholar 

  • Galligan, L., Wandel, A. P., & Hartle, R. T. (2011). Scaffolding distance learning in mathematics for engineering: Identifying key troublesome knowledge. In Proceedings of the 1st international conference of STEM in education. Retrieved from http://stem.ed.qut.edu.au/index.php/conference -proceedings.html.

    Google Scholar 

  • Garrison, D. R., Anderson, T., & Archer, W. (2000). Critical inquiry in a text-based environment: Computer conferencing in higher education. The Internet and Higher Education, 2(2–3), 87–105. doi:10.1016/S1096–7516(00)00016–6.

    Google Scholar 

  • Goh, S., Galligan, L., & Ku, H. (2013, June 23–26). Wireless tablet PCs for enhanced teaching at an Australian regional university teaching both campus and distance modes. Paper presented at the 120th annual conference of the American Society for Engineering Education, Atlanta, GA. Retrieved from http://www.asee.org/public/conferences/20/papers/6128/view.

    Google Scholar 

  • Harman, C., & Dorman, M. (1998). Enriching distance teaching and learning of undergraduate mathematics using videoconferencing and audiographics. Distance Education, 19(2), 299–318. doi: 10.1080/0158791980190208

    Article  Google Scholar 

  • Heilesen, S. (2010). What is the academic efficacy of podcasting? Computers & Education, 55(3), 1063–1068. doi:10.1016/j.compedu.2010.05.002

    Article  Google Scholar 

  • Hojjatie, B., Hooshmand, H., Leader, L., Brevik, E., & Groszos, M. (2008). How can the use of tablet PCs in science and engineering improve teaching and learning? In R. H. Reed, D. Berque, & J. Prey (Eds.), The impact of tablet PCs and pen-based technology on education: Vignettes, evaluations and future directions (pp. 47–53). West Lafayette, IN: Purdue University Press.

    Google Scholar 

  • James, R., Krause, K., & Jennings, C. (2010). The first year experience in Australian universities: Findings from 1994–2009. Melbourne, Vic, Australia: Centre for the Study of Higher Education, University of Melbourne.

    Google Scholar 

  • Kanter, B. (2007, March). Introduction to screencasting. Retrieved from http://www.idealware.org/articles/introduction-screencasting-0.

    Google Scholar 

  • Lamborn, J., & Loch, B. (2013, December 8–11). Demonstrating the relevance of mathematics to first year students in engineering courses – what are the critical elements for a successful project? Paper presented at the annual conference of the Australasian Association for Engineering Education, Gold Coast, Qld, Australia.

    Google Scholar 

  • Loch, B. (2005). Tablet technology in first year calculus and linear algebra teaching. In M. Bulmer, H. MacGillivray, & C. Varsavsky (Eds.), Proceedings of Kingfisher DELTA’05: Fifth southern hemisphere conference on undergraduate mathematics and statistics teaching and learning (pp. 231–237). Brisbane, Qld, Australia: University of Queensland.

    Google Scholar 

  • Loch, B. (2009). USQ deploys new lecture recording software. DE Quarterly, Summer 2009/2010, 3, 2.

    Google Scholar 

  • Loch, B. (2012). Screencasting for mathematics online learning – a case study of a first year operations research course at a dual delivery mode Australian university. In A. A. Juan, M. A. Huertas, S. Trenholm, & C. Steegman (Eds.), Teaching mathematics online: Emergent technologies and methodologies (pp. 43–59). Hershey, PA: IGI Global.

    Chapter  Google Scholar 

  • Loch, B., & Donovan, D. (2006, September). Progressive teaching of mathematics with tablet technology. e-JIST: e-Journal of Instructional Science and Technology, 9(2). Retrieved from http://www.ascilite.org.au/ajet/e-jist/docs/ vol9_no2/papers/current_practice/loch_donovan.htm.

  • Loch, B., & Fisher, W. (2010). Facilitating change – tablet PC trials across two distance education focused universities. In C. H. Steel, M. H. Keppell, P. Gerbic, & S. Housego (Eds.), Curriculum, technology & transformation for an unknown future: Proceedings ASCILITE Sydney 2010 (pp. 548–555). Sydney, NSW, Australia: Australasian Society for Computers in Learning in Tertiary Education. Retrieved from http://www.ascilite.org/conferences/sydney10/ procs/Loch-full.pdf.

    Google Scholar 

  • Loch, B., Galligan, L., Hobohm, C., & McDonald, C. (2011). Learner-centred mathematics and statistics education using netbook tablet PCs. International Journal of Mathematical Education in Science and Technology, 42(7), 939–949. doi: 10.1080/0020739X.2011.611910

    Article  Google Scholar 

  • Loch, B., Gill, O., & Croft, A. (2012). Complementing mathematics support with online MathsCasts. ANZIAM Journal, 53(EMAC2011), C561–C575. doi: 10.0000/anziamj.v53i0.4984

    Google Scholar 

  • Loch, B., Jordan, C., Lowe, T., & Mestel, B. (2014). Do screencasts help to revise prerequisite mathematics? An investigation of student performance and perception. International Journal of Mathematical Education in Science and Technology, 45(2), 256–268. doi: 10.1080/0020739X.2013.822581

    Article  Google Scholar 

  • Loch, B., & McDonald, C. (2007). Synchronous chat and electronic ink for distance support in mathematics. Innovate: Journal of Online Education, 3(3), 1–5.

    Google Scholar 

  • Loch, B., & McLoughlin, C. (2011). An instructional design model for screencasting: Engaging students in self-regulated learning. In N. B. G. Williams, M. Pittard, & B. Cleland (Eds.), Changing demands, changing directions. Proceedings ASCILITE Hobart (pp. 816–821). Hobart, Tas, Australia: Australasian Society for Computers in Learning in Tertiary Education. Retrieved from http://www.ascilite.org.au/conferences/hobart11/downloads/papers/Loch-concise.pdf.

    Google Scholar 

  • Loch, B., & McLoughlin, C. (2012). Teaching threshold concepts in engineering mathematics using MathsCasts. In L. Mann & S. Daniel (Eds.), The profession of engineering education: Advancing teaching, research and careers: 23rd annual conference of the Australasian Association for Engineering Education (pp. 1079–1086). Melbourne, Vic, Australia: Australasian Association for Engineering Education.

    Google Scholar 

  • Logan, M., Bailey, N., Franke, K., & Sanson, G. (2009). Patterns of tablet PC use across multiple learning domains: A comparison program. In D. Berque, L. Konkle, & R. Reed (Eds.), The impact of tablet PCs and pen-based technology on education: New horizons (pp. 83–92). Lafayette, IN: Purdue University Press.

    Google Scholar 

  • Lyons, T., Cooksey, R., Panizzon, D., Parnell, A., & Pegg, J. (2006). Science, ICT and mathematics education in rural and regional Australia: The SiMERR national survey. Retrieved from http://www.une.edu.au/simerr/pages/projects/1nationalsurvey/Abridged%20report/Abridged_Full.pdf.

    Google Scholar 

  • Maclaren, P. (2014). The new chalkboard: The role of digital pen technologies in tertiary mathematics teaching. Teaching Mathematics and Its Applications, 33(1), 16–26. doi: 10.1093/teamat/hru001

    Article  Google Scholar 

  • Marshall, C., & Rossman, G. B. (1999). Designing qualitative research (3rd ed.). Thousand Oaks, CA: Sage Publications.

    Google Scholar 

  • Mason, J., & Spence, M. (1999). Beyond mere knowledge of mathematics: The importance of knowing-to act in the moment. Educational Studies in Mathematics, 28, 135–161.

    Article  Google Scholar 

  • Matthews, K. E., Adams, P., & Goos, M. (2009). Putting it into perspective: Mathematics in the undergraduate science curriculum. International Journal of Mathematical Education in Science and Technology, 40(7), 891–902. doi: 10.1080/00207390903199244

    Article  Google Scholar 

  • McCabe, B., & Hobohm, C. (2012). Promoting asynchronous interactivity of recorded lectures in blended learning environments. In M. Brown, M. Hartnett, & T. Stewart (Eds.), Future challenges, sustainable futures: Proceedings ASCILITE Wellington NZ (pp. 612–621). Wellington, New Zealand: Australasian Society for Computers in Learning in Tertiary Education.

    Google Scholar 

  • McDonald, C. (2013). Evaluating the use of online synchronous communication to enhance learning in statistics. Unpublished Doctor of Education dissertation, Queensland University of Technology, Brisbane, Qld, Australia.

    Google Scholar 

  • McDonald, C., Dunn, P. K., Loch, B., & Weiss, V. (2013). StatsCasts: Supporting student learning of introductory statistics. In D. King, B. Loch, & L. Rylands (Eds.), Lighthouse Delta 2013, 24–29 November, Kiama, Australia: Shining through the fog: The 9th Delta conference on teaching and learning of undergraduate mathematics and statistics: Proceedings (pp. 113–123). Sydney, NSW, Australia: School of Computing, Engineering and Mathematics, University of Sydney on behalf of the International Delta Steering Committee.

    Google Scholar 

  • Musarrat, M., Loch, B., & Williams, B. (2013). Enablers and Barriers to Academic’s Acceptance of Technology: Can “Individual Differences” Make a Difference? In H. Carter, M. Gosper, & J. Hedberg (Eds.), Electric dreams: Proceedings ASCILITE 2013 Sydney (pp. 607–611). Sydney, NSW, Australia: Australasian Society for Computers in Learning in Tertiary Education. Retrieved from http://www.ascilite.org.au/conferences/sydney13/program/ papers/Musarrat.pdf.

    Google Scholar 

  • Nooriafshar, M. (2011). New and emerging applications of tablet computers such as iPad in mathematics and science education. Paper presented at the 11th international conference of the mathematics education into the 21st century project, Grahamstown, South Africa.

    Google Scholar 

  • Olivier, W. (2005). Teaching mathematics: Tablet PC technology adds a new dimension. In A. Rogerson (Ed.), The mathematics education into the 21st century project: Universiti Teknologi Malaysia: Proceedings of the eighth international conference: Reform, revolution and paradigm shifts in mathematics education (pp. 176–181). Retrieved from http://math.unipa.it/~grim/21_project/21_malasya_2005.htm.

    Google Scholar 

  • Parsons, S., Croft, T., & Harrison, M. (2009). Does students’ confidence in their ability in mathematics matter? Teaching Mathematics Applications, 28(2), 53–68. doi: 10.1093/teamat/hrp010

    Article  Google Scholar 

  • Phillips, P., & Loch, B. (2010). Building lectures and building bridges with socio-economically disadvantaged students. Educational Technology & Society, 14(3), 240–251.

    Google Scholar 

  • Reed, R., & Berque, D. (Eds.) (2010). The impact of tablet PCs and pen-based technology on education: Going mainstream. West Lafayette, IN: Purdue University Press.

    Google Scholar 

  • Reushle, S. E., & Loch, B. (2008). Conducting a trial of web conferencing software: Why, how, and perceptions from the coalface. Turkish Online Journal of Distance Education, 9(3), 19–28.

    Google Scholar 

  • Rogers, E. M. (2003). Diffusion of innovations (5th ed.). New York, NY: Free Press.

    Google Scholar 

  • Rylands, L. J., & Coady, C. (2009). Performance of students with weak mathematics in first-year mathematics and science. International Journal of Mathematical Education in Science and Technology, 40(6), 741–753. doi: 10.1080/00207390902914130

    Article  Google Scholar 

  • Skemp, R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26. Retrieved from http://www.nctm.org/ publications/article.aspx?id=20558.

    Google Scholar 

  • Smith, G. G., & Ferguson, D. (2004). Diagrams and math notation in e-learning: Growing pains of a new generation. International Journal of Mathematical Education in Science & Technology, 35(5), 681–695. doi: 10.1080/0020739042000232583

    Article  Google Scholar 

  • Sugar, W., Brown, A., & Luterbach, K. (2010). Examining the anatomy of a screencast: Uncovering common elements and instructional strategies. International Review of Research in Open and Distance Learning, 11(3),

    Google Scholar 

  • Taylor, J. A., & McDonald, C. (2007). Writing in groups as a tool for nonroutine problem solving in first year university mathematics. International Journal of Mathematical Education in Science and Technology, 38(5), 639–655. doi: 10.1080/00207390701359396

    Article  Google Scholar 

  • Taylor, J. A., & Morgan, M. (1996). Engineering studies by distance education the hidden barrier: An Australian perspective. Queensland Researcher, 12(2), 25–32. Retrieved from http://www.iier.org.au/qjer/qr12/taylor.html.

    Google Scholar 

  • Valsiner, J. (2007). Cultures in minds and societies: Foundations of cultural psychology. New Delhi, India: Sage Publications.

    Google Scholar 

  • Varsavsky, C. (2010). Chances of success in and engagement with mathematics for students who enter university with a weak mathematics background. International Journal of Mathematical Education in Science and Technology, 41(8), 1037–1049. doi: 10.1080/0020739X.2010.493238

    Article  Google Scholar 

  • Victorian Auditor-General. (2012). Science and mathematics participation rates and initiatives. Melbourne, Vic, Australia: Victorian Government Printer.

    Google Scholar 

  • Wandel, A. P. (2009, December 6–9). Utilising tablet PCs in tutorials to aid external students. Paper presented at the annual conference of the Australasian Association for Engineering Education, Adelaide, SA, Australia. Retrieved from http://eprints.usq.edu.au/6427/

    Google Scholar 

  • Wandel, A. P. (2010). Student usage of videos containing worked solutions. Paper presented at the annual conference of the Australasian Association for Engineering Education, Sydney, NSW, Australia. Retrieved from http://aaee.com.au/conferences/AAEE2010/PDF/AUTHOR/AE100117.PDF.

    Google Scholar 

  • Wise, J. C., Toto, R., & Lim, K. Y. (2006, October 28–31). Introducing tablet PCs: Initial results from the classroom. Paper presented at the 36th American Society for Engineering Education/Institute of Electrical and Electronics Engineers conference, San Diego, CA. 1–20. Retrieved from http://www.irrodl.org/index.php/irrodl/article/view/ 851/1596.

    Google Scholar 

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Authors
  1. Linda Galligan
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  2. Christine McDonald
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  3. Carola Hobohm
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  4. Birgit Loch
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  5. Janet Taylor
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Editor information

Editors and Affiliations

  1. University of Calgary, Canada

    Jennifer Lock

  2. University of Southern Queensland, Australia

    Petrea Redmond  & Patrick Alan Danaher  & 

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© 2015 Linda Galligan, Christine McDonald, Carola Hobohm, Birgit Loch and Janet Taylor

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Galligan, L., McDonald, C., Hobohm, C., Loch, B., Taylor, J. (2015). Conceptualising, Implementing and Evaluating the Use of Digital Technologies to Enhance Mathematical Understanding: Reflections on an Innovation-Development Cycle. In: Lock, J., Redmond, P., Danaher, P.A. (eds) Educational Developments, Practices and Effectiveness. Palgrave Macmillan, London. https://doi.org/10.1057/9781137469939_8

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