Conceptualising, implementing and evaluating the use of digital technologies to enhance mathematical understanding: reflections on an innovation–development cycle

Edited book (chapter)


Galligan, Linda, McDonald, Christine, Hobohm, Carola, Loch, Birgit and Taylor, Janet. 2015. "Conceptualising, implementing and evaluating the use of digital technologies to enhance mathematical understanding: reflections on an innovation–development cycle." Lock, Jennifer, Danaher, Patrick and Redmond, Petrea (ed.) Educational developments, practices and effectiveness: global perspectives and contexts. United Kingdom. Palgrave Macmillan. pp. 137-160
Chapter Title

Conceptualising, implementing and evaluating the use of digital technologies to enhance mathematical understanding: reflections on an innovation–development cycle

Book Chapter CategoryEdited book (chapter)
ERA Publisher ID2865
Book TitleEducational developments, practices and effectiveness: global perspectives and contexts
AuthorsGalligan, Linda (Author), McDonald, Christine (Author), Hobohm, Carola (Author), Loch, Birgit (Author) and Taylor, Janet (Author)
EditorsLock, Jennifer, Danaher, Patrick and Redmond, Petrea
Page Range137-160
Chapter Number8
Number of Pages24
Year2015
PublisherPalgrave Macmillan
Place of PublicationUnited Kingdom
ISBN9781137469939
9781137469922
Digital Object Identifier (DOI)https://doi.org/10.1057/9781137469939_8
Web Address (URL)https://link.springer.com/chapter/10.1057/9781137469939_8
Abstract

This chapter first outlines the challenges related to reaching 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 It is followed by an analysis of the contribution that our decade of published and unpublished research has made to resolving these challenges.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.

KeywordsOnline Environment ; Educational Development; Online Student; Graphic Tablet; Mathematic Education Research Group
ANZSRC Field of Research 2020390109. Mathematics and numeracy curriculum and pedagogy
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Byline AffiliationsSchool of Agricultural, Computational and Environmental Sciences
Swinburne University of Technology
Southern Cross University
Institution of OriginUniversity of Southern Queensland
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Loch, B. I., Belward, J. A. and Hanan, J. S.. 2005. "Application of surface fitting techniques for the representation of leaf surfaces." Zerger, Andre and Argent, Robert M. (ed.) 16th International Congress on Modelling and Simulation (MODSIM05). Melbourne, Australia 12 - 15 Dec 2005 Melbourne, Australia.
Bridging the divide by screencasting in an introductory statistics class at an Australian university
Khan, Shahjahan, Loch, Birgit and McDonald, Christine. 2010. "Bridging the divide by screencasting in an introductory statistics class at an Australian university." Amin, Zeinab and Hadi, Ali S. (ed.) 10th Islamic Countries Conference on Statistical Sciences. Cairo, Egypt 20 - 23 Dec 2009 Lahore, Pakistan.
Building lectures and building bridges with socio-economically disadvantaged students
Phillips, Peter J. and Loch, Birgit. 2011. "Building lectures and building bridges with socio-economically disadvantaged students." Educational Technology and Society. 14 (3), pp. 240-251.
What do on campus students do with mathematics lecture screencasts at a dual-mode Australian university?
Loch, Birgit. 2010. "What do on campus students do with mathematics lecture screencasts at a dual-mode Australian university? " Green, David (ed.) CETL-MSOR Conference 2009. Milton Keynes, United Kingdom 07 - 08 Sep 2009 Birmingham, United Kingdom .
Employing interdisciplinary collaborations to redefine academic practices in a university Nursing program
Lawrence, Jill, Loch, Birgit and Galligan, Linda. 2010. "Employing interdisciplinary collaborations to redefine academic practices in a university Nursing program." Devlin, M., Nagy, J. and Lichtenberg, A. (ed.) 33rd Higher Education Research and Development Society of Australasia Annual Conference (HERDSA 2010). Melbourne, Australia 06 - 09 Jul 2010 Milperra, Australia.
Scaffolding distance learning in mathematics for engineering: identifying key troublesome knowledge
Galligan, Linda, Wandel, Andrew P. and Hartle, R. Todd. 2010. "Scaffolding distance learning in mathematics for engineering: identifying key troublesome knowledge." Hudson, Peter, Chandra, Vinesh, King, Donna and Lee, Kar-Tin (ed.) 1st Science, Technology, Engineering and Mathematics in Education Conference (STEM 2010). Brisbane, Australia 26 - 27 Nov 2010 Brisbane, Australia.
Preparedness for flexible access to learning materials: how ready are university students and staff?
Albion, Peter, Loch, Birgit, Mula, Joseph M. and Maroulis, Jerry. 2010. "Preparedness for flexible access to learning materials: how ready are university students and staff?" Steel, Caroline, Keppell, Michael, Gerbic, Philippa and Housego, Simon (ed.) 27th Annual Conference of the Australasian Society for Computers in Learning in Tertiary Education (ASCILITE 2010). Sydney, Australia 05 - 08 Dec 2010 Brisbane, Australia.
Building academic numeracy in a first year nursing course using an evaluative model of program development
Galligan, Linda, Loch, Birgit and Lawrence, Jill. 2010. "Building academic numeracy in a first year nursing course using an evaluative model of program development." Coben, Diana and O'Donoghue, John (ed.) ICME 11: Adult Mathematics Education. Monterrey, Mexico 06 - 13 Jul 2008 Limerick, Ireland.
Interaction in synchronous chat tutorials to facilitate learning in introductory statistics
McDonald, Christine, Loch, Birgit and Lloyd, Margaret. 2010. "Interaction in synchronous chat tutorials to facilitate learning in introductory statistics." Reading, Chris (ed.) ICOTS8: Data and Context in Statistics Education: Towards an Evidence-Based Society. Ljubljana, Slovenia 11 - 16 Jul 2010 Voorburg, The Netherlands.
The use of tablet and related technologies in mathematics teaching
Galligan, Linda, Loch, Birgit, McDonald, Christine and Taylor, Janet A.. 2010. "The use of tablet and related technologies in mathematics teaching." Australian Senior Mathematics Journal. 24 (1), pp. 38-51.
Becoming more numerate: the journey of Tania
Galligan, Linda. 2010. "Becoming more numerate: the journey of Tania." Sparrow, Len, Kissane, Barry and Hurst, Chris (ed.) 33rd Annual Conference of the Mathematics Education Research Group of Australasia (MERGA33). Fremantle, Australia 03 - 07 Jul 2010 Sydney, Australia.
Adopting synchronous audiographic web conferencing: a tale from two regional universities
Loch, Birgit, Reushle, Shirley, Rowe, Stephen and Jayne, Nicola. 2010. "Adopting synchronous audiographic web conferencing: a tale from two regional universities." Mukerji, Siran and Tripathi, Purnendu (ed.) Cases on technology enhanced learning through collaborative opportunities. Hershey, PA, United States. IGI Global. pp. 56-72
Go WEST - supporting women in engineering, science and technology: an Australian higher education case study
McDonald, Jacquelin, Loch, Birgit and Cater-Steel, Aileen. 2010. "Go WEST - supporting women in engineering, science and technology: an Australian higher education case study." Cater-Steel, Aileen and Cater, Emily (ed.) Women in engineering, science and technology: education and career challenges. Hershey, PA, United States. IGI Global. pp. 118-132
Distance education teaching and tutoring: two evolving Australian models
Fuller, Anne, McFarlane, Penney, Cretchley, Patricia, McDonald, Christine and Lam, Cam Le. 2005. "Distance education teaching and tutoring: two evolving Australian models." 8th IFIP World Conference on Computers in Education (WCCE 2005): 40 Years of Computers in Education: What Works?. Stellenbosch, South Africa 04 - 07 Jul 2005 Irene, South Africa.
Evolution and emerging trends of university writing groups
Galligan, Linda, Cretchley, Patricia, George, Lucy, Martin-McDonald, Kris, McDonald, Jacquie and Rankin, Janet. 2003. "Evolution and emerging trends of university writing groups." Queensland Journal of Educational Research. 19 (1), pp. 28-41.
Perceived mathematical proficiencies required for first year study at The University of Southern Queensland
Taylor, Janet A., Galligan, Linda and Van Vuuren, Peter. 1998. Perceived mathematical proficiencies required for first year study at The University of Southern Queensland. Toowoomba, Australia. University of Southern Queensland.
Assessment in first year university: a model to manage transition
Taylor, Janet A.. 2008. "Assessment in first year university: a model to manage transition ." Journal of University Teaching and Learning Practice. 5 (1), pp. 19-33.
Learning approaches, personality and concepts of knowledge of first-year students: mature-age versus school leaver
Burton, Lorelle J., Taylor, Janet A., Dowling, David G. and Lawrence, Jill. 2009. "Learning approaches, personality and concepts of knowledge of first-year students: mature-age versus school leaver." Studies in Learning Evaluation Innovation and Development. 6 (1), pp. 65-81.
Evaluating individual teaching on the road to embedding academic skills
Huijser, Hendrik, Kimmins, Lindy and Galligan, Linda. 2008. "Evaluating individual teaching on the road to embedding academic skills." Journal of Academic Language and Learning. 2 (1), pp. 23-38.
An integrative approach to building professional attributes in a first year nursing course: description and preliminary analysis of academic numeracy
Galligan, Linda, Loch, Birgit and Lawrence, Jill. 2010. "An integrative approach to building professional attributes in a first year nursing course: description and preliminary analysis of academic numeracy." Coben, Diana and O'Donoghue, John (ed.) ICME 11: Adult Mathematics Education. Monterrey, Mexico 06 - 13 Jul 2008 Limerick, Ireland.
Using Valsiner
Galligan, Linda. 2008. "Using Valsiner." Goos, Merrilyn, Brown, Ray and Makar, Katie (ed.) 31st Annual Conference of the Mathematics Education Research Group of Australasia (MERGA 31). Brisbane, Australia 28 Jun - 01 Jul 2008 Wahroonga, Sydney, Australia.
Adults returning to study mathematics
Galligan, Linda and Taylor, Janet A.. 2008. "Adults returning to study mathematics." Forgasz, Helen, Barkatsas, Anastasios, Bishop, Alan, Clarke, Barbara, Keast, Stephen, Seah, Wee Tiong and Sullivan, Peter (ed.) Research in mathematics education in Australasia 2004-2007. Rotterdam, Netherlands. Sense Publishers. pp. 99-118
Conducting a trial of web conferencing software: why, how, and perceptions from the coalface
Reushle, Shirley and Loch, Birgit. 2008. "Conducting a trial of web conferencing software: why, how, and perceptions from the coalface." Turkish Online Journal of Distance Education. 9 (3), pp. 19-28.
Spectral schemes on triangular elements
Heinrichs, Wilhelm and Loch, Birgit. 2001. "Spectral schemes on triangular elements." Journal of Computational Physics. 173 (1), pp. 279-301. https://doi.org/10.1006/jcph.2001.6876
Processing laser scanner plant data to extract structural information
Hanan, Jim, Loch, Birgit and McAleer, Tim. 2004. "Processing laser scanner plant data to extract structural information." Godin, Christophe, Hanan, Jim S. and Kurth, Winfried (ed.) 4th International Workshop on Functional-Structural Plant Models (FSPM 2004). Montpellier, France 07 - 11 Jun 2004 Montpellier, France.
Mathematics support program for commencing engineering students between 1990 and 1996: an Australian case study
Taylor, Janet A. and Morgan, Michael J.. 1999. "Mathematics support program for commencing engineering students between 1990 and 1996: an Australian case study." International Journal of Engineering Education. 15 (6), pp. 486-492.
Mathematics for math anxious students studying at a distance
Taylor, Janet A. and Mohr, Joan. 2001. "Mathematics for math anxious students studying at a distance ." Journal of Developmental Education. 25 (1), pp. 30-41.
Change detection through clustering and spectral analysis
Donovan, Diane, Loch, Birgit, Thompson, H. B. and Thompson, Jayne. 2008. "Change detection through clustering and spectral analysis." Brankovich, Ljiljania, Lin, Yuqing and Smythe, William F. (ed.) IWOCA 2007: 18th International Workshop on Combinatorial Algorithms . Newcastle, Australia 05 - 09 Nov 2007 United States.
Making students AWARE: an online strategy for students given academic warning
Taylor, Janet A. and Lawrence, Jill. 2007. "Making students AWARE: an online strategy for students given academic warning." Studies in Learning Evaluation Innovation and Development. 4 (2), pp. 39-52.
A hybrid clough-tocher radial basis function method for modelling leaf surfaces
Oqielat, M. N., Belward, J. A., Turner, I. W. and Loch, B. I.. 2007. "A hybrid clough-tocher radial basis function method for modelling leaf surfaces." Oxley, Les and Kulasiri, Don (ed.) 17th International Congress on Modelling and Simulation (MODSIM07). Christchurch, New Zealand 10 - 13 Dec 2007 Canberra, Australia.
Studying at university: early perceptions and experiences of first year service mathematics students
Taylor, Janet A. and Mander, Alison. 2007. "Studying at university: early perceptions and experiences of first year service mathematics students ." Studies in Learning Evaluation Innovation and Development. 4 (3), pp. 29-43.
Managing staff development for online education: a situated learning model
Taylor, Janet A.. 2003. "Managing staff development for online education: a situated learning model." Journal of Higher Education Policy and Management. 25 (1), pp. 75-87. https://doi.org/10.1080/13600800305742
Overcoming beliefs, attitudes and past experiences: the use of video for adult tertiary students studying mathematics in isolation
Taylor, Janet A. and Galligan, Linda. 2002. "Overcoming beliefs, attitudes and past experiences: the use of video for adult tertiary students studying mathematics in isolation." Australian Senior Mathematics Journal. 16 (1), pp. 20-33.
Self test: a flexible self assessment package for distance and other learners
Taylor, Janet. 1998. "Self test: a flexible self assessment package for distance and other learners." Computers and Education. 31 (3), pp. 319-328. https://doi.org/10.1016/S0360-1315(98)00044-X
Writing in groups as a tool for non-routine problem solving in first year university mathematics
Taylor, Janet A. and McDonald, Christine. 2007. "Writing in groups as a tool for non-routine problem solving in first year university mathematics." International Journal of Mathematical Education in Science and Technology. 38 (5), pp. 639-655. https://doi.org/10.1080/00207390701359396
Research into research on adults in Bridging Mathematics: the past, the present and the future
Taylor, Janet A. and Galligan, Linda. 2006. "Research into research on adults in Bridging Mathematics: the past, the present and the future." Horne, M. and Marr, B. (ed.) 12th Annual International Conference of Adults Learning Mathematics-A Research Forum (ALM) jointly with the Australian Council for Adult Literacy. Melbourne, Australia 03 - 07 Jul 2005 Melbourne, Australia.
A web 2.0/web3D hybrid platform for engaging students in e-learning environments
de Byl, Penny and Taylor, Janet. 2007. "A web 2.0/web3D hybrid platform for engaging students in e-learning environments." Turkish Online Journal of Distance Education. 8 (3), pp. 108-127.
Analysis of student beliefs in a tertiary preparatory mathematics course
Carmichael, Colin S. and Taylor, Janet A.. 2005. "Analysis of student beliefs in a tertiary preparatory mathematics course." Kingfisher Delta '05: 5th Southern Hemisphere Conference on Undergraduate Mathematics and Statistics Teaching and Learning. Fraser Island, Australia 22 - 26 Nov 2005 London, United Kingdom. https://doi.org/10.1080/00207390500271065
Staff perceptions of factors related to non-completion in higher education
Taylor, Janet A. and Bedford, Tasman. 2004. "Staff perceptions of factors related to non-completion in higher education ." Studies in Higher Education. 29 (3), pp. 375-394. https://doi.org/10.1080/03075070410001682637
Mathematics for maths anxious tertiary students: integrating the cognitive and affective domains using interactive multimedia
Taylor, Janet and Galligan, Linda. 2006. "Mathematics for maths anxious tertiary students: integrating the cognitive and affective domains using interactive multimedia." Literacy and Numeracy Studies. 15 (1), pp. 23-43.
Synchronous chat and electronic ink for distance support in mathematics
Loch, Birgit and McDonald, Christine. 2007. "Synchronous chat and electronic ink for distance support in mathematics." Innovate: Journal of Online Education. 3 (3), pp. 1-5.
Progressive teaching of mathematics with tablet technology
Loch, Birgit and Donovan, Diane. 2006. "Progressive teaching of mathematics with tablet technology." Australasian Journal of Educational Technology. 9 (2), pp. 1-6.
Undergraduate mathematics and the role of mathematics learning support
Taylor, Janet A.. 1999. "Undergraduate mathematics and the role of mathematics learning support." Spunde, Walter, Cretchley, Patricia and Hubbard, R. (ed.) Delta '99, the Second Symposium on Undergraduate Mathematics. Laguna Quays, Australia 21 - 24 Nov 1999 Queensland.
Identifying at-risk students: is it possible in a tertiary preparation course for adults?
Carmichael, Colin S., Dunn, Peter K. and Taylor, Janet A.. 2006. "Identifying at-risk students: is it possible in a tertiary preparation course for adults?" Grootenboer, Peter, Zevenbergen, Robyn and Chinnappan, Mohan (ed.) 29th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA29). Canberra, Australia 01 - 05 Jul 2006 Wahroonga, Sydney, Australia.
The evolution of online learning in bridging mathematics at a distance: the tension between learning needs, technological innovation and access restrictions in an Australian regional university
Taylor, Janet A.. 2002. "The evolution of online learning in bridging mathematics at a distance: the tension between learning needs, technological innovation and access restrictions in an Australian regional university." Statham, M. (ed.) Crossing the Bridge: Proceedings of the 10th Australasian Bridging Mathematics. Auckland, New Zealand. UNITEC. pp. 67-74
Learning styles among mature age students: some comments on the approaches to studying inventory (ASI-S)
Fogarty, Gerard J. and Taylor, Janet A.. 1997. "Learning styles among mature age students: some comments on the approaches to studying inventory (ASI-S)." Higher Education Research and Development. 16 (3), pp. 321-330. https://doi.org/10.1080/0729436970160306
Tablet technology in first year calculus and linear algebra teaching
Loch, Birgit I.. 2005. "Tablet technology in first year calculus and linear algebra teaching." Bulmer, Michael, MacGillivray, Helen and Varsavsky, Cristina (ed.) Kingfisher Delta '05: 5th Southern Hemisphere Conference on Undergraduate Mathematics and Statistics Teaching and Learning. Fraser Island, Australia 22 - 26 Nov 2005 Brisbane, Australia.
An innovative learning model for computation in first year mathematics
Tonkes, E. J., Loch, B. I. and Stace, A. W.. 2005. "An innovative learning model for computation in first year mathematics." International Journal of Mathematical Education in Science and Technology. 36 (7), pp. 751-759. https://doi.org/10.1080/00207390500271677
Developing study skills in a first year mathematics course
Taylor, Janet A. and Mander, David. 2003. "Developing study skills in a first year mathematics course." New Zealand Journal of Mathematics. 32 (Supplementary issue), pp. 217-225.