MATHEMATICS


Making sense of maths


Allan Duncan, senior lecturer at the University of Aberdeen School of Education, discusses the role that technology can play in helping pupils to discover the joy of mathematics


increase and renewed emphasis is being placed upon encouraging enthusiasm for the subject. With this year’s crop of graduates facing fewer


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jobs and talk of the economic slowdown continuing, increasing the next generation’s ability to compete in the international employment market is essential. The more competitively placed today’s learners are, the more resilient they will be in the employment market and the stronger our economy will be. The foundations for this lie in education, in motivating pupils and encouraging passion for the subject. The Scottish Curriculum for Excellence encourages


teachers to create learning situations in which students can be open to new thinking and ideas and it would be short-sighted to ignore the role that technology can play in this. It places an emphasis on teaching students to think


creatively and independently, to link and apply new kinds of learning to new situations, communicate in different ways and in different settings. While technology in general can help to achieve these aims, the use of innovative STEM-subject ICT can really help bring a subject such as maths to life.


The case for technology


There is a rich body of research that supports the role of technology in mathematics education. The right technology can help to improve students’ understanding of multiple representations and how they link to one another which, in turn, leads to a more sound understanding of how maths can be applied in the world around them. This relational understanding of the subject enhances


mathematical discovery for students; put simply, it is about knowing how maths works, how the different parts of the subject affect each other and the world around them, that provides a springboard to a greater level of knowledge and enjoyment of the subject. Research indicates that the way teachers use


technology in their classrooms is related to their beliefs about maths in general, and that teachers who emphasise conceptual understanding, making sense of


STEM CPD in Scotland


• STEM Scotland: www.stemscotland.com • Scottish Mathematical Council: www. scottishmathematicalcouncil.org.uk


• T3 – professional development for the appropriate use of educational technology in the teaching and learning of mathematics and science: www.tcubed.org.uk


• Nspiring Learning – a virtual resource centre for TI-Nspire technology: www. nspiringlearning.org.uk


• Scottish Learning Festival: www.ltscotland. org.uk


HE STRENGTH of the STEM workforce is often viewed as an indication of a nation’s ability to sustain itself and, in a time of slow economic growth, this sustainability is crucial. Meanwhile, the role of mathematics in industry continues to


mathematical ideas and drawing conclusions based on mathematical grounds, will reflect their beliefs in their use of the technology. A project that looked into the use of handheld


graphing technology and its implications on classroom practice in 2002 (Burrill et al.) found that students with access to this technology are more flexible in their solution strategies, make conjectures and move more comfortably among algebraic, numeric and graphical approaches. These are just some of the skills that are needed in a STEM-literate workforce.


Scottish research


Despite the rich body of national and international research literature providing evidence of the benefits of using technology to enhance students’ learning in mathematics, it appears that many teachers do not take advantage of the more specialised technology that is available. The Trends in International Maths and Science


Survey report of 2007 ranked Scotland 20th of 36 countries in maths performance, which some would see as a call for an increase in the use of specialist ICT to improve understanding. It seems that lack of familiarity and a shortage of cost-effective CPD are two of the biggest barriers to the regular and widespread use of specialist technology but free training is available for teachers. The international STEM CPD organisation T3


(Teachers Teaching with Technology) provides free curriculum-specific training across Scotland on the use of specialist ICT such as handheld graphing devices. Meanwhile, cost-effective CPD is available at events such as the Scottish Learning Festival, STEM Scotland or the Scottish Mathematical Council. While historical and international research projects


can be an invaluable source of information, there was a clear need for a home-based project that looked into the use of this technology and its impact on the Scottish curriculum and on Scottish students. The research project began in 2008 and was conducted over two years using the TI-Nspire suite of learning tools. The views of teachers using the technology in 66


detailed lessons were collected and mapped against curriculum objectives to provide qualitative evidence that could reliably inform Scottish schools of the effects of technology on mathematical understanding. As part of the evaluation, teachers were asked to assess


pupils’ mathematical activity with respect to Curriculum for Excellence indicators. Of the 66 responses, 91 per cent indicated that the handheld technology had a positive impact on student’s enthusiasm and motivation. The impact was beneficial on other key indicators,


including making reasoned evaluations, openness to new thinking and ideas, along with creative and independent thinking. The ability to learn independently and as part of a group was influenced positively by the use of the handhelds, while problem-solving skills and the ability to make reasoned evaluations – both critical skills in industry – were also enhanced. The teachers involved in the study, no matter


what background experience with ICT they had, were convinced that the use of multiple representations of mathematical concepts enhances their students’ relational understanding. Several teachers commented upon the positive contribution which the handhelds made to the pace and amount of learning.


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The way from A to B: using wise choices to manage challenging behaviour Mike Stanton


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Genetic aspects of autism and implications for treatment Dr Alistair Pagnamenta


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How relationship-based play supports


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40 YEARS OF MEDICAL EDUCATION 13 Ultimately, while technology in general can help


students explore subject content across the curriculum, the effect that specialist ICT such as graphing handheld resources can have on a subject such as maths is proven to be far-reaching, encouraging more understanding of the subject and enabling creativity – something that we need to emphasise in order to support the next generation of innovators and inventors. To support students’ exploration of the subject, we


also need to look at how to support teachers in using specialised technology to enhance teaching. Ensuring that this change is introduced at every


stage, from education policy to the chalkface, is crucial. Whether this support comes in the guise of tailored CPD activities, free workshops, STEM activities or free product training and sharing best practice, it is needed to make the most of what the 21st century has to offer learning. The global marketplace has changed radically


during the technological revolution, and teaching methods in the STEM-subjects should also develop


if we are to offer our students the best possible start in their lives.


SecEd


• Allan Duncan taught secondary mathematics in Scotland before moving to teacher education in 1985. He has been involved in international development work in mathematics education and is a specialist in the use of ICT to enhance teaching. He is a member of the Scottish Mathematical Council, the Maths Advisory Group for Scotland (MAGS), and T3 UK.


Further information


To download a copy of Mr Duncan’s research report, called Teachers’ views on dynamically linked multiple representations and relational understanding of mathematics – an investigation into the use of TI-Nspire in Scottish secondary schools, visit http://www.abdn. ac.uk/education/documents/UofA_Report_Mar10.pdf Printed copies of the report will also be available


at the Scottish Learning Festival from the Texas Instruments stand, H7.


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