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We currently live in a technological world. Every single person in the developed world deals with technology on an everyday basis. The most common forms of everyday technology are based around maths. Barcode scanners, credit cards, computers etc all fundamentally use mathematics in some form. We as teachers need to educate students on the application of technology and more importantly how to maximise its potential. Calculators in maths have increased the ability to push boundaries with mathematical concepts and thus discover more mathematical concepts to aid the technological advancing world.
Should calculators (or technology) be used in mathematical education? Well I certainly would not be typing this onto a piece of virtual paper let alone even discussing such a point. Calculators/technology should be viewed as an aid to education and should be utilised to its full potential. There are many benefits for the use of technology and I will analyse a few.
Technology provides opportunity.
A simple example for this would be the fact that a student using a graphic calculator or graphing software on a computer could graph and analyse a quintic function. Trying to draw such a function with no form of technology is extremely difficult such that such analysis would have never been considered prior to the technology age. This is just one example but there are just so many examples for which it overwhelmingly suggests that technology is essential for development. Student will graduate at the end of this year with a mathematical education similar to that of a PhD student from the early 20th century. We can consider also that in 20, 40 even 100 years time that students may be learning four times as much math in one year than we are now due to development which is only possible by the opportunity that technology provides.
Technology saves time.
As with opportunity technology saves on calculation time and repetition work so that students can progress through work at a quicker rate therefore covering more topics in less time. Using the above example of a quintic function, just imagine inputting x and calculating the y value for ten or more data points, what a nightmare! But in 55 seconds a quintic graph can be shown and then analysed. The instant feedback can be most helpful for students.
Technology engages students.
Students love (as I did) to engage with technology in all forms, from mobile phones to iPods to gaming consoles etc… and so it would be only intelligent to use this interest in technology to engage students in the education of maths. As we know a smarter, more engaging society has long term benefits so the better we can educate the students the better off society will be in the long term. Providing students with technology to complete tasks that are normally completed on paper can be more rewarding purely because the students engaged the technology and therefore showed a genuine interest in the task at hand.
One disadvantage which I believe relates more to the current education situation is the cost. Unfortunately with new technology comes the cost and to put it simply most students and schools cannot afford it. As with all technological trends, as the technology gets older it becomes cheaper, but by then there is always a new one out and so you will always be one step behind. If cost was no issue then the education of mathematics, in my opinion, should utilise the potential of technology to engage students in the understanding and analysis of mathematical concepts, laws and formulae.
2. Metaphors of Technology in Education
I believe the article has pedagogical value as the metaphors categorise relevant situations while acknowledging that some educators are in-between and so can relate to one or more metaphors. They can be used to help identify problems or issues and at the same time be used to plan for the future. From the classroom examples, (Goos, Galbraith, Renshaw & Gieger, 2000, p. 308) 'the teacher lacked personal autonomy in the use of technology' which can result in a technology-poor education. This example would closely relate to many experienced educators who had not grown up with the technology available today and may be intimidated by it. The set of Metaphors can enable the teacher to see the level of knowledge they have of technology and can see a possible direction to progress. This can give teachers confidence in learning the technology and therefore giving them better future planning.
In the cases where technology is the master, teachers may realise that there is too much reliance on the technology as students can show a lack of understanding when assessed without technology which can leave the teacher feeling inadequate and frustrated with the general understanding of technology. In this situation teachers can use the metaphors to plan to improve their approach to technology so that in the future technology can be more of, say, a partner.
It is important to consider the quality of application from the teacher with technology. If the teacher is not presenting the technology in such a way to engage their students then although they are using technology the students are not learning the benefits i.e. technology as the master. The use of technology may need to be presented differently as not all classrooms learn the same, so this diversity needs to be considered also.
In conclusion, the metaphors may or may not be useful for every educator but I still believe they hold value for educators to consider when reflecting on their teaching strategies and student performances. As found through the VCAA pilot study (Evans, Norton & Leigh- Lancaster, 2003, p.315) that technology helped students in extended analysis so educators should be well aware of useful strategies and consider the many resources available to develop ways for a more technology-rich education.
Goos, M. Galbraith, P. Renshaw, P. Geiger, V. (2000) Reshaping Teacher and Student Roles in Technology-Enriched Classrooms. Mathematics Education Research Journal Vol. 12 (No.3), 303-320.
Evans, M., Norton, P. & Lancaster, D.L. (2003) The Victorian Curriculum and Assessment Authority (VCAA) Mathematical methods (CAS) pilot study examinations 2002. In L.
Bragg, C., Campbell, G. Herbert & J. Mousley (Eds) MERINO. Mathematics Education Research: Innovation, Networking, Opportunity. Proceedings of the 26th Annual Conference of the Mathematics Education Research Group of Australasia. (pp. 309-315). Geelong: MERGA.