Last year I did a bit of an action enquiry looking at using graphing software in maths lessons. My enquiry was based around the following question: Does graphing software enhance students’ understanding of key mathematical concepts? I though the following summary might be of interest to some.
I am interested in using technology in mathematics teaching and learning. I have a particular interest in graphing software such as Geogebra and Desmos. Having begun using these packages last year, I believe that students develop a deeper understanding of certain mathematical concepts such as coordinate geometry and trigonometry when using this software. This action enquiry project aims to develop my use of this software with my students and to investigate whether or not using this technology does develop students’ mathematical understanding.
Ofqual (2016) states that “the use of technology…must permeate the study of A-Level Mathematics”. Thus the increased use of technology such as graphing software is particularly important at KS5, especially with the reformed specifications from September 2017 with an emphasis on problem solving, modelling and large data sets. The independent charity MEI recognises that technology “aids understanding” and dedicates a significant part of its funding and training to the embedding of technology in mathematics education. S.Hegedus et al (2017) suggests that technology can “take over a large part of the repetitive calculations….leaving more time for interpreting, reflecting, modelling…”.
However, despite these positive outcomes, care must be taken when it is claimed that
“schools are wasting millions of pounds per year on useless gadgets” (Telegraph 2012) and that some schools in America are successfully shunning the use of technology in favour of a “holistic approach promoting imagination and creativity” (Guardian, 2015)
I attended training during courses run by the FMSP and the MEI on the use of dynamic graphing software. This gave me the skills and confidence to use Geogebra and Desmos in my lessons. I had discussions with teachers in the maths department on the use of such software and I observed lessons on coordinate geometry topics; some using technology and some not using technology. I also reflected on my own teaching techniques of how I used to teach topics that would have benefited from using graphing software. An example of this is when I ran an investigative lesson with Year 12 about y=ex where students spent 20 minutes drawing a graph and by doing so wasted valuable thinking time when the graph could have been produced immediately with the aid of technology.
Using the technology
During the past few months I have incorporated graphing software in my lessons whenever an opportunity arose. For example, my Year 11 students used a Desmos (classroom) activity involving equations of lines and curves. They were actively engaged and deep in thought throughout the hour. I was particular pleased when two students asked what the general equation of a circle was; a topic which is normally introduced only in A-Level Maths.
My Year 12 class have used graphical calculators throughout the year and have been able to plot graphs, solve equations and work with the pre-loaded statistical tables independently. Students particularly liked verifying answers in an exam situation.
My Year 12 and 13 classes have worked extensively with GeoGebra. Topics which worked particularly well with this technology were Circles, Numerical Methods (fixed point iteration, Newton-Raphson), differentiation (optimisation and classifying stationary points), integration and Maclaurin Series. In these topics, the dynamic geometry helped explain why methods worked and encouraged students to ask questions, make predictions and identify limitations of methods.
It would be very difficult to conclude that by teaching maths with the aid of technology that students have developed a deeper understanding of key topics. What I can say is that students were engaged in thinking and exploring more when the technology was used well. The connection between the algebraic form and the graphical form of the mathematics was made explicit and students became more confident with graph work.
I created a questionnaire to gather the opinions of my Year 12 & 13 classes. Many students stated they had a better understanding of concepts using Geogebra because of the visual representation. 72% of students used Geogebra at home. The minority who didn’t find it so useful struggled using the software and wanted more lesson time being taught how to use it.
In order to find out which method of incorporating dynamic graphing software into my lessons has been most effective, I asked students to score three different methods of using the software a score out of 5, with 5 being the most useful. Working individually on the software averaged a score of 3.4, doing so in pairs scored 3.7 and being shown the software on the board scored 4.7. I was surprised by this result and had assumed that students would prefer working on the software themselves. Next year I will look to teach the students more explicitly how to use Geogebra whilst still showing students visuals and examples on the interactive white board.
I aim to continue to use graphing software and other forms of technology to enhance my lessons. My blog and twitter account will continue to document and share how I use dynamic geometry software in lessons. I also plan to cascade my findings to the maths department and to promote the use of dynamic geometry in department meetings and schemes of learning. This year’s action enquiry is centred around using spreadsheets in KS3. I will share that once completed. As usual, any questions or observations are welcomed.