Having started teaching the A-level Statistics 1 module several years ago I wanted to deliver a modern and relevant curriculum and wanted to encourage pupils to understand the uses and applications of graphical calculators. Prior to teaching the course I identified that I would use the graphical calculators to aid the teaching of measures of location, measures of dispersion, correlation and regression.
Several members of my faculty at the time were using graphical calculators in lessons and we used faculty time to do some inset on this. At the time the school was setting up a rental system for graphical calculators in order to make them more readily available to students for a lower price. I had not used graphical calculators before but wanted to utilise the equipment available in the department and highlight to pupils how more efficient methods can be used to aid calculations.
In the initial lesson that we used the graphical calculators I wanted to demonstrate to the class how efficiently they could calculate variance and standard deviation using a graphical calculator. However, I did not want students to miss out on learning the basic principle of what variance is a measure of. To do this I first did a question with two sets of numbers to demonstrate variance. On one I calculated the variance of 99,100 and 101 and on the other the variance of 50, 100 and 150. This helped pupils to grasp the concept.
I then showed pupils a larger tabulated data set and went through the manual calculations they could perform. After these two manual exercises had been completed (and students were all moaning about the amount of sums they had just done on a standard calculator!) we looked at using a graphical calculator to do the analysis.
I followed this process when teaching others areas. I always tell classes that the order is ‘principle then manual sum then calculator. The calculator is not used to replace manual calculation but as an alternative method to speed up the calculation and avoid human error. I also spent time discussing with pupils when using the calculator would be most efficient and when the exam paper was looking for marks for the calculation. It is vital students identify when they are being marked for shown working.
In my classroom the students used the calculators frequently in lessons. However, I did encounter several students who worried about using the calculators in the examination as they feared they would forget how to compute an answer. However, most pupils realised that a proportion of the S1 paper was calculation and computation and using a calculator would allow them more time for other questions.
I have worked with several students with Special Educational Needs who found the calculator gave them more confidence with questions that were otherwise very intimidating given the amount of written work required.
I believe that my emphasis on considering what skill the question was demanding resulted in my students being more reflective and that while using the calculators students are thinking about what information they are inputting into giving the calculator and what information does the calculator need to be able to answer the question they are tackling. For example when looking at the ‘product moment correlation coefficient’ students have to amend the settings to tell the calculator to calculate the relationship between the two variables.
Graphical calculators can help speed up the process of some calculations but can also provide a powerful checking tool for students to help them work more independently. Using the calculators also helps students to understand how technology can aid statistics. I always stress the importance to students of placing the statistics we teach in context of the outside world. To me a statistician understands their work yet will use technology to analyse data as the heart of statistics is interpretation.
Getting pupils to enter the sums and change settings can be a challenge. In future I would like to explore using a visualizer or webcam so students can see me computing my answer on the interactive board and follow the steps. Since I initially started using graphical calculators I have moved to a school where the calculators were relatively unused. My using these has spurred other teachers to explore this resource and now students are appreciating the wider applications of the graphical calculator.