Will Davies has been working with us on the scheme of work for the new A-level. Over the last few years he has predominantly taught the statistics content for the A-level courses. Here are his thoughts on the large data set:
“When the new specifications were announced the introduction of these “large data sets” (LDS) left me sceptical, and unsure of exactly how we were going to work with them. With time came a lot more clarity; actually being able to pick over the data sets that were released with the sample assessment material meant we could start to see how they were going to be assessed, and how they might fit into our teaching.
And I have come to this conclusion: the LDS is my joint-favourite thing about the new A-Level – the other aspect being that we’ve been able to tear up the old order of topics and build a curriculum that we feel teaches maths in the most logical order and in the best manner. Being able to combine the applied topics in with the pure topics they depend on is key: e.g. binomial theorem and binomial expansion, as well as teaching variable acceleration immediately after calculus is taught.
I have read on Twitter a lot of negativity about the LDS, and I am unsure why. My instinct says that the reason is because the LDS is being perceived as a separate topic that needs to be taught in addition to other content (that we’re already unsure whether we can fit it all in satisfactorily). As a department, from very early in the process we realised that this shouldn’t be the case – the LDS is not a separate topic, it is instead the tool that you use to teach all the data-handing parts of the course.
Every time you do an example – it comes from the LDS.
Every time you set an exercise in class – it comes from the LDS.
Every time you set a homework – it comes from the LDS.
The more the students immerse themselves in the LDS the more familiar they become with it. Homeworks can be to do some calculations or create some charts (and email them to use in advance where appropriate) then as a group we can discuss next lesson. My other big idea for embedding the LDS into our lessons is to have at least once per week a Show-me / Tell-me starter (regardless of whether the lesson is going to be on stats or not). Students will be encouraged to do a little investigation themselves, then getting the class to discuss together discuss the potential causes (e.g. our outliers). This will be way in which we can as a class build up a bank of interesting observations of our LDS, just like the observation we made when we were examining the MEI sample assessment material.
This question from the MEI sample A Level assessment – we were drawn to the very long tail at the bottom of the Sub-Saharan Africa box-plot, and wondered which countries were causing this. Looking at the LDS we quickly came up with 3 countries with very low birth rates: Saint Helena, Mauritius, Seychelles – all island nations. Which feels like a nice fact – that the island nations of Sub Saharan Africa have significantly lower birth rates than other countries in that region.
This brings me onto our choice of exam board – the data sets are not provided in the exam, yet students are expected to be able to use some very specific knowledge of them in order to gain some marks in their exams. With the large LDSs (like Edexcel’s weather data) you could study that for a couple of years and maybe still have examined at the key pieces of data.
So, MEI has the smallest large data set (covering information about the 237 countries of the world), and that brings its own advantages – it is printable. The bulk of it fits on 3 A3 pages, and I have created a single A4 page that expands on the Dependency status of relevant countries. So now all our students have a hard copy of their data set to use – meaning that we don’t always have to be in an IT room when we’re working on it. The other major advantage is that on presenting students with the data set they immediately felt that because it actually wasn’t “too big” that knowing it well was going to be achievable.
When it comes to using technology there are various ways in which we plan to incorporate this with the LDS. The ClassWiz calculator is clearly going to be key as, as is learning a bit about Excel. Filters, sorting and a deep look into the inbuilt statistical formulae will all need to take place – not just for the sake of the LDS, but Excel skills are incredibly useful. We’re also going to look to support/enhance teaching & learning by graphing some of the data in Geogebra and Gnumeric. (Gnumeric is apparently a very good tool for creating box-plots although I am yet to explore that any further). I have also built in Excel a sampler tool that will create random samples from the LDs, although it still needs perfecting. When it is complete I will share it here.
When it comes to assessments, starting work on the LDS from lesson 2 means we will be able to include it in assessments from half term 1 – to start with we will make sure we write the assessments so we know that students have seen (in one form or other) what we will be asking about, then we can progressively choose more and more obscure statistics to include. Finally we plan to set students extended projects to do. These like likely asked them to choose some aspect of the data set, be it a group of regions or a groups of fields, calculate some statistics, create some charts, draw some conclusions, and to write up a little report on their findings.
Identifying the smallest data set, and revisiting it weekly for 2 years will give students the best chance of becoming as familiar as they can be with the LDS (aside from dedicating too much curriculum time to it). I suppose the bottom line is that we feel that using the LDS to teach all data topics is going to be such an improvement on using (essentially random) examples that are using a similar approach with our GCSE statistics. In lessons our year 9s and 10s are currently populating their own data-set (containing information about themselves). They have really enjoyed the data collection (although I did receive a complaint from the English classroom underneath the standing long-jump) – now to analyse it!”