Lesson 30 How do I handle the data?

# Episode 1

Reasoning Resources: Worksheets 1, 2 and 3
Introduction and small group work
This is an activity to promote metacognition and bridging.

Given three different contexts, pupils recognise that different modes of data representation are needed to reveal the inner meaning.

Introduce the activity as exploring different ways of analysing three sets of data. Emphasise that one of the most important things a mathematician does is to decide what the question is. Once the question is clarified, good ways of finding answers can be explored. Ask what the pupils understand by ‘handling’ and ‘analysis, and help them to realise in their own way that the task is to group, classify, simplify or represent data in ways that allow some comparisons or ideas to come out. Get them to list data handling methods such as: bar charts, back-to-back stem-and-leaf, tallying, simple graphs, scatter graphs and mean/median/mode/range
Metacognition involves stepping back from the immediate problems, and searching memory for models of data representation which would best fit each. Give out Worksheets 1 to 3 and look at the three sets of data, going over the structure of each. Ask pupils to discuss in groups how they would approach the data.
Thus the whole class will benefit from hearing the possible solutions and why they were chosen, from each working group. They should have about 10 minutes before they report back. While they work on the task, help groups to clarify their ideas and get ready for the discussion.
Class evaluation of ideas
The focus throughout is on the data-handling aspect of the National Curriculum, but strays also into the use of mathematical modelling in science. Share the different groups’ ideas for each of the three data sets, which will mainly be clarifying the main questions in the data sets. Record the suggestions on the board. Accept different ideas if such are evident, and allow all the groups then to choose freely their preferred method of analysis. Emphasise that if a group finds a method unsatisfactory that is also a worthwhile finding; they should try to think why the method was not suitable.
The first problem is one in which, although the average grade of the girls is higher than for boys, just using averages does not tell the whole story. In fact for Grades A to C (in the results given) there is not much to choose between the boys’ and the girls’ results, whereas the boys are worse in the grades below C. Thus they need a form of representation which will reveal the detail.
The second problem actually has two independent variables (amount of chemical A and temperature), and here pupils need to see that the best way of comparing the results is to use Cartesian representation.
The third problem is set up as a correlation one. The pupils need to ‘bridge’ to TM22:Comparing correlations and realise that if they want to check how well pupils’ KS3 English results predict their GCSE results, then what they need to do is to compare the boys’ and girls’ scatters, again with Cartesian representation.