What mathematical skills and understanding are needed?

How well is this set of data matched to pupils' levels of mathematical knowledge and understanding? Children are learning ICT skills and specialised language, but may not yet be able to make the link with underlying mathematical concepts. There is a great risk that the ICT will detract from the Mathematics. To investigate the data using Excel, children must be absolutely sure of the underlying Mathematics.

Differences in mathematical understanding, thinking skills and language ability were in evidence, and were most marked in the low ability groups. The lowest ability pupils found it harder to make direct observations from the data. Thoughts were triggered by association: "You know the flag waving, I watched that with my Dad."

It was best to start with field events for younger pupils. The high jump could be marked on the wall. Although Year 4 had not been introduced to decimals, they showed good understanding of metres and centimetres. Some Year 5 pupils were beginning to show an understanding of decimal notation. I asked what 2.05 m means. A child replied tentatively, "Two metres - and five hundredths. Five - centimetres?"

The data for track events presented problems. Year 4, and many Year 5 pupils, lacked understanding of times such as 10.50, 10.05 seconds and were unable to make comparisons.

Mathematics "warm ups" at the start of the teacher-led sessions in the ICT suite were especially valuable. One teacher began with counting in 4s. Children need this skill in identifying years on the x-axis, since not all the years are labelled. Another useful revision / warm up activity would be to recap how we find the difference. Children need a secure understanding prior to entering a formula to subtract.

Interpreting graphs

All were able to equate the fastest time with the shortest bar, or the longest throw with the highest point. They were able to describe the graphs ("It's getting higher"), but often needed prompting to explain what the trend indicated.

These observations were made by able Year 4 pupils:

The women are getting better as they go up.

They started off really rubbish then all of a sudden they're like growing - from there right up to there.

The men are getting better, but the women are getting much, much better.

The men are going like that - like a slide, it looks like.

If you were to formalise the children's thinking, you would say, "The women are improving at a faster rate." Rate is a difficult abstract concept and would not be introduced in a formal sense at this early stage. In working with this data, and talking about these graphs, children gain experience which may well assist them at a later stage in making sense of formal concepts.

Some Year 4 children found it difficult to read the graphs (see below). It helps greatly to place the mouse pointer on the bar to display the value. Even so, there was some confusion. I was told, "This man is in 1932!" In fact the pointer was showing 19.32 seconds!

Writing tended to be descriptive. A Year 5 pupil wrote, "Mrs - taught us how to use a spreadsheet. After she told us the basics we done a chart about the Olympics and how well each country was doing. It was fun doing it. We used the method of making the differences between the men and the women."

It is important to talk through with the children what their graph shows before they record in writing. Year 6 children were primed to describe their chart, explain what it changes it showed, and to use it to predict this year's result. One wrote:

This is a chart showing the height of the mens high jump since 1896. The results have been getting slightly better over the past 100 years. I think that this year the height of the high jump will be 2.50 metres.

Another showed good understanding of the chart as a basis for prediction:

I think the women will have a good chance of throwing the javelin at least 60.50.

Graph questions

There are three broad types of question that can be asked:

Simple quantitative:

When did a man first jump over 2 metres?

Can women jump over 2 metres?

Which is the highest?

Looking at the graph as a whole, identifying the overall trend:

Are women running faster in recent Games?

Are they catching up with the men's times?

Using the graph as a basis for prediction:

What is the likeliest result in the 2000 Games?

There would appear to be a progression. Only the Year 6 pupils were able to make reasoned predictions of the likeliest result in the 2000 Games. The surprise for me was that some children found answering simple questions about the graph harder than identifying the trend shown by the graph as a whole. This is shown in the following example.

A Year 4 girl in a low ability group told me: "[Men are jumping higher because of] the long lines going this way. First it starts low then it gradually gets higher."

I asked, "Where's the first 2 metre jump?"

She replied, "I can't tell from these." She needed a lot of help to find which bar first crosses the 2m grid line. She did not appear to know how to read an individual height from the graph.

Another Year 4 group gave a confident interpretation of the 200m graph: "Women are getting faster cos their bars is getting smaller. They used to be right up there."

I asked, "How many men have run less than 20 seconds in the 200 metres?"

"About - um - five?" This was a guess. The boys were looking at me for clues, rather than the graph. Again, it emerged that the pupils did not know where to read 20 seconds. They needed a great deal of help. Reading the graph can be harder than making an overall judgement about the trend.

Predicting from the graph

Could children judge from the graph what is the likeliest result in the Year 2000 Games? Here are some examples of Year 5 reasoning:

I think the men's result will be close to that.

[It will be higher because] there is more technology in the year 2000.

It might be higher, or a bit lower, because it goes high, then low.

[The women's results] are levelling off here, as well, so they might just be a bit higher.

Year 4 pupils found prediction from the graph harder. Many children thought results would be spectacularly higher, although they had reasons which they were able to explain. Year 6 took the graph much more into account.

Even when we plotted the Year 4 predictions on the large display, children could not see that their high predictions were wildly outside the trend. The Year 4 teacher wondered whether it would have been better to write out the last four values, so they could see them as numbers. Otherwise, they just think in terms of 'bigger', rather than 'how much bigger'.