Lesson 2 Comparing Across Events

Teacher Advice

Goals of Lesson

- To distinguish between high and low quality enquiries

- To find ways of comparing improvements across events.

Features of the Lesson

- Pupils use their homework reflections to develop the detailed features of a high quality enquiry

- Pupils will indentify whether or not women have been improving faster than men for their event, then identify the need to measure relative improvement so that comparisons can be made across events.

Summary

Part 1: Deciding what is needed for a good enquiry As a class, pupils reflect on what they understand to be the features of a high quality enquiry. (15 minutes).
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Part 2: Moving from absolute to relative improvement Pupils share their results from Part 1 with the class; this shows the need for a measure of relative improvement so that comparisons can be made across events. (15 minutes).
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Part 3: Using relative improvement to compare results Pupils return to their initial answers to add to their measure of relative improvement so that comparisons can be made across events. (15 minutes).

Preparation

- You may want copies of the enquiry process solutions. (see Activity 1 below). Similarly you will need copies of either the assessment rubric template or of a template you have developed.

- You need to be familiar with what the data indicates for the six different events (TL5).

Part 1: Deciding what is needed for a good enquiry (10 minutes)

Pupils draw on their homework to complete the enquiry process handout and develop a rubric for a high quality enquiry.

Activities | Teaching and Learning Notes
Conduct a brief class discussion on what makes a poor, good or excellent enquiry. Key question: · What did we learn from the samples about what makes a good enquiry? | The sample enquires were written with the view that number 1 was the best and number 2 the worst. Number 1 is deliberately not perfect and was written by a pupil. Number 2 identifies the same sorts of problems as 1, but is not as specific. As appropriate, complete the third column of the Enquiry process handout, this may involve giving out copies of the Enquiry process solutions, but you may prefer to use this as a teacher guide to help shape the discussion.
Following this, use the assessment rubric template generate together, a rubric which will be used to assess each enquiry that pupils’ complete during this Case. | There are significant advantages of the pupils sharing ownership over the criteria for a good assignment (see TL8: Sharing ownership over our criteria for quality). However if time is an issue, this activity may be skipped and the teacher could provide pupils with an assessment rubric that is already prepared. TL8: Sharing ownership over our criteria for quality Leaving the first lesson of the Olympic challenge I thought; “why did I spend more time talking than the kids?” Trying to lead discussions was very unusual for my teaching style and I realised I needed to get the pupils doing the talking – not me! They had been given the task of ranking the three enquiries for homework. When they returned, I asked them to talk as a group and agree on an order. I then gathered the pupils together in a circle. “Enquiry 2 was rubbish.” Was all he could come up with – one of the brightest students in the class! This was going to be a disaster… There was a pause whilst he looked for someone to pass the conversation to; I just listened carefully, making notes of their conversations. “It didn’t say anything – was just a lot of numbers with no reasons.” “I thought 3 was best. It was easy to understand and said enough” “But number 1 had more writing – it had more reasons in” The debate continued with students mostly agreeing that number two was pretty poor, but unable to reach a consensus on whether one or three was best. Importantly, the reasons started to emerge as students realised I really wasn’t going to get involved and give them any suggestions. After 10 minutes, the conversation dried up. “So what do we know makes a good enquiry now?” I asked. Having had quality discussion time, all pupils were able to give some kind of response and we finally agreed on how we would judge each other’s enquiries. The pupils seemed pleased – they’d decided how I was going to mark their work and so felt more ownership over and understanding of the outcome. Print TL8 Close Box In the trialing, one teacher spent a whole lesson with her class discussing the features of a good enquiry and developing, with her pupils, an Enquiry Rubric. She knew that this meant she would not complete the case in three lessons, but felt that this investment of time was worth it as she intended that her class would complete other enquiries where this time would not be needed again.

Part 2: Moving from absolute to relative improvement

Pupils come to realise absolute differences do not allow different events to be compared (15 minutes).

Activities | Teaching and Learning Notes
Pupils share with the class their fair comparison for their event. This shows the need for a measure of relative improvement so that comparisons can be made across events. Key questions: Have women improved faster than men? Why are absolute improvements inadequate for comparing across events? | Ask each group to discuss and share their response to the Case question, for their event together with a margin for improvement. The events have been chosen as a set where the relative improvement of women and men varies substantially. See TL5: Key features in the improvements of selected events. As groups provide their different conclusions and margins, highlight that to produce a more conclusive response, a comparison across events would be necessary. Some pupils may have already realised a value of calculating percentage changes and you will need to react accordingly. Point out (if needed) that, comparison across events is difficult with the data expressed in absolute differences.
Class reaches consensus on a common approach Key questions: In what ways could relative improvements be measured? Which way will we use? | Discuss with pupils how improvements in performances might be measured in a ‘fair’ way, and so that they can also be compared across events. See TL9: Fair comparisons which can be used across events for suggestions on running this discussion. Point out that, while there is not a single right or best way to measure relative improvement, the class will need to agree on one common approach so that the original question can be answered. TL9: Fair comparisons which can be used across events There are (at least) three problems to be resolved in comparing performances across events. One is that in field events the performances get larger, whereas in track and swimming they get smaller; a second is the units vary and finally the raw figures are much greater in the longer events, but this does not necessarily mean a greater improvement as 1 second (for example) is a huge margin in a 100 metre sprint and a tiny margin in a marathon. All of these are solved by using a proportional measure of improvement such as a percentage improvement from the first performance. Pupils have previously identified the fact that to have a fair comparison of men’s and women’s improvements they need to hold constant as many variables as possible. Generally this would mean starting from the year the women first competed (though one could take the time period that women have competed and start each gender from their first competition). There are arguments for each of measuring the change to the most recent Olympics or to the best performance. However while so far it has not mattered that different groups may have used different (valid) approaches it is now essential that all events are analysed in the same way. How you shape this discussion will depend on what approaches pupils have used and their familiarity with percentages. Once again, a sample calculation for the 800 metre event is modelled below and, for your information, the results of two ways of analysis are tabulated for all events –this shows that both types of approaches produce similar answers to the overall question about men and women and hence reinforce each other (strengthening confidence in the findings) 800m track model
| 1928 performance (s) | 2008 performance (s) | Difference (s) | % improvement
Men | 111.8 | 104.65 | 7.15 | 6.4%
Women | 136.8 | 114.87 | 21.93 | 16.0%
Two types of analysis
Event | From | Percentage improvement from when women first competed
To the last Olympics | To the best result
Women | Men | Women | Men
100m track | 1928 | 11.6% | 10.3% | 13.6% | 10.3%
400m track | 1964 | 4.6% | 2.4% | 7.2% | 3.6%
800m track | 1928 | 16.0% | 6.4% | 17.1% | 8.2%
Long jump | 1948 | 23.6% | 9.1% | 29.8% | 14.0%
Shot Put | 1948 | 49.5% | 25.6% | 63.0% | 31.3%
Javelin | 1932 | 63.5% | 24.9% | 71.0% | 30.0%
100m freestyle | 1912 | 35.4% | 25.6% | 35.3% | 25.6%
Key principles for reflection To assist in comparing across contexts, relative comparisons must be used. Print TL9 Close Box
As with all Bowland cases, it is important that pupils realise that they have been doing maths and to reflect on what maths they have been doing. Refer to Bowland CPD module ‘Where’s the maths in this? | Sometimes the opportunity to do this will come from a student comment (or complaint) see: TL10: Miss, this isn’t maths (Vignette) TL10: Miss, this isn’t maths (Vignette) This is the sort of pupil comment that can be used constructively for a (generally fairly brief) discussion about whether or not they are doing maths, and, if so, what the maths is. There are two aspects to this; one is that they clearly are engaged in the sorts of calculations (such as calculating percentages) that are the focus of conventional text book exercises. However this Case also involves issues that are important to how maths is often used in the real world and that are typically missing from text book exercises; the data is real data and thus is messy, with outliers, there is no single ‘right’ way to approach the task and the conclusions contain uncertainty –this last issue is an important aspect of the predictions to be made in lesson 3. Trials have shown the value of incorporating more than one debrief with the pupils on the issue of finding the maths into your teaching. More broadly, the media is full of stories where the issue of being ‘fair’ in mathematical analysis is important. This issue is discussed in the first Bowland CPD module (see Where’s the maths in this?). Print TL10 Close Box

Part 3: Pupils use relative improvement to compare results (15 minutes)

Pupils arrive at an answer to the original question by looking at relative improvements across events

Activities | Teaching and Learning Notes
Pupils return to their initial answers and use a common approach to measure relative improvement so that comparisons can be made across events. Key questions Have women improved faster than men in our event? | Allow pupils time to return to their enquiry and develop it further, by completing some further calculations around relative improvements, to allow comparisons across events.
Collect and compare results across all the events. Key question Is the answer similar across different events? | After appropriate time, collate the data from all groups on the board, and get pupils to record this for use in their final reports. Provide groups with time to analyse these data to produce a more general response to the Case question considering all events, not just the one they analysed. The concept of using relative improvements to compare across events/contexts is one of the key ideas of this Case. Reflect with pupils on the key principles of comparing across events/contexts.
Optional extension to other events | As a teacher resource, we have included detailed lists of track and field and swimming performances in many more events that the six selected. It may be that some pupils are keen to explore others events and these resources will allow this.
Homework Pupils finish this portion of their final report. You may include a task where they select and explore another event from the full list of performances.