Year 7 Common Task: Average Student

Mathematical Issues: Awareness of designing questionnaires to; avoid bias, ease data collection, get the information you want - use of categories.
Presenting data in a meaningful way, interpreting others' graphs.
Ways of averaging data.
Issues of sampling.
Ethics of data collection e.g. sensitive issues, confidentiality.

What follows is a suggestion for a sequence of lessons, taken from my experiences over the last two years.

Lesson 1
~ Imagine we had to bury a time capsule, for people in the future to find, which contained information about what year 7 students were like at Kingsfield School in 2002. How can we find things out about what a typical year 7 student is like in 2002, what information might people in the future want to know about us and what we were like?

'We could do a questionnaire' [someone has always suggested this, but if they didn't I would say that's what we are doing]

~ So, what questions would you want to ask, what questions would help us find out what year 7 students are really like?

[Write a few student suggestions on the board.]

~ Okay, we've got some great ideas there. What I want you to do now is to write down six questions in your book. You are then going to get ten people in the class to answer them. I need to see the six questions you have written before you ask anyone. You could choose some of the ones on the board, but try others as well. I will give you 20 minutes to do that, and we will then discuss what people have found out.

[I suggest you don't mention any issues of wordings of questions, or ways of collecting data, since these will come out of the discussion after they have had a go.]

[After 20 minutes …]

~ You have all had a go at getting people to answer your questions. Did anyone have any problems with the questions they asked, was anything difficult?

[Typically, some of these issues arise; (a) answers people gave were too long, (b) issues of who decided e.g. what hair colour you are, the questioner or the person questioned (in real questionnaires it is always the person questioned who chooses what category they are in), (c) people weren't being honest about their answers, (d) some questions were too personal and shouldn't be asked, (e) there was too big a variety of answers that people gave to be able to say what was most common. An issue you might want to raise is one of bias - e.g. Do you think school uniform should be abolished? (Y/N) is much more likely to get a positive answer than: What are your views on school uniform? (It should change colour / It should stay the same / It shouldn't exist). Time could be spent creating biased questions as a way of working on this issue - e.g. for homework.

The discussion can be turned to ways of avoiding some of these problems e.g. take a question that someone asked and decide on categories for their answers (including 'other'). If not many problems are being raised, the question of whether anyone found anything out about year 7 students in 2002 at Kingsfield may provoke more issues.]

[Homework can be to write ten questions (including categories, if that has been discussed) that they want to ask the class, given the discussion about problems in collecting data.]

Lesson 2
~ The task for the first part of this lesson is to agree on a list of ten questions that everyone in this class will answer, so that we can start trying to work on what a typical or average student in year 7 is like.

[Go around the class writing up questions, discussing whether any questions are too similar to ones already written, or whether two can be merged. If the list gets over 10 (or whatever number you choose) then the class can vote on which to keep in. Make sure some of the questions have numerical answers. Again issues of confidentiality, and not asking personal questions may arise.

Once the questions have been decided, the class then need to agree on categories, where appropriate, it will help if at least one numerical question does not have categories, to force the need for the mean/median as a way of representing the answers - this is a task that could first be done by pairs/groups and then agreed by the class.

When the final questionnaire has been decided, all students can answer the questions, writing their answers on paper. Take these in when they have been completed.

Any spare time in this lesson could be spent by students e.g. writing down predictions of what they think the average student will be like.]

Lesson 3
[Before this lesson, transfer the students' answers onto a single sheet of paper e.g. in landscape, the questions can be across the top and each student's entry (without names) in rows underneath. Photocopy this sheet so that every student has one.]

~ On the sheet infront of you are the results of the whole class' answers to the questions we asked. Spend a few minutes looking at this data, what do you notice? Can you tell anything about what year 7's are like? or what the typical or average year 7 is like?

[It may be that if the data is not very good, e.g. the categories have resulted in lots of people answering 'other' that the questions can be worked on again and re-done. Otherwise issues about how to get an average value from a set of data will inevitably arise.

Typically students will suggest mode as the way of averaging the data. This is the only average useable with qualitative data. If there is at least one column that contains non-categorised numerical data, then the mode will probably not exist or at least not be representative, some students will know about the mean and median, which can be explained to all.

The task can then be for students to find average values for each question. There is also the opportunity for students to represent the data graphically. Other issues include: is there one student who has all the average values? or comes closest? are there any links between people's answers to the questions?]