Recently I have been teaching averages to Year 7, and in the second lesson we looked at the mean average. Of course as soon as I asked the class what the mean was, I got the stock response "Add them all up and divide by how many there are". "Why?" was my response; stunned silence the result. As suspected, not one of them knew why they were adding up, or why they were dividing.

I literally got them all to stand up, reach into their heads, and throw the idea out of the window. I then replaced it with a new idea; to me a better idea

Mean = Total of data points shared equally amongst each point..

I much prefer this definition for a number of reasons. Firstly it tells you why you are "adding up" (although I have still banned the term in my classroom); you are adding to find the total. Secondly it tends to stop the problem of pupils dividing within the sum line of their calculator - a classic mistake in the calculation. My pupils have now gotten into the habit of finding and writing down the total and then sharing it out. Thirdly, and for me most importantly, it can be applied to a much wider range of problems then the usual definition.We looked at measuring totals with tape measures or scales, solving problems in finding missing values given the mean, and particularly mean from a frequency table. The use of the language "total" and "shared" meant pupils were much more open to the idea of multiplication to find totals in each row of a frequency table and were better able to see why we weren't dividing by the number of rows in the table, as they are not data points.

I know it is a relatively short post, but it highlights an important point; I will end with a plea - don't be satisfied in teaching pupils

I literally got them all to stand up, reach into their heads, and throw the idea out of the window. I then replaced it with a new idea; to me a better idea

Mean = Total of data points shared equally amongst each point..

I much prefer this definition for a number of reasons. Firstly it tells you why you are "adding up" (although I have still banned the term in my classroom); you are adding to find the total. Secondly it tends to stop the problem of pupils dividing within the sum line of their calculator - a classic mistake in the calculation. My pupils have now gotten into the habit of finding and writing down the total and then sharing it out. Thirdly, and for me most importantly, it can be applied to a much wider range of problems then the usual definition.We looked at measuring totals with tape measures or scales, solving problems in finding missing values given the mean, and particularly mean from a frequency table. The use of the language "total" and "shared" meant pupils were much more open to the idea of multiplication to find totals in each row of a frequency table and were better able to see why we weren't dividing by the number of rows in the table, as they are not data points.

I know it is a relatively short post, but it highlights an important point; I will end with a plea - don't be satisfied in teaching pupils

**how**to calculate the mean by "adding them all up and dividing by how many there are"; instead teach them what the mean is doing sharing a total to create equal valued points.
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