I find this interesting that classroom sizes continue to be considered as a measure of how good a school or an education system is.   In the case of the comments on BBC the person making the comments was equating classroom size to an improvement in the quality of education.

Hanushek (1998) suggested that the linkage between smaller class sizes and improved students results was “generally erroneous”.     Kahneman (2011) went further in suggesting that the fact associated with such a claim were “wrong”.

Kahneman’s explanation (2011) was that the reason for the findings relates to statistics and what he refers to as the “law of small numbers”.     A small class is made up of a smaller number of students which therefore results in higher levels of variability in terms of the average.    He uses an example of drawing coloured marbles from a jar to demonstrate this.   Consider randomly picking marbles from a jar containing red and blue marbles.  There is a higher probability of drawing out 3 of acolour (3 high achievers in a small class) than of drawing out 6 of a colour (6, the equivalent number of, high achievers but in a bigger class).

Within a larger class size there is a greater tendency towards regression to the mean and therefore a more stable and less variable average across schools.

The association of improved results resulting from more teacher time, more support, etc resulting from a smaller class sizes is therefore unfounded.    The improved results in schools with smaller class sizes is simply a feature of the statistical analysis of small sample sizes.   Kahneman suggests that if the researchers were to change their question and look at if poor results could be linked to small classes they would find this to be equally true.

My feeling on this is that generally class size doesn’t have a significant impact on student results within lower and upper limits.    Where the ratio is 1 teacher to 2 or 3 students I would expect to see a positive impact and equally at 50+ students I would expect to see a negative impact.   Within the larger range between 5 and 50 I would expect the impact to be minimal if evident at all.

Care needs to be taken with the use of statistics and care has to be taken in believing them.   As Kahneman explains, it is easy to create a causal explanation for why a given set of statistics such as those on class size make sense.   The ease with which a causal explanation comes to mind however doesn’t necessarily make the explanation and resulting judgement true.

Sources

Hanushek, E. A. (1998), The evidence on class size, W. Allen Wallis Institute of Political Economy

Kahneman, D. (2011), Thinking, fast and slow, Penguin Books