Posted by: Alexandre Borovik | July 16, 2008

Family caring and maths: a comment

This is my comment on my previous post, Now we are fifty. I’ll attempt to decipher and re-write in plain English a long quote from

Michael, R. T. (200 8) Children’s Reading and Math Skills: The Influence of Family Caring. CLS Working Paper, London: Centre for Longitudinal Studies.

The Centre for Longitudal Studies accumulated a huge amount of data on all aspects of life of a large group of people born in the same week in 1958, their families, children, etc. Of course, no-one measured family caring; social statistics resorts in this situation to a kind of black magic and invents a proxy, a combination of measurable and detectable factors which can be thought to be related to caring. For example, if a mother breast feeds her child, she perhaps cares about the child; if parents quit smoking on birth of a child, perhaps they care even more about of child.  A regression model for maths performance of a child in terms of “proxy for caring” and is carefully analysed for  intrinsic flaws  such as endogeneity. If the model is satisfactory, another generous serving of black magic comes is used, this time in interpretation of correlation coefficients  in the model.

What was found is that a proxy for caring built from observables such as breastfeeding, quitting smoking, etc. in the behaviour of parents correlates with  good maths performance of children.

Policy implications? In effect, none, because the “caring” itself remains unmeasurable and invisible, and thus out of control of government. The key phrase in the conclusions of the report is that

Both the income and the caring indexes show statistically significant and nontrivial relationships with the children’s skills in reading and math, and they do seem to supplement each other and to act additively, even compensatorily.

The government can influence income (by tax breaks and other social benefits), but cannot directly influence people’s behaviour in their families, especially in respect of such intangible entities as “caring”.

In short, the report describes one of the many natural limits of social policy making.

But if we accept that social policies have natural limits, why do we believe that certain educational targets are achievable in principle?

A sad thing about mathematics and mathematicians is that we have a clear understanding that a problem might happen to be unsolvable. This does not endear us to politicians. But maybe the levels of numeracy and literacy in population, or 50% participation in higher education as desired by the government are not achievable for social reasons? Maybe, to achieve them, Britain should stop being what it is now?



  1. Your last paragraph is one of the truest things I have read all year.

  2. […] practices). (The same recent “Now we are 50” report has already been discussed on Mathematics under the Microscope, so I won’t go into it here.) The teaching of mathematical ideas such as the rudiments of […]

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