You may think this a large order; you may think I am demanding linguistic prodigies; but remember that I am upon my own ground here; I am a trained teacher and a student of pedagogic science, and I am a watchful parent; I know how time and opportunity are wasted in school, and particularly in language teaching. Languages are not things that exist in water-tight compartments; each one illuminates the other and--unless it is taught with stupefying stupidity--leads on to others. A child can acquire the polyglot habit almost unawares. This widening grasp of languages is or was within the capacity of nearly everyone born into the world--given the facilities. I ask you to note that qualification--"given the facilities." And now let us turn from the language side to the rest of schooling. A second main division of our schooling was mathematical instruction of a sort. It fell into the three more or less isolated subjects of arithmetic, algebra and Euclid. We carried on in these closed cells what was, I now perceive, a needlessly laborious and needlessly muddled struggle to comprehend quantity, series and form. In all these matters, looking back upon what I was taught, comparing it with what I now know, and comparing my mind with the minds of more fortunate individuals, I cannot resist the persuasion that I was very badly done indeed in this section. And it is small consolation to me to note that most people's minds seem to be no better done than mine. My arithmetic, for instance, is mediocre. It is pervaded by inaccuracy. You may say that this is probably want of aptitude. Partly, no doubt, but not altogether. What is want of aptitude? Bad as my arithmetic is now it is not so bad as it was when I left school. When I was about twenty I held a sort of inquest upon it and found out a number of things. I found that I had been allowed to acquire certain bad habits and besetting sins--most people do. For instance, when I ran up a column of figures to add them I would pass from nine to seven quite surely and say sixteen; but if I went from seven to nine I had a vicious disposition to make it eighteen. Endless additions went wrong through that one error. I had fumbled into this vice and--this is my point--my school had no apparatus, and no system of checks, to discover that this had occurred. I used to get my addition wrong and I used to be punished--stupidly--by keeping me in from exercise. Time after time this happened; there was no investigation and no improvement. Nobody ever put me through a series of test sums that would have analysed my errors and discovered these besetting sins of mine that led to my inaccurate arithmetic. And another thing that made my arithmetic wrong was a defect in eyesight. My two eyes haven't quite the same focal length and this often puts me out of the straight with a column of figures. But there was nothing in my school to discover that, and my school never did discover it.