Anne Brontë on feedback in mathematics

Anne Brontë’s Agnes Grey is — to my mind at least — saved from the insipidity of so many Victorian heroines by the astringency and accuracy of her remarks on teaching. Here she is on the difficulties of educating a child whose parents insist on too much feedback:

His minute portions of Latin grammar, &c., were to be repeated over to him, till he chose to say he knew them; and then, he was to be helped to say them: if he made mistakes in his little easy sums in arithmetic, they were to be shewn him at once, and the sum done for him, instead of his being left to exercise his faculties in finding them out himself; so that, of course, he took no pains to avoid mistakes, but frequently set down his figures at random without any calculation at all.

(Agnes Grey, chapter VII)

(Compare the approach taken by at least one of my students to “clicker” questions…)

The other passage that I suspect might resonate with my fellow-sufferers at the chalkface concerns the joys of being trapped between — as we’d say today — quality assurance and student satisfaction:

I returned, however, with unabated vigour to my worka more arduous task than any one can imagine, who has not felt something like the misery of being charged with the care and direction of a set of mischievous turbulent rebels, whom his utmost exertions cannot bind to their duty; while, at the same time, he is responsible for their conduct to a higher power, who exacts from him what cannot be achieved without the aid of the superior’s more potent authority, which, either from indolence, or the fear of becoming unpopular with the said rebellious gang, the latter refuses to give. I can conceive few situations more harassing than that wherein, however you may long for success, however you may labour to fulfil your duty, your efforts are baffled and set at naught by those beneath you, and unjustly censured and misjudged by those above.

(Agnes Grey, chapter IV)

I hear you, Miss Grey, and you are not alone.

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