A Boolean Anthology - Part 2
Compiled by D. G. Tahta
Dick Tahta was my maths tutor at St Luke's College Exeter. A brilliant and often quite unorthodox thinker in the field of mathematics education. He put together this anthology in a small booklet, now long out of print, and as a tribute to him, I am posting it up here.
SELECTED WRITINGS ON LEARNING AND TEACHING
By Mary Boole
On influence
In all ordinary works on education, we may notice constant discussion about the particular mode in which influence should be brought to bear, whether by individual commands, unvarying rules, hopes of fears about consequences, appeals to affection, the cogitation of example, or that more subtle form of influence called by the pious 'intercessory prayer,' and by modern Science 'suggestion,' or 'telepathy.' The whole discussion usually turns on the rival merits of the various modes of bringing influence from without to bear on the pupil. It seems assumed that it is always legitimate to exert influence. In mathematics, however, the main question kept in view is: When may the teacher exert influence?
For mathematical purposes, all influence from without, which induces the pupils to admit a principle as valid before his own unbiased reason recognises its truth, come under the same condemnation. (72 7)
A village schoolmaster
Monsieur Deplace was asked to come for two hours a day to teach us French and arithmetic. The only time he could spare was from six to eight in the morning, and those hours he spent with us, winter and summer, as long as we stayed at Poissy.
Monsieur Deplace is the hero of my idyll. I wish, though I know that the wish is vain, that I could convey any adequate impression of the way in which he enveloped my life with a protecting influence without the slightest interference with either my thoughts or my feelings. The influence was all the stronger because he showed no desire to gain influence; I was quite unconscious of it then and for many, many years afterwards. In those days the distinctions of rank were more sharply defined than they are now. The village schoolmaster was not supposed to take rank with gentlefolk, and though Monsieur Deplace himself was a gentleman in every sense of the word, he accepted the social position into which he had fallen (or risen?) in all seriousness.
I do not remember anything passing between us in the slightest degree resembling either a caress or an affectionate word. The relation between us was, I believe, entirely subconscious on my part, then, for a quarter of a century later after I left him. I remember distinctly the first arithmetic lesson he gave me at home. Mother had been trying to teach me long division, but could not make me understand, chiefly, as I now know, because she herself did not understand. The difficulty was referred to Monsieur Deplace; then it disappeared as if by magic, and it was the last difficulty that I was ever in my life able to see in connection with arithmetic.
The next thing that I remember is a sum in compound proportion, or what used to be called 'double rule of three.' The master told me nothing, he asked me a succession of questions and made me write down each answer as I gave it, and then let me perceive that the answer to the complicated question on which we had started came out of its own accord in my own handwriting. (1514)
A university professor
She seemed so unlike the stuff of which mathematicians are made, that I one day said to her, "I cannot think mathematics is your true function."
"Oh, no!" she replied, "my function is to understand whatever Professor Clifford wants to get understood." Of course every occultist will know what fatal magnetic interlocking must have been going on before such a thing could be said. To non-occultists I must explain that it was not at all the utterance of sentimental gush; the girl was, in the most straightforward manner, expressing her honest, though too limited, knowledge of the nature of her own mental activities.
Compiled by D. G. Tahta
Dick Tahta was my maths tutor at St Luke's College Exeter. A brilliant and often quite unorthodox thinker in the field of mathematics education. He put together this anthology in a small booklet, now long out of print, and as a tribute to him, I am posting it up here.
SELECTED WRITINGS ON LEARNING AND TEACHING
By Mary Boole
On influence
In all ordinary works on education, we may notice constant discussion about the particular mode in which influence should be brought to bear, whether by individual commands, unvarying rules, hopes of fears about consequences, appeals to affection, the cogitation of example, or that more subtle form of influence called by the pious 'intercessory prayer,' and by modern Science 'suggestion,' or 'telepathy.' The whole discussion usually turns on the rival merits of the various modes of bringing influence from without to bear on the pupil. It seems assumed that it is always legitimate to exert influence. In mathematics, however, the main question kept in view is: When may the teacher exert influence?
For mathematical purposes, all influence from without, which induces the pupils to admit a principle as valid before his own unbiased reason recognises its truth, come under the same condemnation. (72 7)
A village schoolmaster
Monsieur Deplace was asked to come for two hours a day to teach us French and arithmetic. The only time he could spare was from six to eight in the morning, and those hours he spent with us, winter and summer, as long as we stayed at Poissy.
Monsieur Deplace is the hero of my idyll. I wish, though I know that the wish is vain, that I could convey any adequate impression of the way in which he enveloped my life with a protecting influence without the slightest interference with either my thoughts or my feelings. The influence was all the stronger because he showed no desire to gain influence; I was quite unconscious of it then and for many, many years afterwards. In those days the distinctions of rank were more sharply defined than they are now. The village schoolmaster was not supposed to take rank with gentlefolk, and though Monsieur Deplace himself was a gentleman in every sense of the word, he accepted the social position into which he had fallen (or risen?) in all seriousness.
I do not remember anything passing between us in the slightest degree resembling either a caress or an affectionate word. The relation between us was, I believe, entirely subconscious on my part, then, for a quarter of a century later after I left him. I remember distinctly the first arithmetic lesson he gave me at home. Mother had been trying to teach me long division, but could not make me understand, chiefly, as I now know, because she herself did not understand. The difficulty was referred to Monsieur Deplace; then it disappeared as if by magic, and it was the last difficulty that I was ever in my life able to see in connection with arithmetic.
The next thing that I remember is a sum in compound proportion, or what used to be called 'double rule of three.' The master told me nothing, he asked me a succession of questions and made me write down each answer as I gave it, and then let me perceive that the answer to the complicated question on which we had started came out of its own accord in my own handwriting. (1514)
A university professor
She seemed so unlike the stuff of which mathematicians are made, that I one day said to her, "I cannot think mathematics is your true function."
"Oh, no!" she replied, "my function is to understand whatever Professor Clifford wants to get understood." Of course every occultist will know what fatal magnetic interlocking must have been going on before such a thing could be said. To non-occultists I must explain that it was not at all the utterance of sentimental gush; the girl was, in the most straightforward manner, expressing her honest, though too limited, knowledge of the nature of her own mental activities.
Professor Clifford, however, attributed the wonderful work done by his pupil to a personal vocation of her own for mathematics. The result was that her health broke down: then she took a fit of Evangelical piety—(i.e. found out too late that her function in life was to understand things which Professor Clifford did not particularly care to have understood), and died in the odour of sanctity—one of the countless victims of the cruel delusion of teachers who mistake the reflection of their own mental processes on the brain of an intuitional pupil for personal mental action in the pupil.
In this case, as in many others, Nature seems to have avenged the wrong. From my own observation of Professor Clifford at classes of his which I attended, I venture to think that his premature decay, as well as much of his over-brilliant success, was due to a habit of recklessly over-magnetizing his pupils.
The Prophets of Palestine may not have known everything, but some of them did know that it is inadvisable to undermine one's own health and other people's for the sake of spreading one's special views and increasing one's influence, by random indulgence in the wonderful and awful delight of contact between intellect and intuition. (596)
Teacher lusts
The teacher (whether school-teacher, minister of religion, political leader, or head of a family) has a desire to make those under him conform themselves to his ideals. Nations could not be built up, nor children preserved from ruin, if some such desire did not exist and exert itself in some degree.
The Prophets of Palestine may not have known everything, but some of them did know that it is inadvisable to undermine one's own health and other people's for the sake of spreading one's special views and increasing one's influence, by random indulgence in the wonderful and awful delight of contact between intellect and intuition. (596)
Teacher lusts
The teacher (whether school-teacher, minister of religion, political leader, or head of a family) has a desire to make those under him conform themselves to his ideals. Nations could not be built up, nor children preserved from ruin, if some such desire did not exist and exert itself in some degree.
But it has its gamut of lusts, very similar to those run down by the other faculties.
First, the teacher wants to regulate the actions, conduct, and thoughts of other people in a way that does no obvious harm but is quite in excess both of normal rights and of practical necessity. Next, he wants to proselytise, convince, control, to arrest the spontaneous action of other minds, to an extent which ultimately defeats its own ends by making the pupils too feeble and automatic to carry on his teaching into the future with any vigour. Lastly, he acquires a sheer automatic lust for telling other people 'to don't,' for arresting spontaneous action in others in a way that destroys their power even to learn at the time what he is trying to teach them.
What is wanted is that we should pull these three series tight so as to see their parallelism, and not go on fogging ourselves with any such foolish notion as that sex-passion is a lust of the flesh and teacher-lust a thing in itself pure and good, which may legitimately be indulged in to the uttermost.
Few teachers now are so conceited as not to know that they have a great deal to learn, and that their methods need revising and improving, but the majority are seeking for improved methods of doing more of what they are already doing a great deal too much of. The improvement which they most need is to be brought under conviction, to be made see their conduct, their aims, their whole attitude towards their pupils and their work, in the light reflected on them from those of the drunkard and the debauchee. (1412)
Qualities of a teacher
Constant recognition that man is as liable to error while his transcendental faculties are active as at any other time; and, moreover, that errors which otherwise would have been immediately detected and corrected, tend, if made at that time, to become fixed and to appear like solid truths, unless carefully checked by some well-selected mode of correction (e.g., the 'proving' of a sum).
Great reserve on the part of the teacher in even stating to pupils the special conclusions to which he has been led, lest he should arrest the normal exercise of their investigating faculties.
Especially stern self-control in the use of personal influence to convince or to persuade.
Modest reticence in the matter of courting applause by proclaiming any partial result before one has brought back into consciousness all those elements of a question which one had discarded from attention, in order to fix it for a time solely on some selected elements of the question.
Constantly accepting apparent disturbances of harmony and order as proofs that the true law of the case belongs to a higher order than that in which the investigator is at the time working. (637)
Few teachers now are so conceited as not to know that they have a great deal to learn, and that their methods need revising and improving, but the majority are seeking for improved methods of doing more of what they are already doing a great deal too much of. The improvement which they most need is to be brought under conviction, to be made see their conduct, their aims, their whole attitude towards their pupils and their work, in the light reflected on them from those of the drunkard and the debauchee. (1412)
Qualities of a teacher
Constant recognition that man is as liable to error while his transcendental faculties are active as at any other time; and, moreover, that errors which otherwise would have been immediately detected and corrected, tend, if made at that time, to become fixed and to appear like solid truths, unless carefully checked by some well-selected mode of correction (e.g., the 'proving' of a sum).
Great reserve on the part of the teacher in even stating to pupils the special conclusions to which he has been led, lest he should arrest the normal exercise of their investigating faculties.
Especially stern self-control in the use of personal influence to convince or to persuade.
Modest reticence in the matter of courting applause by proclaiming any partial result before one has brought back into consciousness all those elements of a question which one had discarded from attention, in order to fix it for a time solely on some selected elements of the question.
Constantly accepting apparent disturbances of harmony and order as proofs that the true law of the case belongs to a higher order than that in which the investigator is at the time working. (637)
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