© 2018 Richele Baburina
“It’s hard to believe the term is almost over.” Jeanne greeted her friend Erin, “So, have you been enjoying that mountain perspective in mathematics we discussed?”
“It’s funny you ask. This week’s reading of Heidi again reminded me of our conversation so I brought it to share with you,” replied Erin, reaching into her bag. “Having been taken from her life of freedom in the Alps to one of confinement in the city, Heidi is to begin lessons alongside Clara, who is homebound with frail health. Clara describes her kind tutor this way—
‘But mind, when he explains anything to you, you won’t be able to understand; but don’t ask any questions, or else he will go on explaining and you will understand less than ever.’
“Oh, that truly is an amusing illustration of an all too real danger,” concurred Jeanne. “Charlotte definitely cautioned of drowning a math lesson with too many words. According to her philosophy every subject can be approached in a living way, in cooperation with the one who is Life, or in a stale and deadening way—which opposes life.”
Erin continued her friend’s thought with excitement, “Charlotte’s approach to mathematics kindles the spirit and is as stimulating as the mountain air. Using the careful progression in teaching math she advised, we allow for a gradual unfolding of absolute truth. A young child who becomes aware that 2+2=4 and will never equal anything else—whether he is adding beads, popsicle sticks, or toy cars—is seeing one of God’s unchangeable laws in its simplest form.
“Rather than filling our children with facts and rules, math becomes exciting when we take our children alongside great mathematicians as they discovered truths established by God, whether His hand was recognized by them or not.”
“That reminds me of Charlotte’s warning to not divide our lives into the intellectual, secular and spiritual,” Jeanne added. “The remarkable order we have in math gives us confidence in our Creator, filling us with wonder and praise for the One through whom these laws came. Furthermore, the use of real life problems shows us that math is much more than an intellectual pursuit by presenting it as a useful tool given by Him—a tool that helps us in our daily life as well as one that can be used to record His truths. If we teach our children math as just rules and numbers, it could be seen as something man-made or independent from God.”
“You know,” remarked Erin, “Charlotte’s often-quoted words on the importance of the teacher over the textbook and how there are ‘few subjects worse taught’ previously stood like a scowling guard forbidding me to trespass into the domain of the math teacher. Now I see that I can enter with confidence, holding the key that the One through whom mathematical laws came to be instructs not only my daughter but myself as well.”
1. Education tends to mistakenly be divided into the religious and the secular.
“In the first place, we divide education into religious and secular. The more devout among us insist upon religious education as well as secular. Many of us are content to do without religious education altogether; and are satisfied with what we not only call secular but make secular, in the sense in which we understand the word, i.e. entirely limited to the uses of this visible world.” (Vol. 2, p. 270)
2. Charlotte held that there is a ‘Great Recognition’ required by parents—that God the Holy Spirit imparts knowledge, instructs youth, and inspires genius—and that this divine teaching waits upon our cooperation as parents.
“Many Christian people rise a little higher; they conceive that even grammar and arithmetic may in some not very clear way be used for God; but the great recognition, that God the Holy Spirit is Himself, personally, the Imparter of knowledge, the Instructor of youth, the Inspirer of genius, is a conception so far lost to us that we should think it distinctly irreverent to conceive of the divine teaching as co-operating with ours in a child’s arithmetic lesson, for example.” (Vol. 2, pp. 270-271)
3. To illustrate the idea that all knowledge—including the sciences of Geometry and Arithmetic—is gifted from God and was once accepted in simple faith, Charlotte made use of John Ruskin’s detailed description of the fresco Allegory of the Sciences from his book Mornings in Florence.
“Our immediate concern is with the seven mythic figures representing the natural sciences, and with the figure of the Captain-teacher of each. First we have Grammar, a gracious figure teaching three Florentine children; and, beneath, Priscian. Next, Rhetoric, strong, calm, and cool; and below, the figure of Cicero with a quite beautiful face. Next, Logic, with perfect pose of figure and lovely countenance; and beneath her, Aristotle—intense keenness of search in his half-closed eyes. Next, Music, with head inclined in intent listening to the sweet and solemn strains she is producing from her antique instrument; and underneath, Tubal Cain, not Jubal, as the inventor of harmony—perhaps the most marvellous record that Art has produced of the impact of a great idea upon the soul of a man but semi-civilised. Astronomy succeeds, with majestic brow and upraised hand, and below her, Zoroaster, exceedingly beautiful—‘the delicate Persian head made softer still by the elaborately wreathed silken hair.’ Next, Geometry, looking down, considering some practical problem, with her carpenter’s square in her hand, and below her, Euclid. And lastly, Arithmetic, holding two fingers up in the act of calculating, and under her, Pythagoras wrapped in the science of number.
‘The thoughts of God are broader than the measures of man’s mind,’
but here we have the breadth of minds so wide in the sweep of their intelligence, so profound in their insight, that we are almost startled by the perception that, pictured on these walls, we have indeed a true measure of the thoughts of God.” (Vol. 2, pp. 269-270)
4. Not only were the Liberal Arts considered to be directly inspired by the Holy Spirit, so were all worthwhile ideas and innovations—including those in mathematics—regardless if its divine origin was acknowledged.
“But the Florentine mind of the Middle Ages went further than this: it believed, not only that the seven Liberal Arts were fully under the direct outpouring of the Holy Ghost, but that every fruitful idea, every original conception, whether in Euclid, or grammar, or music, was a direct inspiration from the Holy Spirit, without any thought at all as to whether the person so inspired named himself by the name of God, or recognised whence his inspiration came.” (Vol. 2, p. 271)
5. We have scriptural authority for thinking both great discoveries and practical wisdom come ‘by the Spirit.’
“But we must not accept even an inspiring idea blindly. Were these people of the Middle Ages right in this plan and conception of theirs? Plato hints at some such thought in his contention that knowledge and virtue are fundamentally identical, and that if virtue be divine in its origin, so must knowledge be also. Ancient Egypt, too, was not in the dark in this matter. ‘Pharaoh said unto his servants, can we find such a one as this, a man in whom the Spirit of God is?’ Practical discernment and knowledge of everyday matters, and of how to deal with emergencies, were not held by this king of Egypt to be teachings unworthy of the Spirit of God. ‘The Spirit of God came upon him and he prophesied among them,’ we are told of Saul, and we may believe that this is the history of every great invention and every great discovery of the secrets of Nature. ‘Then David gave to Solomon his son.… the pattern of all that he had by the spirit, of the courts of the house of the Lord.’ We have here a suggestion of the source of every conception of beauty to be expressed in forms of art.” (Vol. 2, pp. 271-272)
6. Charlotte also spoke of the scriptural authority we have regarding the origin of the first ideas of even common things—it is God who instructs and teaches.
“We cannot think of ourselves as living without knowing these things; and yet each one must have been a great idea when it first made a stir in the mind of the man who conceived it. Where did he get his first idea? Happily, we are told, in a case so typical that it is a key to all the rest:—
‘Doth the plowman plow all day to sow? doth he open and break the clods of his ground? When he hath made plain the face thereof, doth he not cast abroad the fitches and scatter the cummin, and cast in the principal wheat and the appointed barley and the rie in their place? For his God doth instruct him to discretion, and doth teach him. For the fitches are not threshed with a threshing instrument, neither is a cart wheel turned about upon the cummin; but the fitches are beaten out with a staff, and the cummin with a rod. Bread corn is bruised; because he will not ever be threshing it, nor break it with the wheel of his cart, nor bruise it with his horsemen. This also cometh forth from the Lord of Hosts, which is wonderful in counsel, and excellent in working.’—Isa. xxviii. 24, etc.” (Vol. 2, pp. 272-273)
7. Every mother has a key to the whole of each child’s education; that God instructs each child.
“…above all, he recognises the divine co-operation in the direction, teaching, and training of the child.” (Vol. 2, p. 247)
“In the things of science, in the things of art, in the things of practical everyday life, his God doth instruct him and doth teach him, her God doth instruct her and doth teach her. Let this be the mother’s key to the whole of the education of each boy and each girl; not of her children; the divine Spirit does not work with nouns of multitude, but with each single child. Because He is infinite, the whole world is not too great a school for this indefatigable Teacher, and because He is infinite, He is able to give the whole of his infinite attention for the whole time to each one of his multitudinous pupils. We do not sufficiently rejoice in the wealth that the infinite nature of our God brings to each of us.” (Vol. 2, p. 273)
8. Charlotte wanted all to see that the Holy Spirit’s involvement is not restricted to the impartation of virtues. Every area of instruction, even practical skills and courses of study including geometry and arithmetic, comes from the Lord.
“And what subjects are under the direction of this Divine Teacher? The child’s faith and hope and charity—that we already knew; his temperance, justice, prudence and fortitude—that we may have guessed; his grammar, rhetoric, logic, music, astronomy, geometry, arithmetic—this we might have forgotten, if these Florentine teachers had not reminded us; his practical skill in the use of tools and instruments, from a knife and fork to a microscope, and in the sensible management of all the affairs of life—these also come from the Lord, which is wonderful in counsel and excellent in working. His God doth instruct him and doth teach him. Let the mother visualise the thought as an illuminated scroll about her newborn child, and let her never contemplate any kind of instruction for her child, except under the sense of the divine co-operation.” (Vol. 2, pp. 273-274)
9. This “Great Recognition” is profound but it is also absolutely relevant to the practical application of Charlotte Mason’s method of education in that each subject can be taught in a way that either invites or excludes the divine cooperation.
“Our co-operation appears to be the indispensable condition of all the divine workings. We recognise this in what we call spiritual things, meaning the things that have to do more especially with our approaches to God; but the new thing to us is, that grammar, for example, may be taught in such a way as to invite and obtain the co-operation of the Divine Teacher, or in such a way as to exclude His illuminating presence from the schoolroom. We do not mean that spiritual virtues may be exhibited by the teacher, and encouraged in the child in the course of a grammar lesson; this is no doubt true, and is to be remembered; but perhaps the immediate point is that the teaching of grammar by its guiding ideas and simple principles, the true, direct, and humble teaching of grammar; without pedantry and without verbiage, is, we may venture to believe, accompanied by the illuminating power of the Holy Spirit, of whom is all knowledge.” (Vol. 2, p. 274)
“Such teaching as enwraps a child’s mind in folds of many words that his thought is unable to penetrate, which gives him rules and definitions, and tables, in lieu of ideas—this is teaching which excludes and renders impossible the divine co-operation.” (Vol. 2, p. 274)
“The child, who has been allowed to think and not compelled to cram, hails the new study with delight when the due time for it arrives. The reason why mathematics are a great study is because there exists in the normal mind an affinity and capacity for this study; and too great an elaboration, whether of teaching or of preparation, has, I think, a tendency to take the edge off this manner of intellectual interest.” (Vol. 1, p. 264)
“How interesting arithmetic and geometry might be if we gave a short history of their principal theorems; if the child were mentally present at the labours of a Pythagoras, a Plato, a Euclid, or in modern times of a Viète, a Descartes, a Pascal, or a Leibnitz. Great theories, instead of being lifeless and anonymous abstractions, would become human, living truths, each with its own history, like a statue by Michael Angelo, or like a painting by Raphael.” (Vol. 2, p. 128)
“The mediæval Church recognised this great truth—as Mr Ruskin has eloquently pointed out, showing how the ‘Captain Figures,’ the inventors, as it were, of grammar and music, astronomy and geometry, arithmetic and logic, all spake that which was in them under the direct outpouring of the Holy Spirit, even though none of them had any such revelation of the true God as we recognise. What a revolution should we have in our methods of education if we could once conceive that dry-as-dust subjects like grammar and arithmetic should come to children, living with the life of the Holy Spirit, who, we are told, ‘shall teach you all things.’” (Vol. 3, pp. 117-118)
“There is no one subject in which good teaching effects more, as there is none in which slovenly teaching has more mischievous results.” (Vol. 1, p. 254)
“I have said much of history and science, but mathematics, a mountainous land which pays the climber, makes its appeal to mind, and good teachers know that they may not drown their teaching in verbiage.” (Vol. 6, p. 51)
“If the use of words be a law unto itself, how much more so the language of figures and lines! We remember how instructive and impressive Ruskin is on the thesis that ‘two and two make four’ and cannot by any possibility that the universe affords be made to make five or three. From this point of view, of immutable law, children should approach Mathematics; they should see how impressive is Euclid’s ‘Which is absurd,’ just as absurd as would be the statements of a man who said that his apples always fell upwards, and for the same reason. The behaviour of figures and lines is like the fall of an apple, fixed by immutable laws, and it is a great thing to begin to see these laws even in their lowliest application. The child whose approaches to Arithmetic are so many discoveries of the laws which regulate number will not divide fifteen pence among five people and give them each sixpence or ninepence; ‘which is absurd’ will convict him, and in time he will perceive that ‘answers’ are not purely arbitrary but are to be come at by a little boy’s reason.” (Vol. 6, p. 152)
“We take strong ground when we appeal to the beauty and truth of Mathematics; that, as Ruskin points out, two and two make four and cannot conceivably make five, is an inevitable law. It is a great thing to be brought into the presence of a law, of a whole system of laws, that exist without our concurrence,—that two straight lines cannot enclose a space is a fact which we can perceive, state, and act upon but cannot in any wise alter, should give to children the sense of limitation which is wholesome for all of us, and inspire that sursum corda which we should hear in all natural law.” (Vol. 6, pp. 230-231)
“Arithmetic, Mathematics, are exceedingly easy to examine upon and so long as education is regulated by examinations so long shall we have teaching, directed not to awaken a sense of awe in contemplating a self-existing science, but rather to secure exactness and ingenuity in the treatment of problems.” (Vol. 6, p. 231)
“Mathematics depend upon the teacher rather than upon the text-book and few subjects are worse taught; chiefly because teachers have seldom time to give the inspiring ideas, what Coleridge calls, the ‘Captain’ ideas, which should quicken imagination.” (Vol. 6, p. 233)
“How living would Geometry become in the light of the discoveries of Euclid as he made them!” (Vol. 6, p. 233)
“Where science does not teach a child to wonder and admire it has perhaps no educative value.” (Vol. 6, p. 224)
10. If we divide our lives into the intellectual and spiritual, we may ourselves become divided, having a life separate from God. Charlotte believed this was the source of youth falling into unbelief in God.
“Is it not a fact that the spiritual life is exigeant, demands our sole interest and concentrated energies? Yet the claims of intellect—mind, of the æsthetic sense—taste, press upon us urgently. We must think, we must know, we must rejoice in and create the beautiful. And if all the burning thoughts that stir in the minds of men, all the beautiful conceptions they give birth to, are things apart from God, then we too must have a separate life, a life apart from God, a division of ourselves into secular and religious—discord and unrest. We believe that this is the fertile source of the unfaith of the day, especially in young and ardent minds. The claims of intellect are urgent; the intellectual life is a necessity not to be foregone at any hazard. It is impossible for these to recognise in themselves a dual nature; a dual spirituality, so to speak; and, if there are claims which definitely oppose themselves to the claims of intellect, those other claims must go to the wall; and the young man or woman, full of promise and power, becomes a free-thinker, an agnostic, what you will.” (Vol. 2, p. 275)
11. Knowing the relationship between Teacher and taught in everything allows for uninhibited growth. Development in mind or spirit is mutually seen as progress toward a fuller knowledge of God.
“But once the intimate relation, the relation of Teacher and taught in all things of the mind and spirit, be fully recognised, our feet are set in a large room; there is space for free development in all directions, and this free and joyous development, whether of intellect or heart, is recognised as a Godward movement.” (Vol. 2, p. 275)
“By degrees children get that knowledge of God which is the object of the final daily prayer in our beautiful liturgy—the prayer of St. Chrysostom—‘Grant us in this world knowledge of Thy truth,’ and all other knowledge which they obtain gathers round and illuminates this.” (Vol. 6, p. 64)
Questions to Ask about the Great Recognition
- Have I been teaching math as something independent from God?
- Do I recognize the Holy Spirit’s role in instructing my child?
- Do I cooperate with the divine teaching in my child’s math lessons by not over-teaching or using too many words?
- Am I patient to advance slowly in mathematics, allowing my child to wonder, to discover mathematical truths, and permitting ideas to germinate in my child’s mind?