So…What About Math??? by Cindy Rushton

“We find that, while children are tiresome in arguing about trifling things, often for the mere pleasure of employing their reasoning power, a great may of them are averse to those studies which should, we suppose, give free play to a power that is in them, even if they do not strengthen and develop this power. Yet, few children take pleasure in Grammar, especially in English Grammar, which depends so little on inflexion. Arithmetic, again, Mathematics, appeal to only a small percentage of a class or school, and, for the rest, however intelligent, its problems are baffling to the end, though they may take delight in reasoning out problems of life in literature or history. Perhaps we should
accept this tacit vote of the majority and cease to put undue pressure upon studies which would be invaluable did the reasoning power of a child wait upon our training, but are on a different footing when we perceive that children come endowed to the full as much with reason as with love; that our business is to provide abundant material upon which this supreme power should work; and that whatever development occurs comes with practice in congenial fields of thought. At the same time we may not let children neglect either of these delightful studies.” Charlotte Mason, page 151 Toward a Philosophy of Education

I would suppose that I am one of those that never found Math to be appealing! Have any of those children in your home? What to
do? Lessen the pressure and focus, but still give them abundant opportunity and abundant material to develop their intellectual muscles. Miss Mason found much value in the teaching of Math. Because of this, she did not allow the natural tendencies of the child to dictate the focus on Math. She balanced the presentation of all ideas, including Arithmetic and Math. She wrote…

“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 and 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 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. Mathematics are delightful to the mind of man which revels in the perception of law, which may even go forth guessing at a new law until it discover that law; but not every boy can be a champion prize-fighter, nor can every boy ‘stand up’ to Mathematics. Therefore perhaps the business of teachers is to open as many doors as possible in the belief that Mathematics is one out of many studies which make for education, a study by no means accessible to everyone. Therefore it should not monopolise undue time, nor should persons be hindered from useful careers by the fact that they show no great proficiency in studies which are in favour with examiners no doubt, because solutions are final, and work can be adjudged without the tiresome hesitancy and fear of being unjust which beset the examiner’s path in other studies. We would send forth children informed by ‘the reason firm, the temperate will, endurance, foresight, strength and skill,’ but we must add resolution to our good intentions and may not expect to produce a reasonable soul of fine polish from the steady friction, say, of mathematical studies only.” Charlotte Mason, page 152-153 Toward a Philosophy of Education

“We do not live on gymnastics, the mind like the body, is invigorated by regular spells of hard exercise. But education should be a science of proportion, and any one subject that assumes undue importance does so at the expense of other subjects which a child’s mind should deal with…Mathematics are to be studied for their own sake and not as they make for general intelligence and grasp of mind. But then how profoundly worthy are these subjects of study for their own sake, to say nothing of other great branches of knowledge to which they are ancillary! Lack of proportion should be our bÃ?te noire in drawing up a curriculum, remembering that the mathematician who knows little of the history of his own country or that of any other, is sparsely educated at best.” Charlotte Mason, page 231-232 Toward a Philosophy of Education

This reminds me of the educational system of our day. Really so much emphasis is made on so many trivialities that most educated
in our culture are sparsely educated.

Even those who ARE educated are not educated for the right reasons. Thus, the whole purpose of the studies is never realized.
For example, what do you think of when you think of studying Math? How do you think Math is best taught? Most answers would probably include one or more aspects of the true study of Math, but rarely all aspects of Math! Math includes several areas: critical thinking, problem solving, understanding concepts, and, finally, using skills. If any area is not taught, there will be a hole in Math. Let’s dig into Charlotte Mason’s writing to understand these aspects more fully AND to find out how to teach Math most effectively…

Math Develops Intellectual Muscles!

“Mathematics, grammar, and logic, etc., are not purely disciplinary, they do develop intellectual muscle. We by no means reject the familiar staples of education in the school sense, but we prize them even more for the record of intellectual habits they leave in the brain tissue, than for their distinct value in developing certain ‘faculties.’ Charlotte Mason, page 174 School Education

Math Gives IDEAS!!

“Mathematics depend upon the teacher rather than upon the textbook and few subjects are worse taught; chiefly because teachers seldom have time to give the inspiring ideas.” Charlotte Mason, page 233 Toward a Philosophy of Education

As we have been homeschooling, I have learned far more by watching my children work through problems. We now have a habit of working through until we find a way! This sets us way ahead!

Does this seem like “the blind leading the blind?” It is really one of the greatest keys to teaching Math. Being a teacher who is able to learn with the children! We are learning to be flexible…to search…to keep trying! This goes beyond merely answering questions…we are searching for ideas!

Math CAN BE Interesting AND Delightful!

Math need not be dull and lifeless! It can actually be challenging, interesting, delightful and EASY! Here are some tips for making math more interesting and fun…

–> Scrap texts when you can teach naturally. Any time you are teaching measurement, reasoning, time, simple sums, etc…try to
teach through REAL LIFE! It will be easier to teach AND to learn.

“On the same principle, let him learn ‘weights and measures’ by measuring and weighing; let him have scales and weights, sand or rice, paper or twine, and weigh, and do up, in perfectly made parcels, ounces, pounds, etc. The parcels, though they are not arithmetic, are educative, and afford considerable exercise of judgment as well as of neatness, deftness, and quickness. In like manner, let him work with foot-rule and yard measure, and draw up tables for himself. Let him not only measure and weigh everything about him that admits of such treatment, but let him use his judgment on questions of measure and weight. How many yards long is the tablecloth? How many feet long and broad a map, or picture? What does he suppose a book weighs that is to go by parcel post? The sort of readiness to be gained thus is valuable in the affairs of life, and, if only for that reason, should be cultivated in the child. While engaged in measuring and weighing concrete quantities, the scholar is prepared to take in his first idea of a ‘fraction,’ half a pound, a quarter of a yard, etc.” Charlotte Mason, page 259-260 Home Education

–> Present ONE difficulty at a time. One thing that we have tried to do with our children is slow down to teach concepts bit-by-bit, little-by-little. The fruit of this approach is comprehension and deep understanding. You can use ANY curriculum with this approach. Most curriculum is written with new principles introduced, followed by lots of practice. Take more time on the concepts of the new principle being introduced. IF the child understands the concepts, let them move on. IF NOT, then let them take more time on the concept and work through more of the practice problems. This works! It did for Charlotte Mason as well…

“Engage the child upon little problems within his comprehension from the first, rather than upon set sums. The young governess
delights to set a noble ‘long-division sum,’–953,783,465 ? 873–which shall fill the child’s slate, and keep him occupied for a good half-hour; and when it is finished, and the child is finished too, done up with the unprofitable labour, the sum is not right after all: the two last figures in the quotient are wrong and the remainder is false. But he cannot do it again–he must not be discouraged by being told it is wrong; so, ‘nearly right’ is the verdict, a judgment inadmissible in arithmetic. Instead of this laborious task, which gives no scope for mental effort, and in
which he goes to seas at last from sheer want of attention, say to him–‘Mr. Jones sent six hundred and seven, Mr. Stevens eight hundred and nineteen, apples to be divided amongst the twenty-seven boys at school on Monday. How many apples apiece did they get?’ Here he must ask himself certain questions. ‘How many apples altogether? How shall I find out? Then I must divide the apples into twenty-seven heaps to find out each boy’s share.’ That is to say, the child perceives what rules he must apply to get the required information. He is interested; the work goes on briskly: the sum is done in no time, and is probably right, because the attention of the child is concentrated on his work. Care must be taken to give the child such problems as he can work, but yet, which are not difficult enough to cause him some little mental
effort.” Charlotte Mason, page 254 Home Education

–> Give them TIME to think, reason, and use their minds without boring them. Thinking and reasoning will exercise their minds. They will develop the powers of their minds. Miss Mason said,

“Of all his early studies, perhaps none is more important to the child as a means of education than that of arithmetic. That he should do sums is of comparatively small importance; but the use of those functions which ‘summing’ calls into play is a great part of education…The practical value of arithmetic to persons in every class of life goes without remark. But the use of the study in practical life is the least of its uses. The chief value of arithmetic, like that of higher mathematics, lies in the training it affords to the reasoning powers, and in the habits of insight, readiness, accuracy, intellectual truthfulness it engenders. There is no one subject in which good teaching effects more, as there is none in which slovenly teaching has more mischievous results.” Charlotte Mason, page 254 Home Education

–> No cramming! No testing!

“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.” Charlotte Mason, page 264

–> Incorporate narration. As you are working through different operations whether in the early stages with beans, buttons, etc OR as they get older and work with abstract ideas, allow the child to explain the concepts or operations through narration. Remember
that whatever they take inside and make their own, will STICK.

She continues, “A bag of beans, counters, or buttons should be used in all the early arithmetic lessons, and the child should be able to work with these freely, and even to add, subtract, multiply, and divide mentally, without the aid of buttons or beans, before he is set to ‘do sums’ on his slate.”

“Dominoes, beans, graphic figures drawn on the blackboard, and the like, are, on the other hand, aids to the child when it is necessary for him to conceive of a great number with the material of a small one; but to see a symbol of the great numbers and to work with such a symbol are quite different matters…nothing can be more delightful than the careful analysis of numbers and the beautiful graduation of the work,’only one difficulty at a time being presented to the mind.'” Charlotte Mason, page 262, Home Education

(Miss Mason continues on pages 256-264 with wonderful ideas for teaching the principles of arithmetic…LOOK it up!)

–> Use visual aids. BUT let the children make them! Children will enjoy making their own resources like multiplication tables or hundred charts. Not to mention, they will probably learn more as they make it! My son, very bright in the study of Math, really hit
a HUGE snag when we got to multiplication. He understood the concept and could figure any problem given, but simply could not memorize his multiplication tables to help him with his speed. I was troubled for MONTHS before I came across the idea of letting him make a multiplication chart to use with his lessons. He never did learn his multiplication tables, but he can figure in his mind any of the equations. This may be the answer to your little ones too. AND it is OK!

–> Use songs to help remember facts that are difficult to remember! Math facts will simply take time to learn. However, one
tool that can be used effectively and PAINLESSLY is music! Use either commercially prepared tapes OR give the children their own tapes to creatively produce their OWN songs.

–> Play LOTS of games! Children can easily and naturally learn Math through their play. Use games to break up daily lessons, introduce new concepts, practice skills, or to develop thinking skills. Games can be found at department stores, school supply stores, OR you can MAKE your own! FUN and INDIVIDUAL!