First posted August 2010
"In our age of calculators and computers, we must question how much time even good students of arithmetic should spend working pages of problems of ever-increasing size....Curriculum improvements come slowly in the school world. But homeschoolers have an advantage. With just a decision of one or two people, you can make any changes you want. Will you skip the pages with three- and four-place divisors and let your children, instead, learn some BASIC computer programming? The choice is up to you."--Ruth Beechick, You CAN Teach Your Child Successfully (1984)
P.S. In case you're too young to know this, BASIC here refers to the programming language, not the fact that it was basic.
Showing posts with label arithmetic. Show all posts
Showing posts with label arithmetic. Show all posts
Thursday, August 31, 2017
Sunday, January 12, 2014
The Parents' Review on Geometry and Synthesis (and the argument over taking flowers apart)
"Before the child has to work at geometry, see that he realizes:-- That there are in nature no lines, except the edges of solids, nor surfaces, except the sides of solids. That natural movements and growths take place usually in curves, not straight lines. That axes, diameters and co-ordinates are not part of any natural figure, but measuring rods introduced for man's convenience. Connect in the pupil's mind these devices with that earlier invention, mentioned in the former paper, of breaking big numbers into tens and hundreds; explain that man extracts no more real instruction out of such devices than a monkey gets by breaking things in bits, unless he completes the cycle of study by the transcendental (or supra-simian) act of synthesis. The parent will translate these words into such as she finds suit the child; the essential thing is for the parent herself to grasp the idea clearly. If she does not, she should get herself taught to do so by some competent person.
"In connection with this idea of synthesis, a child should be taught that if he wants to learn anything about an object by breaking it open, he should not break it till he has taken a good look at it in its original state, so as to be able to reconstruct it in his mind as a whole.' ~~ "Home Algebra and Geometry," by Mary Everest Boole, in The Parents' Review, Volume 3, 1892/93, pgs. 854-857
And check this one out (emphases mine):
"May I make an example of flowers to illustrate the application of the science of appearances? Amongst other sciences applicable to them is horticulture, which treats of their civilization, the robustness of their constitution, their span of life, their propagation, their cultivation, the improvement of their characteristics of form and colour, the soil suitable to them, its texture, and its chemical constituents. There is also botany, a science which deals with their habits, their structure, their organs, their classification and variety. These are all concrete facts, to acquire which we examine the flowers from every point of view. We uproot them, we dissect them, we remove them from their surroundings, and consider them almost without reference to them. The facts of their appearance are different. They depend, not only upon the aspect and condition of the flowers themselves, the relation of the parts to the whole, and of the parts to each other, in different qualities and characteristics, but their aspect also depends upon their relation to surroundings, and to the aspect and condition of surroundings, and to relations, conditions, influences outside themselves and their immediate surroundings.
"We may be able to change their surroundings and the outside influences, but we cannot disassociate them, We may take flowers from the field, or hedgerow, or garden, and bring them indoors, place them in a vase or upon a table or in a box, we may change their conditions in a countless number of different ways, but do what we may, we cannot see them without some surroundings. Any change of surroundings or change of relation of outside influences will cause change of appearance. Their appearance amongst the green grasses in the field will be different from their appearance as they grow in the garden soil against the red-brick wall, or as they lie indoors upon a polished mahogany table. They will appear different under the influence of sunshine, or gray weather or rain, at a distance from us or near at our feet. The appearance of the flowers will in every possible case have certain fixed relations to surroundings and outside conditions and influences. We cannot see or conceive flowers or any other object except under aspects influenced by outside conditions, for that is the way nature conveys to us the impression of them." ~~ "The Fine Arts and Education, Part 1," by Francis Bate, in The Parents' Review, Volume 7, 1896, pgs. 561-571.
Do you get the feeling we're talking about a lot more than botany here?
"In connection with this idea of synthesis, a child should be taught that if he wants to learn anything about an object by breaking it open, he should not break it till he has taken a good look at it in its original state, so as to be able to reconstruct it in his mind as a whole.' ~~ "Home Algebra and Geometry," by Mary Everest Boole, in The Parents' Review, Volume 3, 1892/93, pgs. 854-857
And check this one out (emphases mine):
"May I make an example of flowers to illustrate the application of the science of appearances? Amongst other sciences applicable to them is horticulture, which treats of their civilization, the robustness of their constitution, their span of life, their propagation, their cultivation, the improvement of their characteristics of form and colour, the soil suitable to them, its texture, and its chemical constituents. There is also botany, a science which deals with their habits, their structure, their organs, their classification and variety. These are all concrete facts, to acquire which we examine the flowers from every point of view. We uproot them, we dissect them, we remove them from their surroundings, and consider them almost without reference to them. The facts of their appearance are different. They depend, not only upon the aspect and condition of the flowers themselves, the relation of the parts to the whole, and of the parts to each other, in different qualities and characteristics, but their aspect also depends upon their relation to surroundings, and to the aspect and condition of surroundings, and to relations, conditions, influences outside themselves and their immediate surroundings.
"We may be able to change their surroundings and the outside influences, but we cannot disassociate them, We may take flowers from the field, or hedgerow, or garden, and bring them indoors, place them in a vase or upon a table or in a box, we may change their conditions in a countless number of different ways, but do what we may, we cannot see them without some surroundings. Any change of surroundings or change of relation of outside influences will cause change of appearance. Their appearance amongst the green grasses in the field will be different from their appearance as they grow in the garden soil against the red-brick wall, or as they lie indoors upon a polished mahogany table. They will appear different under the influence of sunshine, or gray weather or rain, at a distance from us or near at our feet. The appearance of the flowers will in every possible case have certain fixed relations to surroundings and outside conditions and influences. We cannot see or conceive flowers or any other object except under aspects influenced by outside conditions, for that is the way nature conveys to us the impression of them." ~~ "The Fine Arts and Education, Part 1," by Francis Bate, in The Parents' Review, Volume 7, 1896, pgs. 561-571.
Do you get the feeling we're talking about a lot more than botany here?
Thursday, April 08, 2010
A Month with Charlotte Mason, #9
In our moral as in our intellectual education, we work too entirely upon narrow utilitarian lines: we want the impulse of profounder conceptions.--Charlotte Mason, preface to OurselvesRather than talk about how you do every school subject CM style...because you can get a lot of that information on places like the Ambleside Online FAQ page...I am going to pull some quotes from Home Education, and I’d like you to note the most-repeated words and themes, so that you can see how Charlotte Mason's ideas are really interchangeable from subject to subject. Remember that these are from descriptions of lessons for children under nine (the focus of Home Education), so there isn’t a lot here about Latin or other typical subjects for older ones. School Education (Volume 3) and Philosophy of Education (Volume 6) have more about teaching older students.
“Children’s lessons should provide material for their mental growth, should exercise the several powers of their minds, should furnish them with fruitful ideas, and should afford them knowledge, really valuable for its own sake, accurate, and interesting, of the kind that the child may recall as a man with profit and pleasure.”A wide horizon, full of persons and events taking shape...to open, to awaken, to furnish, to stimulate, to excite, to exercise...to nourish.
From page 221, on learning to read: "He has considerable power to attack new words with familiar combinations; what is more, he has achieved; he has courage to attack all ‘learning,’ and has a sense that delightful results are quite within reach. Moreover, he learns to read in a way that affords him some moral training. There is no stumbling, no hesitation from the first, but bright attention and perfect achievement."
From page 254, on arithmetic: "The chief value of arithmetic, like that of the 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….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…. Carefully graduated teaching and daily mental effort on the child’s part at this early stage may be the means of developing real mathematical power, and will certainly promote the habits of concentration and effort of mind."
From page 267, a quote from Edward Holden's The Sciences: "....to awaken the imagination; to convey useful knowledge; to open the doors towards wisdom. Its special aim is to stimulate observation and to excite a living and lasting interest in the world that lies about us."
From page 249, on Bible lessons: "But let the imaginations of children be stored with the pictures, their minds nourished upon the words…and they will come to look out upon a wide horizon within which persons and events take shape in their due place and in due proportion."
From page 272, on geography: "The peculiar value of geography lies in its fitness to nourish the mind with ideas, and to furnish the imagination with pictures….[Its educational value] is the developing of power, the furnishing of the mind….the child’s geography lesson should furnish just the sort of information which grown-up people care to possess."
From page 279: [History too] is a subject which should be to the child an inexhaustible storehouse of ideas, should enrich the chambers of his House Beautiful with a thousand tableaux…
Again I'll post that definition of leisure:
Having the freedom (time, space, opportunity) to discover what makes you fully human.
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