How Children Learn - Art, Math & Other Things

Kids can use sharp tools?  Really?
p. 202  "I agree strongly with Mr. Wesley that even very young children should be given or have access to art materials of high quality, and shown how to use them carefully and well, just as we would show them how to use any other quality tools.  Freed of the limitations of bad tools, they can then begin to explore, express, and enlarge their own artistic powers.  We should not assume that they will be too clumsy, impatient, and uncaring to use these tools properly.  They are perfectly able to learn how to use many kinds of tools, including sharp woodworking tools, cooking tools, musical instruments, and cameras, that most people would insist they could not use."

Messing About
p. 219  Always let children have free play with materials before directing them.

The Montessori materials provide ample materials
for "messing about" with numbers and building up
a mental model of the territory.

p. 222 "Children need what we rarely give them in school--time for "Messing About" with reading--before they start trying to learn to read, to make the connections between letters and sounds.  They need time to build up in their minds, without hurry, without pressure, a sense of what words look like, before they start trying to memorize particular words.  In the same way, they need time for "Messing About" with numbers and numerals, before they start--if they ever should start--trying to memorize addition facts and multiplication tables.  They need to know how big 76 is, or 134, or 35,000, or a million.  They need to see, again without hurry or pressure, how numbers change and grow and relate to each other.  They need to build up a mental model of the territory before they start trying to talk about it.  We teachers like to think that we can transplant our own mental models into the minds of children by means of explanations.  It can't be done."

Crossing the line
p. 223 "Professor Hawkins rightly says, "All of us must cross the line between ignorance and insight many times before we truly understand."  Not only must we cross that line many times, but, in the words of the old spiritual, nobody else can cross it for us, we must cross it by ourselves.  Being shoved or dragged across does no good."

Children see the world as a whole and make their own connections according to their interests
p. 232  "[Children] see the world as a whole, mysterious perhaps, but a whole none the less.  They do not divide it up into airtight little categories as we adults tend to do.  it is natural for them to jump from one thing to another, and to make the kinds of connections that are rarely made in formal classes and textbooks.  They make their own paths into the unknown, paths that we would never think of making for them.  When they are following their own noses, learning what they are curious about, children go faster, cover more territory than we would ever think of trying to mark out for them, or make them cover.
 
Our task is to keep a child's curiosity well supplied with good food.
p. 233  "People have often said to me, nervously or angrily, that if we let children learn what they want to know they will become narrow specialists, nutty experts in baseball batting averages and such trivia.  Not so.  Many adults do this; the universities are full of people who have shut themselves up in little fortresses of artificially restricted private learning.  But healthy children, still curious and unafraid, do not learn this way.  Their learning does not box them in; it leads them out into life in many directions.  Each new thing they learn makes them aware of other new things to be learned.  Their curiosity grows by what it feeds on.  Our task is to keep it well supplied with food.

Keeping their curiosity "well supplied with food" doesn't mean feeding them, or telling them what they have to feed themselves.  It means putting within their reach the widest possible variety and quantity of good food--like taking them to a supermarket with no junk food in it (if we can imagine such a thing).