Lillian Jones “The pages are simple and crisp, with nice big illustrations...this is wonderful!!!”
The Delights of Exploring Math With Your Child - From www.Besthomeschooling.org
Note: A number of excellent resources are referred to below, but none of them are ads.
The question of how to provide our children with a good math education often causes undue anxiety. With a clearer and more relaxed understanding of what it is that we’re trying to accomplish, we can present it as just one more interesting part of life - one that anyone can easily explore and delight in.
Not everyone will become fascinated with math, any more than everyone will become fascinated with painting or creative writing - but anyone can at least become acquainted with the fun to be found in it, so that they can learn math as a useful and accessible tool rather than as a dull and exhausting set of mysterious processes understood only by people who are “good at math.”
Math has always been a natural and necessary part of life. People throughout history have continually come upon wonderful discoveries and innovations for working with relationships, patterns, and quantities to solve problems or fulfill needs - but, unfortunately, we’ve managed to narrow our focus to those procedures, removed from the patterns being navigated by them.
Suki Glenn, is the one of the inspiring authors of the Pattern Press children’s math books - a program that uses a multi sensory approach developed in an experimental education program called The Farm School at U.C. Irvine. In the Pattern Press web site, she explains her philosophy of teaching children to think like mathematicians:
“What do mathematicians do? They are good at constructing models, looking for number patterns, and using those patterns to develop reliable procedures for solving problems. The procedures we all use to add, subtract, multiply or divide were created by mathematicians who generalized a physical reality to an abstract mathematical formula. They invent short cuts and easy recording systems (like place value) and then teach them to all of us.
The skills of a mathematician can be developed in children by allowing them to use manipulatives to build models of the physical reality of addition, subtraction, or whatever subject with which they find and use patterns, and then create their own procedures for doing arithmetic operations. If children are given the chance to discover the procedures instead of being told how to do it and then drilling it in, you will find the results superior, the learning more of an adventure. You will have experiences of delight as your young mathematicians surprise you with methods and models you have never seen.”
Professor Emeritus Michael Butler, in a foreword to the children’s math books, Patterns in Arithmetic: Book 1, by Suki Glenn and Susan Carpenter, recalls his early exploration of new ways that math can be taught:
“Years ago I was a young professor at UC Irvine, and although I had long been fascinated by the act of learning, this was my first teaching job. Among other things I taught mathematics. The experience was immensely rewarding but unsettling. I thought of math as beautiful, richly ordered, and fun. Most of my students in those required courses appeared to think of it, at least at first, as arbitrary, impenetrable, incoherent, and dull; some of them found it scary.
A few students did not - cheerfully pushing and pulling at a formula, for instance, and asking: ‘What would happen if this part of the denominator were in the numerator? What would happen if I reversed this and that part? What would happen if I made this piece very large or very small? What would be a simpler form or a more general form of the expression?’ They engaged in this systematic play for the fun of it, but their reinventing or recasting of the material of mathematics also helped them see why something was the way it was; it helped them understand. In fact, the students I started listening to each seemed to carry with them a kind of ‘understanding kit.’ They had an expectation that math would make sense; they knew when a particular expression or idea did not yet make sense to them, and when it did; and they had developed skills and stamina for getting from the first state to the second, and the habit of doing so. The math they came to know in this way, they owned.
These happy few were regarded by the others (and by most of my colleagues) as having a peculiar knack. There was no shame in not having it; that was just the luck of the genetic draw. Or did the attitude of the rest of the class toward math have to do with the way they had been educated? Their reports of their pre-college math study matched what I found when I started visiting schools, especially elementary schools, and reading texts of that era: my students had been spending most of their time memorizing calculation recipes and learning to run them more or, often, less well.
But that wasn’t at all what the kind of people who had discovered the math did. Mathematicians look for and find patterns in formal objects, extend them, seek counter-examples, figure out why the patterns work, and then, finally, publish an account of one way that they work. The last is the public part, but the rest is what they do. Almost none of my undergraduate students seemed to have had much experience with that. There was an odd disjunction between what practitioners did and what schools asked students to do, a disjunction that was deeper and odder the more you looked at it. It was as though we had plucked the fruit “mathematics” for use in schools, peeled it, and fed students the rind instead of the flesh.”
Lancelot Hogben was a professor of medical statistics at Britain’s University of Birmingham when he wrote a popular book called Mathematics for the Million: How to Master the Magic of Numbers, first published in England in 1937 and revised up until 1967. Albert Einstein said of the book, “It makes alive the contents of the elements of mathematics.” Hogben once commented:
“The best therapy for emotional blocks to math is the realization that the human race took centuries or millennia to see through the mist of difficulties and paradoxes which instructors now invite us to solve in a few minutes.”
I wasn’t even aware of his feelings on that many years ago when reading his wonderful children’s book to my young son - The Wonderful World of Mathematics - but it was exactly my reaction at the time.
Lillian Jones's website: http://www.besthomeschooling.org/