Recently I attended a homeschool conference where I was able to hear back from many people who bought Magical Math last year and have been using it with their children. Their feedback was interesting and fun to hear. One mom told me that her eleven year-old had been going through a "hatred of math" phase, so she sat down with him and read the stories and did the activities in the book. Now he's back in his regular math curriculum but he has a totally different attitude: math is awesome. This has dramatically increased his ability to comprehend what he's being taught.
Another mom told me that they like to put a line of rocks on their sidewalk and label a number line beneath the rocks. Then they play the Pixie Race game (p. 26) writ large--literally. These and similar comments show that a playful approach to math engages young minds, drawing them in and getting them to spend time thinking about math, which after all, is the goal. When that happens, learning math facts becomes easy
"Schoolish" elementary math education is characterized by teaching children that math is all about learning the symbols for the numbers, and which symbols go together with other symbols to make a third symbol (3 + 4 = 7). But this isn't math, it's more akin to calligraphy! Many children enjoy math at the beginning because it tickles something in their brains with a new kind of thinking. But instead of a playful approach to mathematical thinking, they are very soon coerced into "practice this and then let me test you to see if you know it," which takes all the fun out of it. Arithmetic isn't difficult to master unless it's forced into a brain that has not yet developed enough logic skills, in which case, memorization takes the place of understanding.
From the book And There Was Light: Autobiography of Jacques Lusseyran, Blind Hero of the French Resistance: "Our teacher that year was a slow-moving, gentle man who had an even temper except for rare outbursts of anger at the stupid ones. From these outbursts I felt secure, and set to work sytematically to learn the foundations of arithmetic.... (T)hey gave me a vulcanite slate with cube-shaped holes and a set of steel cubes (with which to "write" the numbers)....But within a few months I found I could dispense with the cubes and the holes. To make the mind work, only the mind is needed. I began to visualize all the processes in my head, except, of course the ones which extended to an embarrassing number of data. Having a good memory, I became extremely adept at mental arithmetic, and that in turn helped develop my memory." (p. 42 - my emphasis in bold)
This and similar passages struck me recently as I reread this book. It's very useful for educators (including home educators) to reflect on our own early education, but it can be difficult to remember. Perhaps because of his blindness Lusseyran seems to have retained a lot of the details of what was going on in his internal world. His description of visualizing the processes of math in his mind is exactly what math educators describe as the best process to develop math skills: going from hands-on, to mental image, to being able to perform abstract math. Manipulatives provide the play element in an early math education,
Playing with math gives children the chance to discover math for themselves, which they can and will do. Schoolish math "poison(s) the students’ enjoyment of this fascinating and beautiful subject, and permanently disabl(es) them from thinking about math in a natural and intuitive way." (from A Mathematician's Lament, by Paul Lockhart, a fascinating glimpse into a research mathematician's view of the state of modern math education).