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glad to find that pas t el crayons still exist. Th e se t I like best is called Cray- Pas and is made by Sakura. I prefer them to Niji, the other brand I found, because they seem slightly less likely to break and their box is easier to use . I feel so strongly about these crayons that we've made arrangements to sell them through this office: $1 . 50 for a box of 12 Cray-pas; this price includes postage. (As for books and reprints, make checks payable to HOLT ASSOCIATES, INC . ) Cray-pas are a little more expen sive than ordinary wax crayons, but the vivid, exciting colors make the difference well worth it. Another advantage is that it is very easy to blend one color into another. I hope that many families will try these pastel crayons, and that they will tell us about their experiences. ... AND PAINT
The other art materials I looked into recently were gouache paints. They come in hard cakes or pastilles - you moisten your brush and then mix up the paint right on the cake (water colors often come this way). A box of eight of these cakes cost about $4 . 50. Gouache also comes in tubes; I got a box of ten small tubes for $8.00, but if you were going to use a lot of paint it would make sense to buy larger tubes. On the whole, I found the gouache colors slightly less vivid than the pastel crayons, though the cobalt blue and the green were very close . The red, on the other hand, was quite dull. The liquid paint has its advantages, how ever. You can put it on much more smoothly, dilute it to many different strengths, and get many effects with the brush that you could not get with the pastel crayons . The two mediums are different; you can do some things with one and other things with the other. I like them both . I plan soon to tryout some acry lics; their colors may prove to be the most vivid of all . I did not try out pastels, though I like them; they break very easily, and the chalky dust tends to get allover every thing. If people have had some experi ence with pastels, or other mediums that we have no t mentioned here, I hope they will write. While experimenting with the gou ache paints just described, I made a mini-discovery that may be helpful to anyone, adult or child, working with gouache or water color paints, or any other kind (if there are any) in which the paints are diluted and mixed with water. I began with the problem that we all face when we start working with such paints. How are we going to keep a supply of clean water to dip our brushes in when we are painting, and also, to clean off paint of one color before we put on another color? Usual ly the amateur painter, child or adult, starts off with a number of containers of clean water, which are soon full of a muddy brown liquid, useless for either mixing or clean ing. Every so often the jars or dish es must be emptied and refilled. All this is distracting, makes for much walking back and forth, and with lit tle children, often leads to a cer tain amount of mess. What I did, somewhere along the line, instead of dipping my paint laden brush into my clean water sup ply, thereby making it less clean, was to dip one (clean) finger into
GROWING WITHOUT SCHOOLING #16
the clean water and let the drop of water that formed on the end of the finger touch the brush, which soaked it up immediately. I then squeezed the brush gently in some toilet paper (paper towels or Kleenex would do just as well.) When no more paint came out on the paper, the brush was clean. You could also drop water on the brushes using a medicine dropper, or a straw (dip the s t raw in some water, put your finger over the top when you have as much water as you need, hold the straw over the brush, take the finger off the top) . However you do it, when you take the clean water to the paintbrush, ~n stead of the paintbrush to the clean water, it solves the problem of all those containers full of mud-colored water. This does away with the main argument against giving children good water color or gouache to paint with, namely, that mixing the colors makes such a mess . I pass along this little tip to whoever may be able to make use of it. Happy painting! LOOKING UP ANSWERS
A mother wrote: ... 1 still don't know why my daughter doesn't like me to take the time to look things up for her when she asks me a question. I think she likes a simple answer, so I have to do the research on the sly. I think she doesn't want to have to sit if someone expects her to. Perhaps it may have something to do with her schooling in kindergarten. She hated all the sitting they had to do. They could only be active if the teacher said they could. I am really not sure. If I ever discover why I will let you know ...
I wrote in reply: ... My hunch is that what she wants to find out is not so much accurate information as what think about it. She wants to now what-~ know or think about some par ticular subject . I don't think that she feels you know everything or that you are always right, though I have to guess at this. It's more that she is interested in the world, and in your ideas about that world ...
kOU
MATH AT HOME
From a mother in Washington: .. . My oldest son is just comple ting first grade and I have already reached a level of extreme frustra tion and concern wi th what school is doing to him . . . He, in fact, looked forward to kindergarten with great joy and could hard l y wait to begin . Less than one month passed before the question "How was school today?" would produce tears . To make a long story short, we have spent the last two years "in conference" with teach ers and administrators, trying to make school a better place for my son. . .. 1 would like to comment on the "Exchange on Math" section in GWS #14. I am amazed at the difficulty and confusion with which most child ren approach math . My own son's great est love is math and I believe the reason is that for him playing with numbers has always been a part of "real" life . From reading GWS I have
concluded reading/writing is "candy" for mos t unschooled kids because those children see that language skills playa big part in the lives of the adults around them, and there fore they need it and do learn it . My husband and I are avid-readers and therefore by only one year of age my son would sit during our quiet times and "read" his books too. Naturally, by the age of four he was in truth reading. In a similar manner, he saw that numbers were important to us. My husband is an engineer who often does his work at home . Since his father used a calculator and played with num bers, Greg naturally wished to do the spme. All he wanted for his third Christmas was a calculator . He subse quently spent hours play~ng with it and has taught himself with little help from us except for brief explana tions when it came to "borrowing and carrying . " Similarly he loves mazes, logic pro blems, and crossword puzzles because (I feel) these are things he can see we enjoy doing. So, in response to Nancy Wal lace's question "Reading is candy, but why don't most people feel the same about math?" I would respond that if we as parents feel comforta ble with and enjoy doing math (in all its forms) our children will feel the same . I t is only because most adults feel that this is foreign territory that children learn to think of math as incomprehensible ... BOOTLEG MATH
The school I went to for my first four years was very tradition al. It taught arithmetic by pure rote memorization, as if we were parrots, or talking laboratory rats. No teach er that I can remember ever discussed mathematical ideas with us, or showed us inte r esting mathematical tricks . All they did was give us "facts," show us how to do problems, give and correct homework, and drill and test us. But just as we childen had our private secret world of games, tricks, jokes, taunts, and insults, so we had our private mathematical world as well. A number of mathemati cal tricks and games floated round the school, certainly not encouraged by the teachers, and perhaps without their even knowing about them . Often we worked on these mathematical games in class or study hall, hiding our work behind our official math books. One of these games was "Think Of A Numbe r ." Student A would come up to Student B, preferably with students C, D, and E nearby, and there would follow a conversation about like this: A. Think of a number . Don't tell me what it is, but be sure to remember it.
B. OK, I've got it. A. Make sure you don't forget it' B. Don't worry, I won't' A. Now add three to it - and don't tell me the answer . B. Got i t. A. Now add ten to it. B. Got it . A. Now take away seven from it. (No one ever said "subtract," though the teachers tried to make us.) B. OK. A. Now add five to it. B. OK. A. Now take away the number you started with. B. OK. A. (Triumphantly) The answer is eleven'