Science, in the Poll-Parrot period, arranges itself naturally and easily around collections--the identifying and naming of specimens and, in general, the kind of thing that used to be called "natural philosophy." To know the name and properties of things is, at this age, a satisfaction in itself; to recognize a devil's coach-horse at sight, and assure one's foolish elders, that, in spite of its appearance, it does not sting; to be able to pick out Cassiopeia and the Pleiades, and perhaps even to know who Cassiopeia and the Pleiades were; to be aware that a whale is not a fish, and a bat not a bird--all these things give a pleasant sensation of superiority; while to know a ring snake from an adder or a poisonous from an edible toadstool is a kind of knowledge that also has practical value.
The grammar of Mathematics begins, of course, with the multiplication table, which, if not learnt now, will never be learnt with pleasure; and with the recognition of geometrical shapes and the grouping of numbers. These exercises lead naturally to the doing of simple sums in arithmetic. More complicated mathematical processes may, and perhaps should, be postponed, for the reasons which will presently appear.
I have four children now, and because I don't want big messes, I rather discourage physical collections. Blame the four months I spent as an au pair/housekeeper in Germany back in my college years, but clutter depresses me. However, I think my science practices are basically in line with Sayers' educational philosophy because I encourage my children to read nonfiction books about science all the time. Do they really need to have pinned butterflies on cards to learn about the natural world? I think it's adequate to have a supply of engaging science books ready at hand and read them to my children on occasion. They get hooked and before you know it, they are reading DK's Big Book of Knowledge in bed at night instead of fairy tales. Besides providing science books, I also show my children science videos (they love Bill Nye and the National Geographic videos starring Dustin Hoffman as a globe named "Spin"), and when the weather is nice we go to the zoo and nature centers.
Math. Amen, Dorothy. Help them memorize those math facts as young as possible. Dd8 is still struggling to get to automaticity with her addition facts, while dd6 consistently outdoes her in addition drills on their daily Xtra Math practice sessions. Dd8 can memorize poems, no problem, but I think I waited too long to get serious about requiring her to memorize the addition facts and contributed to her developing a math facts mental block.
I wish I could buy a Barney or Dora DVD that helped children sing and memorize the basic addition facts. Computer math games haven't worked because my children want to have fun when they play on the computer, and math fact recall is not yet easy enough to be "fun" for them. Besides games and flashcards, I could find only lame math fact song collections or number "appreciation" cartoon DVDs. I'm positive my children would appreciate numbers more if they could use them with greater facility! If someone from Nick Jr. is reading this, I beg you to produce a good addition fact memorization DVD using Diego and exotic animals; the same goes for PBS and the Dinosaur Train characters.