He recommends a much faster introduction of the letters than my previous plan (which is similar to Christopherus, Live Ed, Marsha Johnson, etc.) He says,
"I recommend a rapid introduction of the Arabic numbers. Neither the reciting of numbers nor their writing down on paper is a methematical activity. THe math curriculum has to include both these conventional elements becasue they are required for communicating, but they should not take up more room than is their due. Therefore, we should not waste time on slowly introducing the written numbers.
The second reason I like to introduce numbers quickly and without pictures (unlike the consonants) is that their pictureless nature reaches toward the musical and rhythmical realms. In anthroposophical terms, we say that numbers are characteristically inspirative and not imaginative. We honor this by practicing numbers rhythmically and musically. In the end, the root of our ability to grasp amounts of spatially arranged items is a movement process."
This sentiment is similar to that in Ron Jarman's math book, which seems to be very popular amongst Waldorf educators. I don't have a great explanation for my switch, just that I devoured the book and Schuberth's ideas somehow feel right to me. Yoav knows how to count by twos, fives and tens and knows quite a bit of the multiplication tables, so I'm also just a bit antsy to move on with him. Jarman and Schuberth both think math is quite different than language and can and should be taught at a quicker pace than most Waldorf curricula. Schuberth (and I've seen this elsewhere as well) says that, whereas there is not a correlation (statistically) between age at which a child learns to read and reading ability in upper grades, with math, there are definite windows in which learning must happen. One example (that I think is in the Jarman book - I'll look when I have time for the quote) is that multiplication tables should be learned by third grade for them to be ingrained in the child and for the child to easily be able to quickly and easily recall any individual multiplication pair.
Anyway, so I'm using the basic structure for the first math block as laid out in Schuberth's book.
The first day I introduced the roman numerals 1-5. For each number, we discussed where the number exists in nature. Examples we used:
1 - G-d, sun, world, moon, me
2 - eyes, ears, hands, feet
3 - head/body/legs, thinking/feeling/willing, finger has three parts, insects have three segments
4 - seasons, legs for dogs/cats/etc., people in our family
5 - fingers, toes
On the first day, I drew the roman numerals (one by one) on the board and he practiced in the air and the drew on his main lesson paper. The second day, I wrote the arabic letters (one by one) and he practiced in the air and then on scrap paper and then onto the main lesson page. The number two was particularly difficult for him to write - he kept making a semi-circle and then trying to add the line at the bottom rather than a semi-heart... At the end of the second day, he wrote out the five numbers with a stick crayon. Then, on his own, he decided it wasn't so beautiful and wanted to write them in rainbow colors, but even then, he thought the numbers looked lonely I guess and was compelled to draw a picture around the numbers ;)
|Yoav's roman and arabic numbers 1-5 for his Main Lesson Book|
|Yoav's 1-5 Number Drawing|
Wednesday I introduced the roman numerals 5-10 and on Thursday we'll do the arabic numbers 5-10. Associations we discussed for the higher numbers:
6 - six legs on insects, people in my and my husband's families
7 - days of the week
8 - days of Hanukkah
9 - months of average pregnancy
10 - fingers, toes (Yoav said 10 10s is 100, which makes ten special)
We are also including a lot of rhythmic math-related verses - like poems in which we stomp and say a word louder ever second step or every third step as well as poems about numbers. I like a lot of the verses in Eric Fairman's "Path of Discovery".
Elie tunes in and out during our Main Lesson. He was interested in the roman numerals and particularly liked the three (since he's three). It's very sweet to see him sitting alongside Yoav and drawing alongside Yoav. I actually posted about this on the WaldorfHomeEducators Yahoo group (run by Marsha Johnson), as I'm concerned about exposing Elie to too much, especially given how cautious I've been with Yoav (and how thrilled I am with how things are unfolding with Yoav). Luckily Elie has not been interested in the Fairy Tales or the letters (I think because the Fairy Tales are over his head, so he tuned out most of the Language Arts block). Since I'm not doing stories with math (which work to dis-engage Elie), he is so far sitting at his desk for the whole of the lesson. I'm going to have to trust that he is learning at a very different level of understanding and the experience won't be too awakening, although I'll certainly have to monitor over the coming months and years...
|Elie's Roman Numeral Three|
Yesterday, for the first time, he drew a picture of an actual thing and it was himself! It was so sweet to witness - he drew a picture of himself and then lifted it to show me and beamed, "Look! I made me!"
The top picture is him with arms and the bottom one is with fingers - he drew the fingers and said, "I have a pinky!" Oh and as he was whipping out his drawings (he made about ten with different variations, some with two people), he turned and said to me, "I'm a really good draw-er!" :P