# SuperGirl Math 3: Meditative Doubling

We began with a continuation from our last lesson: “What is the highest number that you can name, can write, and would know how to count up to?” When we left off that highest number was 12, 999. After another fifteen minutes of new answers and discussion, in which I kept responding, “…And what would be one higher than that number?” they rested at a new summit, 99,999. After that, the abyss. We also reviewed number circles from last lesson. We used the number circle to chant the 2’s times tables. Then we moved to today’s lesson. The scroll suspended from the ceiling shows the pattern of doubled numbers: 1 , 2 2 , 4 3 , 6 … 19 , 38 20 , 40 . We noticed various patterns in the chart, and talked about how you could use those patterns to try to predict, “What would be double 14?” etc. You may be wondering what is an accordion doing there. I wanted to give them a calm, even serene experience of doubling. So I played a calming Phillip Glass piece as I questioned and they answered on beat, “18?” (beat 2 .. beat 3 .. beat 4..) “36” …. I had asked the girls to bring meditation cushions. Some took it quite seriously and chanted their doublings with upright posture. Then break. After break, we observed doubling through folding newspapers, 1, 2, 4, 8, 16. When they returned to our room, the scroll had been changed. It had been taken down and a new one put in its place, but this one was blank on both sides. They were surprised. We ended with a final doubling practice with only the blank scroll to focus their attention. The very last problem, accompanied by the Glass, was “0?” (beat 2 .. beat 3 .. beat 4..) “0.”

# SuperGirl Math, info

The Second Grade SuperGirl Math Class is currently full. Who: 8 Girls When: alternate Mondays, 4:00 – 5:30 Where: parent houses in Berkeley Why: challenge + review, to help girls to be excited about math, and to be strong in math How much: \$150 for five meetings through December A second session will begin in January. Registration will open in early December. From the SuperGirl Math Camp over the summer: Well first off let me say it’s  been great, thank you, and Shira went in one day from saying “I don’t like math” to saying “camp was great”. What can I say, you’re a gem! … I’d love to have it continue during the school year. — Tamar, parent I am very impressed with your commitment to this camp, and Naima is having a great time! … I would like to continue something with you during the school year …. Thanks again for making this so engaging for the girls!

# K. Building Imagination: The Castle, the Challenge, and the Secret Hideout

Parent Krista (mother of Riley) observed class yesterday and has generously shared her observations. I was able to observe my daughter’s class this week and found it fascinating. The kids were building a castle with blocks. I watched them negotiate their thoughts about the construction project…., “no, I think this round piece should go here in the corner because it looks more like a castle that way”. I noticed that the kids naturally broke into smaller groups of 2-4 to conquer a section of the castle. There was a side project going on in which the kids were trying to fit different shapes together to match the shape of a rectangle. Some really got into this and praised other kids when they thought of a creative way to do it different. What a fun class! I see my daughter learning team building skills and early geometry lessons all in one! For another view, our castle-building in pictures.  I wasn’t able to get a good shot of everyone, but this will give an idea of the overall circus, with its three simultaneous rings.   First Ring: The Castle Second Ring: The Challenge Third Ring: The Secret Hideout Epilogue:

# Math Circles: info

In General: Math Circles began a generation ago in Eastern Europe, originally for high school students. Their purpose isn’t to cover topics in the usual algebra through calculus sequence, but instead to instill passion for math by presenting advanced math topics that a student would typically not see, topics that hint at what math looks like to a mathematician. Or more radically, as I have told some of my students, “What you think math is, is not math.” In recent years, Math Circles have been attempted for younger children in elementary school. But at each level, the structure is the same: a carefully chosen problem is presented to the students, and they take it from there. They come up with ideas, they discuss, they argue, they bump forward. They are guided by the teacher, but they make their own discoveries, they are free to make their own mistakes. It may take us an hour or two or three more to work through a problem. One solution may suggest other problems, perhaps a conjecture, a generalization. We begin again. Done well, the process gives students a sense of excitement and wonderment for the beauty of higher mathematics. This Session: I teach three Math Circle classes at Jefferson, Berkeley Arts Magnet, and Malcolm X schools. We will cover four new topics: – constructions with compass and straightedge, hopefully rediscovering the beginning of Euclid’s geometry – some math behind Braille + graphing our learning – making and solving Soma Cube puzzles – playing and understanding the game of Set I’m excited to be doing two topics that get at spatial reasoning, as research indicates that girls especially can use more experience with this — and we’ll even have a tactile dimension with our Braille.

# Chess: Tournament

[From a parent letter describing the second year of the Malcolm X Chess Tournament, two years ago.] — My vote for the best quote of the tournament, so far, is a fourth grade student, speaking of her last round of play:  “My heart was pounding so much that I could feel my glasses moving up and down.” — I overheard one student telling a friend how big a deal it would mean to be second grade champion.  Overall, people played much more seriously, especially third and fourth rounds.  A few faculty told me about how the tournament was all the buzz in their classrooms, and we had more children spectators than last year. [It has kept growing, from 32 students the first year to 62 last year, the third.] — There were several notable upsets of a student winning who wasn’t “expected” to win.  For better or worse, the students do come with their own hierarchies in how they see each other — “I am better than him, and he just beat that person, so I will be able to beat that person.”  Sometimes it was hard on people who used this logic and still lost.  The children are more even in ability than they realize.  For example, none of the students who were grade level champions last year could hold on and repeat as champions this year. [From last year’s tournament.] There will be a couple new awards in the tournament this year, one for the most beautiful checkmate and one for a pair of students who together create a great game.  Current contender for #1 is [a student] who had a very spare mate using bishop, knight, and pawn.  Often students prefer to get two queens and bludgeon their opponent to death.  His solution is much more elegant. Current contenders for #2 are a pair of students.  When one didn’t understand the rule about pawn promotion, the other, instead of being frustrated or condescending, gave her a series of hints and made a game out of the situation.  That attracted a few other students who also tried to help out; it was a very sweet scene.