Teaching math with Go

Recently, I have been insinuating Go playing into my time with the 3 Js. This was initially motivated by a quote I saw on one of the Mathpickle pages (Gamers under Inspired People):

Schools should experiment teaching go* instead of a regular math curriculum for one year to students around the age of 7.  It is my prediction that the strong problem solving skills that this will engender will make superior students than any existing mathematics curriculum.

Now, when we first decided to have kids, my objective was to help them develop into people with whom I would enjoy spending time. In particular, I wanted to be able to play games with them. With that in mind, the Mathpickle idea resonated with another idea from Richard Garfield (via Math Hombre):

play each game so as to increase your chances of winning all games

With these three ideas in mind, I went looking for a way to properly introduce Go to our clan.

Curriculum outline

Not surprisingly this is a question other gaming and math people have asked before. Quickly putting together the ideas I liked the most from other sources, we basically started following the curriculum shown in the Go GO Igo videos with Yoshihara Yukari (Umezawa Yukari at the time of filming):

Yukari Sensei Go Go Igo Part 1

(1) basics

- placing stones

- black vs white

- capturing single stone

(2) capture game

- 6x6 board

- first to capture wins

- etiquette

(3) illegal moves

- playing where your stone will have no liberties

- playing where the stone has no liberties but captures an opponent's stone(s)

(4) expanded capture games

- first to capture 3 stones wins

- infinite capture

- Ko rule

(5) territory

- counting territory at the end of the game

(6) simple capture puzzles

- one move

- two moves

- three moves

Yukari Sensei Go Go Igo Part 2

(7) Etiquette: 

- Nigiri: choosing white vs black

- komi and first player advantage (maybe useful to play some 5x5 or 7x7 games to make the first player advantage clear?)

(8) eyes and false eyes

(9) Scoring

- Dame, 

- kyu, 

- Japanese vs Chinese scoring

- agehama: stones considered captured 

How important is this?

(10) standard patterns

- stair-step (shichou)

- geta (also kosumi? 45 degree cut to capture enemy stones)

Part 3

(11) more puzzles/standard patterns

Part 4

(12) Tsumego

(13) maxims

Some early lessons

Since we don't actually have a Go board or stones, we started with the electronic board CGoban. This works well for J1 and J2. We have also used J1's chess/checkers set as a makeshift 9x9 board (playing on the lines instead of the squares).

For J3, we started playing the simple capture game using the blank side of our 100 board.
For the first lesson, we arranged things like this:

She played the centimeter cubes (which substitute for black stones) and I played the Bananagram tiles (substituting for white stones). I gave her a four stone advantage and we played three games with me starting in different places (center, corner, side) and saw that she could easily capture at least one of my stones without trouble.

Some of J3's observations along the way:

• There are 11 blue tiles forming the boundary
• There are 25 squares in our playing area
• There are five squares along each edge of our playing area
• The placement of the four handicap stones is symmetric in the playing area. There are several symmetries
• Stones in the corner have two directions to live
• Stones on the edge have three directions to live
• Stones inside have four directions to live

For the second lesson, we made the board a little differently based on J3's preference for a blue-green-yellow-red pattern around the border:

This time, J3 made some different observations:

• The pattern continues around the border (at no place, did we have to break the pattern). A more advanced question: will this always happen with our Blue-Green-Yellow-Red pattern around a square board?
• The colors in opposite corners are the same (blue-blue and yellow-yellow)
• There are more than 11 tiles on the border now.
• Still 25 squares on the board and 5 squares along each side

For the third session, J3 was willing to reduce her starting advantage and she wanted to place the handicap stones herself:

This is a losing position (remember, we are still playing where the first to capture at least one stone is the winner):

She didn't take losing especially well, but this is a nice feature of playing these kinds of short games. The kids can make a mistake, they have to deal with failure, but it isn't very costly since each game only takes a couple minutes and the next game starts right away.

Some Go concepts we are still developing
At this stage, we are still working on the basic concepts:

1. once placed, the stones don't move
2. only the main compass directions (north, east, south, west) are liberties. Diagonals don't give life.
3. liberties are shared for a group, not just the individual stones. For example, a stone surrounded by its own color is not dead (if the overall group still has liberties).
4. I need to remember to announce "Atari" when a stone or group has only one remaining liberty.

Observations

From a Go/games perspective, I think it is helps to start playing a lot of low-cost games: fast games where the winning condition is easy to identify and immediate. This allows the kids to make mistakes, see clearly the consequences of those mistakes, and lose, then immediately try again.

From a math perspective, there is a huge amount of elementary math that comes out of the simple games:

1. counting
2. addition
3. patterns
4. some basic multiplication, particularly with the array model

In addition, we had the usual experience with using physical manipulatives: something extra always comes up. For example, using the 100 board inspired J3 to show off to me that she can count to 100 now (using the board as a reference).

I'm looking forward to future sessions.