Saturday, May 14, 2011

Not Quite Math: Playing Chess

I talk a lot about playing with math, and learning math through games. I'm not sure whether playing chess has anything to do with learning math, but a connection is often claimed. I think that playing chess can help people develop a taste for deep thinking, and a willingness to approach hard problems, both important to learning math.

My dad taught me chess when I was in elementary school, and I eventually beat him once in a while. So when there was a tournament at my  junior high, I entered. It was double elimination, meaning you were out after two losses.

I lost my first game after just a few moves, and I remember wondering how that had happened. I had never read any chess, knew no 'openings', and had no easy way of working out what each move had been. So I didn't really 'get' what had just happened. I played my second game, and lost in the same exact way. This time, I wasn't going to let it go. I asked my opponent to show me what he'd done. He did. I also learned (apparently incorrectly) that it was called Fool's Mate. I just learned last night that the name Fool's Mate is (now?) reserved for a mate in two moves that only happens if one person makes some pretty bad opening moves.

What had happened to me is called Scholar's Mate. I started hearing that name for it when I began taking my nephew to chess school, but thought it was just a sweet alternate name. I sat in on his first few lessons, and loved the teaching. The teacher talked about Foolish Freddy and Sneaky Sam, asked lots of questions, and kept the kids excitedly trying to figure things out. He showed them the Scholar's Mate opening, and explained how to defend against it. I also remember him showing the kids (and me) why moving King's bishop's pawn in the beginning is a bad move. (Of course Foolish Freddy kept thinking he'd start that way and Sneaky Sam kept beating him a different way each time.)

Back to that long ago junior high tournament. I had learned how the Scholar's Mate worked, and could find a way to avoid it, but I was out of the tournament. Or so I thought. There were maybe 30 or 40 boys in the tournament, and only 7 girls. Every girl had lost her first two games. So the organizers decided to create a girls' tournament, and we got to do a round robin (everyone plays everyone else). I wanted to keep playing chess, so I didn't question it. I played all 6 of the other girls, and I think I beat all of them. I probably used that new trick on a few of them. I got a first place trophy, which I found terribly embarrassing. I threw it in the back of my closet, and may have lost interest in chess at that time.

[I did try to learn a bit more at some point, and loved learning from the book Bobby Fischer Teaches Chess. It had pictures drawn of the chess board, which made it easy to see what he was talking about. When I wanted to read more, I couldn't find another book that used pictures. They all used the standard 'algebraic' notation, which may be a good way to remember your game, but which sucks for trying to learn. Hmm, is there a lesson for math educators there?]

I was angry about that trophy. I'd lost fair and square in the original tournament. Why would I want a trophy for winning in a consolation tournament? The word 'sexism' wasn't in general use yet, and even now, it's a little complicated - feeling angry about getting a positive treatment. (Kind of like men opening doors for women. I was never comfortable with it, nor with complaining when it happened. I developed the habit of trying to open the next door for the guy who'd opened a door for me, hoping to raise his consciousness a wee bit, or at least to return the favor.) I never connected my loss of interest in chess with what happened at that tournament until now, but it would make sense...

I've been taking my nephew J. to chess school on Friday nights since January. He's had trouble in school (bounces around too much, talks back to teachers, gets in fights, ...), but he's a good kid, and I've wanted to help him connect with the world in positive ways. He was already interested in chess when this opportunity came up, so I jumped on it. Class meets from 5:30-7, and then there's tournament play from 7 to maybe 8. I knew nothing about chess tournaments, and had never seen a chess class before that first night. When I wanted to follow J. into the tournament room, I was told parents weren't allowed. I flashed on the scene in Searching for Booby Fischer where the parents are kicked out of their kids' tournament room because the parents are behaving badly. It made me giggle.

After 4 months of carting J. to class each Friday night and hanging around North Berkeley for a few hours with my son, I was eager to join in the fun when a Friday night adult tournament started up at the same time (and place). Last week I hadn't signed up properly yet, and was paired with someone for a 'casual game'. I ask people their ratings to try to understand the system. He hadn't played in many years but used to be rated around 2000. I knew I'd lose each game at first, and lost as I expected. It was the most delightful loss I could have imagined.

I often beat J., and he's winning trophies in the kids' tournaments, so I know as much as a kid who's getting good. But that's nothing, apparently. One of the things I use to measure how I'm doing is how many of my pieces have crossed the midline of the board. I think I never managed to get a piece past that line that night. I loved thinking about the game as it progressed, and thought of his pieces as exerting a kind of pressure. It was fascinating.

Last night I had gotten my U.S. Chess Federation membership, and signed up for a game. I was paired with Gerl (rated 1484), and lost after we'd each made 12 moves (faster than in my previous game). We went over to the 'analysis room' afterward, and talked through the game. I was once again fascinated, totally intrigued by it all.

Would you like to see how much of a rank beginner I am? Our moves follow. I absolutely can't make sense of this without putting the pieces on the board and moving them. If you're interested enough, try playing this out. Rows 2 and 7 are where the pawns start, and the lettering left to right from White's point of view; pawn moves just show the square moved to, N is for knight; x means a piece was taken, + means check. White's second move was bishop to C4.

White Black
1 E4 E5
2 BC4 BC5
3 NC3 C6
4 NF3 D6
5 D3 NF6
6 H3 o-o (castle)
7 G4 G5
8 BxG5 A6
9 QD2 B5
10 BH6 RE8
11 QG5+ KH8
12 QG7++
I used to play to capture pieces. In the last two games I've played, it has become clear to me how silly that is. Both times the checkmate was almost bloodless.

I'm hoping I can get the guy I played last night to come give a few chess lessons at my son's school.

What do you think - does playing chess help us learn math?


  1. Hi Sue,

    The United States Chess Federation (USCF) has a scholastic section devoted to promoting chess to children:

    There is also Chess 'n Math, which operates in Canada, but may have some resource of interest:

    I haven't looked into this in some time (used to be a serious chess player long ago), but I recall there being a fair amount of research showing that when chess is integrated into the school system as a subject academic performance improves, not just in mathematics, but also in reading and other subjects. You can try these sources as a start if you're interested:

    I enjoy your blog! All the best wishes, Santo D'Agostino

  2. I used to play chess pretty seriously, starting in elementary and tapering off after high school. A friend on my high school team observed that there wasn't any particular correlation between how they did in math class on their ranking on the team. But there are two aspects of tournament chess that could help in math:

    1) Thinking deeply and analyzing the game several moves in advance. Since one cannot touch the pieces during the game, this is done mentally. The stronger the player, the deeper he/she can "see" the possibilities of future positions.

    2) (for kids, especially) One tournament game typically lasts at least one hour. That's one hour of silent, sustained thinking. And that's real brain exercise!

    Maybe it's not a direct correlation, but similar to how (supposedly) the ability to manipulate objects mentally in 3D relates to performance on the SAT.

    By the way... 2000 is a rather strong rating! 1500 is considered the "average" of all current tournament players; above 2500 would put you among the top players in the world.


  3. i learned from my dad, too.
    he taught me the "fool's mate"
    and "scholar's mate", by those names.
    this must've been around 1962.
    we lived in zagreb for a while
    (where chess was very popular)
    right in there so i was able to
    play casually with lots of strangers
    with very little fuss. never got good.

    when my kid brother started studying
    he soon got able to beat me pretty routinely
    and i sort of lost interest. there's probably
    a lesson *there* for educators.
    i don't know which notation you're rating
    as easier than the other but they're
    the same to me: useless without
    an actual chess set to work on
    and transparent with.

    chess *is* quite a bit like math
    (or music in particular among
    the arts, but also drawing and
    some of the others): one can
    *make obsession pay*.

    hence the child prodigies.
    also all the crazies.

    crazies, what crazies.
    well, bobby fischer in chess.
    john (beautiful mind) nash
    or nearly any other math-head
    ever appearing in a movie.
    (that guy in _revolutionary_road_
    was so right-on i went out
    and read the book. good book.)
    music? _hillary_and_jackie_.
    _shine_. heck, maybe even
    _amadeus_ if you squint
    and tilt your head just right.

    one of my fellow adjuncts at
    the community college for
    a few quarters was a math
    ph.d. student but literally
    obsessed with chess.
    you'd only ever see him
    in the office playing online.
    which wouldn't be a problem.
    thing is, he'd talk to his *classes*
    about chess, and at some length.
    or so rumor had it. everybody
    knew he was nuts. more so than
    me, even.

    nabokov had a chess-and-madness story.
    a million years ago i read a book called
    _idle_passion_ that impressed me.
    by, wow. alexander cockburn.
    i didn't know his political stuff then.
    (i just looked it up.)

    hmm. is this still a response to your post?

    anyhow. studious types... the non-obsessive
    majority... do well in math and music and
    chess (and drawing and for that matter
    long-distance running and bodybuilding
    [and other sports without, ugh, "teamwork"]).
    no surprise if there's *some* correlation
    in moderately-high performance in these
    pairwise. to get *really* good, you have
    to pretty much ignore everything else
    a la fischer or ramanujan.

    very cool that you're taking it up.
    i haven't played since the last time
    i was in jail. if and when i go back,
    i'll probably play it again. (i won one
    and lost two, by the way.)

    oh, one more thing: i've actually
    had somebody offer me the "fool's
    mate" worst-possible first two moves
    and i'm pretty sure they weren't kidding.
    anyhow i beat him in two moves of course.


  4. Lo sentimos, pero no hemos podido llevar a cabo tu peticiĆ³n.

    1. I learnt to lose from chess. I think it is a good lesson to learn that sometimes someone is doing something better than you.

    2. Chess is a nice game, but so is Hsiang Chi, Shogi, and Go. Please don't think that Chess is the only intellectual game worth pursuing.

    3. My son JT and I visited often El Palacio de Ajedrez in Samaipata, Bolivia when he was 2.5 years old. He didn't know very well how to move the pieces, but he could set them up correctly. Now he is 5.5 and thanks to the computer program Dinosaur Chess he has taught himself the rules, including en passant, castling, and stale mate. Tomorrow he will go to his first chess lesson here in Tenerife, Spain. I like the sign on the wall in the local chess club. "No smoking". I changed from Chess to Go 45 years ago as I wanted oxygen while playing.

    4. Is there a relationship between Chess and Math? I am afraid I could not care less. Chess, and the other games I have mentioned are fun to play, they are social, they are challenging, and, most importantly to me, they can teach you to lose properly.

    Jan Nordgreen

  5. Owen, I'll look up some of those books (if I remember when I have time - in a few weeks).

    Jan, I love your response. Yes, go sounds like a great game too. I just don't know anything about it.

    >Chess, and the other games I have mentioned are fun to play, they are social, they are challenging, and, most importantly to me, they can teach you to lose properly.

    I think of math as 'fun to play', challenging, and teaching you to accept failure gracefully. I need the social aspect to enjoy math.

  6. Hey Sue,
    Well Written. Just want to put some light on connection between math and chess. Math and chess do have some interconnection because both of these require brainstorming. A good chess player is expected to perform better in mathematics and this has been proven many times.
    Also, i would like to appreciate the work that you are currently doing. I myself teach mathematics try to see different methods that can help the students to grasp the concepts in easy way. We give math and chess lessons in sunnyvale and are going to make use to some tactics to implement.


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