There’s been quite a conversation on the math ed corner of twitter about Michael Pershan’s thoughts about hints. Henri Picciotto wrote a great piece that I just saw tonight.
The two big takeaways for me from that piece are:
“Improvisation is absolutely required in every facet of teaching . . . .”
“All the hints Anna lists may be useful, depending on the situation.”
That second quote finally got me unstuck.
After both reading and watching some of Michael’s thoughts, my mind had drifted to a description of a Bobby Fischer / Tigran Petrosian game from 1971. Specifically the commentary from Graham Burgess here:
The quote I was thinking about relates to Fischer’s 22nd move. I’ll add emphasis on the parts that I thought were relevant to Michael’s hints:
“This is one of the most talked-about moves in chess history. It looks extremely unnatural to exchange off the strong, beautifully-placed knight for Black’s bad, awkward bishop. Yet it wins the game quickly and efficiently. Is there something wrong with the principles that would lead many players not even to consider the move? Not really. Nine times out of ten (if not more frequently) it would be wrong to exchange a good knight for a bad bishop. The problem is if a useful general principle takes on the status of a hard-and-fast rule, rather than it always being governed by the proviso, “unless the specifics of the position demand another move.” “
So, thanks to Henri, I now see the connection better. If you get too caught up in general principles, you risk failing to improvise when you need to (or at least making it much harder to improvise). You also risk the possibility of dismissing hints that may well be useful in different situations.
I’m glad that I can now stop thinking about descriptions of chess games from 40+ years ago – ha!
Also, thanks for writing the wonderful Zome Geometry book, Henri. I use it with my kids all the time 🙂