Puzzles and exercises to improve mathematical and spatial intelligence

[Aleoa]

In your childhood or adolescence, or maybe as an adult, have there been types of exercises or puzzles that you think have improved your mathematical intelligence and in particular the spatial thinking? If yes, which ones?

 

[DrClaude]

Legos.

 

[berkeman]

In your childhood or adolescence, or maybe as an adult, have there been types of exercises or puzzles that you think have improved your mathematical intelligence and in particular the spatial thinking? If yes, which ones?

• Learning to play chess was a big help (dad taught me when I was about 6 y/o). I didn't get good at chess until I'd graduated college and had some extra time on my hands. I bought a Radio Shack electronic chess board, and got my butt kicked on its lowest level setting (which was a pretty moderate level it turned out). I bought a few books on chess and read up, and learned a lot of stuff dad left out of our lessons. I eventually got good enough to beat the board about half of the time, and really enjoyed the games. I'll post the one book that helped me the most when I can find it at home tonight...
• We always had a 2-volume set of "How Things Work" (or similar title) in the house, so I could look up things that I was interested in or had heard about somewhere
• There is a fun intro Physics book (high school level) called "Thinking Physics" -- see below
• I got a lot out of the book "Rapid Math Tricks and Tips" -- see below. It helped me get a lot faster at estimating answers, which helped me double-check my detailed calculations

 

[Klystron]

Swimming. Moving at the interface between two fluids, the smooth flow of water and wind both relaxes and focuses my mind to review what I have read and integrate new ideas. The simple repetitions swimming laps acts like a meditation technique to clear distractions, maintain awareness and visualize n-space.

Card games. A regular deck of cards is easily represented mentally as a 4x13 matrix or a 4x9 matrix of minor cards -- two to ten -- plus the 4x4 major arcana -- jacks, queens, kings, Aces -- depending on the game. I use a substitution matrix to track which cards have been played from the deck plus temporary vectors to remember known cards in opponent's hands and adjust probability calculations accordingly.

Example from 5-card stud poker: the pot contains $700 with one last card to come. The bet to you is $10. You hold 6-7-8-9 in one suit; the nine in the hole. You have seen 24 cards including your 4 but none other of your suit, no 5's and 1 ten. Compute the probability of improving your hand, particularly completing the flush or a straight. You are last to act. Call the bet ($10 to win $710), raise ($20 against $720, if no call) or fold?

 

[berkeman]

I bought a few books on chess and read up, and learned a lot of stuff dad left out of our lessons. I eventually got good enough to beat the board about half of the time, and really enjoyed the games. I'll post the one book that helped me the most when I can find it at home tonight...

Here is the chess book that I mentioned I liked so much. It does a great job of covering the basic attacks and defenses. A list of some of the chapters:

• The Pin
• The Knight Fork
• Double Attack
• Discovered Attack
• Discovered Check
• Double Check
• The Overworked Piece
• Removing the Guard
• No Retreat
• The Skewer
• The Vulnerable First Rank
• The Surprise Move
• Design for Checkmate

 

[Mark44]

My time as a kid was before Legos, but we had Lincoln Logs and Erector Sets, and I spent many hours playing with them, building cabins and machines and whatnot. I've always been sort of a tinkerer, and had my bicycle apart several times, including taking apart the rear hub with its coaster brake. The odd thing about coaster brakes is that they work on the same principle as motorcycle clutches. Later, when I had cars, many of which didn't run for much of the time I had them, I had the engines out and all apart.

Regarding spatial thinking, I've always had a fondness for maps, and remember sending away to the U.S. Geological Survey office in Denver for 15' topo maps. I still have about 40 to 50 topo maps of the areas where I go hiking, the Olympics and Cascades in my home state, plus a few in the Sierra Nevada. If you know how to read a topo map, you have a good idea of the terrain it represents.

 

[symbolipoint]

In your childhood or adolescence, or maybe as an adult, have there been types of exercises or puzzles that you think have improved your mathematical intelligence and in particular the spatial thinking? If yes, which ones?

NO.

That does not mean that I am correct.

I remember looking at the holes in the ceiling tiles of one of my classrooms, starting to count them, and then decided to count just the holes in one single tile, count the number of tiles (by multiplying rows and "columns") including the tiles on the sides, and then estimated the number of holes; this was in elementary school.

 

[collinsmark]

In your childhood or adolescence, or maybe as an adult, have there been types of exercises or puzzles that you think have improved your mathematical intelligence and in particular the spatial thinking? If yes, which ones?

Playing Kerbal Space Program has improved my intuition and understanding of orbital mechanics, vastly better than anything I would have otherwise predicted.

(Pun both not intended but still kind of intended.)

 

[symbolipoint]

Yes actually being introduced to the deck of cards for some common card games quickly made apparent the 4 by 13 arrangement for multiples and products involving 52 (and of some of the lower 13's).