I’ve seen some interesting ideas from Tracy Johnston Zager over the last week about the relationship between learning math and intuition. For example:
Although I’ve been traveling a bit for work this week the relationship between learning math and intuition has stayed in my head. Sometimes my thoughts have drifted to and old blog post about a problem from the European Girls’ Math Olympaid:
A Challenge / Plea to math folks
That post, in turn, was inspired by an old post by Tim Gowers where he “live blogged” his work while he solved a problem from the International Mathematics Olympiad.
It can be really hard for anyone to know what math intuition looks like because everyone sees polished solutions way more often than they see the actual process of doing math.
That’s part of the reason I make the “what a kid learning math can look like” posts – so everyone can see that the path kids (or anyone!) actually takes to the solution of a problem is hardly ever a straight line:
Our “what a kid learning math can look like” series
The other thing on my mind this week has been some old AMC 10 problems that have really given my older son some trouble. These are pretty challenging problems and require quite a bit of mathematical intuition to solve.
So, I’d like to make the same challenge with these problems that I made with the problem from the European Girls’ Math Olympiad – “live blog” yourself solving one of these problems. Post the though process rather than a perfect solution. Let people see *where* your mathematical intuition came into play.
Mike's Math Page 
For the last one…
To score the mean, she must be part of a total that is an odd number, narrowing it to:
B. 23 -> 69 total students
D. 25 -> 75 total students
Since she did best on her team, her rank has to be better than 37th.
The mean of 75 is 38 so D.’s out leaving B. 23
My response to your challenge: some problems.
Over the coming weekend, I will pose the # of schools question to my kids and try to write notes on their approach. I’ll also show them the other two, but expect only one of the three would be accessible to them now.
In problem 19, the “intuitive” diagram puts the points in the wrong relative positions and leads to a contradiction, which admittedly caused some head scratching and a reread of the problem. The paper here shows that first diagram with a dark line of disgust scribbled across it and a second, smaller and more timid, diagram drawn below.
Only part of your comment came through.