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I, like most teachers on this list, like these simple thinking problems.
Most students, at least the ones I teach, don't. They can't/don't think
like we do. They don't really care about these ratio/scaling problems
as they find them irrelevant. They feel the same way about most of
what they learn in math classes. In physics, they just want a formula
to solve a problem. Their critical thinking skills are generally poor,
mainly because they are not taught how to critically think in high
school. What courses do this, besides physics? And with all the new
handheld devices these days, students are weaker at fixing things
and solving real problems. However, they can text very efficiently! Sad...
I assume others on this list feel the same way.
I also like the question about making the sides of a square and triangle
two times longer. I might incorporate some of these into my "placement"
survey I give each year to assess kids' thinking skills and whether they
are in
the right physics class (honors or regular).
When I teach electricity, I give each student a battery, bulb, and wire
and ask them to make it light. Most can't initially. I tell them not to
look at their neighbors and what they are doing. I eventually give them
some hints, and they all eventually get it. It's a good thinking activity
for kids
at any level (regular, honors, even middle school). I then show the Harvard
video clip, where the graduates can't do this simple task. These are
"smart"
kids ("engineers") who don't know the basics of electricity. Maybe they
were
never taught?