> if one asks children a question such as the following: a number 35 bus pulls up at a bus stop and 8 passengers get on; what is the age of the bus driver? A large percentage of children, their minds numbed by years of symbol manipulation, will give the answer 43. This is a tragedy: rather than being trained to think, these children have been trained to do the opposite.

Also here: https://www.theguardian.com/commentisfree/2016/mar/11/maths-...

This is basic stimulus-response behaviour: school education is effectively a game that the children are playing to win points, and within that environment “thinking” is wasteful and disincentivized.

(See also: Lockhart's Lament https://www.maa.org/external_archive/devlin/LockhartsLament...., the heart-breaking How Children Fail by John Holt, etc.)

Gowers also had a couple of posts on a very different way of teaching mathematics:

https://gowers.wordpress.com/2012/06/08/how-should-mathemati...

https://gowers.wordpress.com/2012/07/07/a-trip-to-watford-gr...

Or maybe you wouldn’t. In any case, in my experience, about once a week. Essentially, your sponsors lets you know they want an answer to an unanswerable question (“how can we best weaponize salmon?”). Then we play “guess the answer the sponsor wants”.

2016: https://news.ycombinator.com/item?id=12720571

Kids brains are not developed well at that age, plus being given endless questions at school to which there are answers will accustom them to assuming an answer exists. Standing up to authority is something they aren't taught to do, in fact the opposite. I can understand what's going on. At that age I'd say what I think (and sometimes get into trouble for it) but most wouldn't - and as adults I still find a lot of people won't, which is beyond saddening.

Can anyone recall the study where adults were asked to estimate something (IIRC whether one line was shorter or longer than another) and when actors were there to give the wrong answer, some people were pressured into agreeing with something that was obviously wrong.

The question may also be thought of as a trick, per the old riddle: "A man stepped out of his tent with his rifle and walked 1 mile south, 1 mile east and 1 Mile north. Then he shot a bear in front of his tent. What color was the bear?".

Some of this problem lies with us adults I guess.

There's a lot of authority issues involved. Do you admit to an authority that you don't know how to solve X? Do you challenge an authority that they don't know either? Do you doubly challenge that authority by alleging they gave you a bullshit question for kicks?

And after authorities throw such a question at students, they're happy to draw conclusions about what feeble solution efforts the student made?

And this is after students have been inured to treating math as a bondage and discipline exercise in following instructions, after math has been drained of any large meaning.

The people did this experiment should be whipped with a wet noodle.

You get one question “how old is the shepherd” and then two pieces of information A: there are 125 sheep B: there are 5 dogs.

The alternatives for answering the question is whether it can be answered using A alone, B alone, requires both A and B, can be solved with either A or B, or can’t be solved at all.

This is a failure if 13-14 year olds are so used to being given questions that can be answered, that they are uncomfortable telling an authority that “it’s not possible to answer this”. It’s probably universal and I’m sure the same result could be found in Sweden despite our SAT’s (done later) have a whole section on finding nonsense.

My guess would be that the young pedants who refuse to answer the question, saying "not enough information", do worse on average for each of these metrics than their more compliant but completely wrong peers.

(I would have been one of the young pedants)

It's like watching a video about asking people where the matters in a tree comes from. You now know the answer instead of being made to think it out.

   5 < age < 100