Difficult puzzle, scaffolding & automatisation

Difficult puzzles need a strategy to be able to solve them. Smart children just try solving them, trusting their solving skills rather than a strategy. This works until they face a puzzle that seems not to work in that way. Then they have to try something called multilayered strategy. This is exactly the aim of scaffolding, getting insight in structure of solution, rather than being able to just solve the puzzle without having to worry how they did it.
In the midst of this comes emotions that are new to smart children: failure, frustration, stress... These emotions are often successfully avoided because smart children often can solve problems easily. When the puzzle is difficult enough, they get the chance to experience these emotions. A good teacher knows that emotions are a part of education. It is good to reflect on the emotions. What happened? How did you feel?
Then the child has to finish the task anyway. This means perseverance. The more perseverance, the better the child will feel when it does succeed to solve the problem in the end.
When they succeeded to solve the difficult puzzle, accompanied with the necessary frustration, the next step is to teach the child to automatize the puzzle.

neurology à la carte

For more depth on neuroblogging, I suggest you try the à la carte of Olivier.

coffee, no regularity

Does coffee influence sequential thinking? I wondered after seeing pictures of spiders that made webs after drinking coffee. I was shocked to see how much effect coffee has on the pattern made by the spider.
I already quit drinking sugar in my coffee. Maybe I should quit coffee and drink herbal tea instead.
Maybe my coffee drinking behaviour is responsible for my "but first syndrom", rather than a chaotic nature?

binary principle and elephant puzzle

How is a puzzle like the elephant puzzle used to scaffold? (in education, but you can do it among friends too) Well, for one the trick is that you don't need to know how to solve every independent puzzle (exceptions disregarded) to know how to solve a puzzle. For some puzzles, understanding laws is necessary or useful. How switches can be written down as either on or off may be helpful for solving a binary puzzle. Also, the idea of how to list numbers may be important. 00001 comes before 00010 and after 00000.
In the list 00, 01, 10, 11, 100, 101, 110, 111 notice that the last digit changes every time from 0 to 1, before the left digit can change. This also is the case with the elephant puzzle.
This is how a puzzle gives deep insight of maths and logic. Deep because it is a direct experience. It makes a connection between a concept in your head and a visual tactile experience in your hands.

puzzle sunday (1)

I love thinking puzzles and my children do to. Here are some of the ones we enjoyed.
Elefant spinout is great for automatisation. This is a process wherein the solution is not only mastered by solving the puzzle, but by making it route. This is very important for some children that tend to find a solution easily and try to avoid route. Also this puzzle is a good model for binary maths. The elefants have two positions while solving the puzzle, 0 and 1, or facing the exit or to the side.

U = E x V / I x D

A few weeks ago I gave you this difficult puzzle: what does the equation U = E x V / I x D signify? hint: (probably Social) Psychology.


I gave a hint: E is for Expectation of success
Another hint is that V is the value of completion of a task

Who finds out what is the answer gets on top of my blogroll.

Bayesian maths for intuition

I read an article today that reflects my ideas on thinking. Brain patterns make noise, says Pouget, but the noise makes sense, he calls it "variability". The noise follows a pattern that can be predicted through Bayesian mathematics. It would explain why intuition appears after some time. It would be the result of an accord between neurons. These Bayesian patterns would make sense without looking as if they make sense.
This remembers me the time I was learning mathematics. One teacher made me sigh and I didn't understand much that year. Another teacher was able to explain the amazing relationships that I failed to see the year before. I learned maths and I learned that who teaches makes a difference and changes whether you perceive yourself as a possible mathematician or not.