Playing with puzzles and solving problems during play increase children's ability to solve real problems.
Now, children do not think like grown-ups, so how can we teach them - or rather prepare them for - the abstract knowledge that they will have to learn in later grades? I will give you an example.
Probability and logic are usually taught to seconcary school pupils. This is how I teach it to pre-shoolers and 1st-graders:
The wizard brings with him two bags. (The teacher shows two bags that she has prepared in advance.) In one bag there are presents and in the other one there are blocks (like Duplo).
-Come and play! the wizard says. Anyone who takes a blue block will win a present!
Dixie takes a... yellow block. Pixie takes a... red block. Dot takes a ... green block. (Teacher acts this out as she is telling the story!)
-I'm sorry, the wizard says, you can't have any presents! I'll keep them for myself! (Make a greedy gesture.)
-Now, what is this?! grandmother says. Do you call this entertainment? This is not the least funny!
-Let me see that bag of blocks! Pixie says and pours out all the blocks on the floor (in front of the chidren).
-You have been cheating us! grandmother says to the wizard.
Let the children, in their own words, explain in what way the wizard has been cheating them. There are no blue blocks in the bag. It is impossible to win anything from him!
-I know a better game! Dixie says. Give me the blocks and the presents!
She (the teacher) does something behind her back and then she shows the bag of blocks.
-Anyone who takes a yellow block from this bag will win a present! she says.
Pixie takes... a yellow block! (Enthusiasm!)
Dot takes... a yellow block! (Dito.)
Grandmother takes a... yellow block! (Children cheering: - )
Dixie gives a present to Pixie, Dot and grandmother. They are all happy!
-May I take a block too? asks the wizard (doubting but yet hopeful)
-Yes, you may, says Dixie.
(Great drama!) The wizard puts his hand in the bag. (Teacher acting it out.) He takes a block... and pulls it out... slowly... Guess what?! (Make a brief pause and let the children have a guess!)
-A yellow block! (Wizard-teacher jumps around the classroom with joy, children still on their chairs, unable to get up from mere laughter!) May I have a present too?! (Point your toes and knees inwards and put your hands on your back: - )
-Yes, you may! Dixie says and gives a present to the wizard.
He (the teacher) takes it, looks at it (can hardly believe it is for him).
-Thankyou, the wizard says, I like your game!
-Yes, I like everyone to win and everyone to get a present and everyone to be happy! All the time.
CAN YOU GUESS WHAT WAS IN DIXIE'S BAG OF BLOCKS?
-Yes, only yellow blocks, of course: - )