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EASIER THAN YOU THINK...

Hands On

Two hands manipulating a Rubik's CubeSo much good mathematics begins with play … with arranging, manipulating, folding, cutting, and drawing objects and shapes. Except for the drawing, there need be no pens or pencils in sight!

Even the abstract thinker draws on his/her experiences with manipulating objects.  They have sorted them, placed them in groups, stacked them, compared them, arranged them in patterns, etc.  All our fundamental abstract concepts are learned in this way.  We even develop different problem-solving strategies, extrapolate and interpolate results, discover and analyse patterns, and make inferences and generalisations about the objects that we play with.  Even older children (and adults) can benefit from such play, although it is of fundamental importance for the developing child.

Having been inspired by W W Sawyer’s book, The Search for Pattern, as a teenager I must admit to the belief that all mathematics is based upon pattern and our search for it.  I also believe that it is important that we manipulate shapes and objects because the same part of our brain that controls our fingers is involved in our calculating with numbers and discerning the patterns that they make.  In other words, we are training that part of the brain.

It will take time to populate this part of my site with ideas and puzzles/problems that you can use and solve, but that does not diminish their importance!

Arranging

Manipulating

Folding

Cutting

Drawing

Brilliant!!! This helps so much!!! So much easier than anything else I have found. This is now simple.
Thanks again for showing the simple way of doing this. I look forward to the next video!! Absolutely brilliant.
Once again, excellent! I’ve watched many others, that have not helped nearly as much as these. Thanks for making it so easy to understand. When things get complicated, it is easy to make a mistake, but your method of writing down the structure helps to prevent mistakes.
Thanks a million!!! I’ve watched many videos and read tutorials, but still could not get two in a row correct on Khan Academy. Your explanation was so clear and simple that it finally made sense to me and now I can get all of the problems correct!!! Thank you very much.
It all makes total sense now! Thanks very much for all the derivative videos!!! Very helpful.
MemorizeAndLearn (on four different CCM YouTube videos about Differentiation)

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