So 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!
How I wish you could be my professor – I have been having a consistent problem with the chain rule for what seems like weeks. I couldn’t grasp it at all. The first couple minutes of your video – it all instantly clicked for me. You are a life saver and a wonderful teacher. Thank you so much for your explanations!!!!!!!
Taikrys (on a CCM YouTube video about the Chain Rule)
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