Thursday, January 15, 2015

Numbers, numbers, numbers.

This is my four hundred and first entry in my Mostly Math Blog making my last one my 400th. By blogging standards this is probably quite insignificant but for me it is quite the milestone. As a math geek fascinated by numbers and the relationships between them there is always something special about a nice round number; something to be celebrated as one does one's 21st birthday or one's 50th wedding anniversary.  Numbers, by themselves, are the markers of our life stories, the moments of significant achievement, the tale of the tape measure so to speak. They bring specificity to life as well as precise comparisons. The also bring a sense of accomplishment or failure, success and challenge. Imagine a life without numbers where we lived in a land of 'ish" in which we only used words like some, many, few, lots to quantify our lives. I am told there are some indigenous peoples in the Amazon jungle who have three counting words; 'one', 'two', and 'many'.

This is all fine and good but when it comes to problem solving in he elementary school the numbers really are just the details. It is what is going on with all the words that surround the numbers that is the most important thing to be thinking about. Does it really matter that much if one train is going 40mph, and not 45mph, and the other 60mph, and not 70mph, when we have to solve the problem involving when they will crash into each other, or how far apart they will be in half an hour. The numbers are, of course, important for calculating the specific answer but they don't tell us what we have to do. It's all the words around the numbers that we have to decipher in  order to work out how to solve the problem.

If Mary has 16 Hotwheel cars and Michael has four more Hotwheel cars than Mary has, how many Hotwheel cars does Michael have? To solve this problem the numbers themselves are pretty useless. The most important thing is what the words around the numbers are telling us is happening. The understanding of the situation we can construct from deciphering the words is what tells us what we have to do in order to solve the problem. Recognition of the numbers themselves only provides us with the accuracy for our solution. Our understanding of the linguistic structure will tell us if this is a joining, separating, comparing or part-part-whole problem. 

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