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Thursday, 12 April 2012

Solving problems is what mathematics is all about!

What some of you might not know is that I have a younger brother whose older son is in Grade Two.  Recently, my brother called and asked if I "understood the new math"?  I laughed!  There is nothing new  about math.  What is new is that the students are not taught only one method to find an answer.  Instead, the students are encouraged to explore possibilities, play with numbers, look for strategies that are efficient, and most importantly, understand the meaning of numbers.
Seldom are the students asked to find the answer.  Instead, they are asked to solve a problem.  It might sound like semantics, but there is an underlying message.  I want the students to feel comfortable with the process of trying to solve a problem, rather than worry about getting a correct answer.

Today we met for our 'math congress' which basically is an opportunity for us to share, safely, as a group, the manner in which a problem was attempted to be solved.  It never ceases to amaze me how deeply and richly the students think when they are not tied to following one particular way to do things!  In the photo above, the girl was demonstrating how she figured out how much money would be needed to buy 17 party hats, it each one cost 15 cents.  Look at her rich understanding of numbers, as she added 15 to each previous number to create a counting or number line:  15, 30, 45, 60. 75. etc.  She did it!
We shared our different ways to try this problem.  What 5 coins could you use to equal 45 cents?
Note the thinking here:  This child didn't need to count each dime, instead recognizing 4 X 10 is 40!  He was multiplying and didn't even now it!
No child is ever reprimanded for mistakes.  One of our beliefs in our math community of learners is that WE LEARN FROM MISTAKES.  This gal didn't  realize that she had only used 4 coins, or that they added to 50 cents until she shared.  It was the perfect opportunity to reinforce that once a solution is figured out, the student should go back and check it again. By doing this is a group setting, all of the students got the benefit of hearing this valuable feedback.
Sharing is encouraged and valued.  When one student is 'stuck', the others volunteer to 'whisper in his/her ear', allowing one student to practise their learning, and the other to have 'a hand up' to assist them in being successful.
How would you count out 6 coins to equal 55 cents?  We found more than one way!
This little guy choose one nickel, then five dimes.  The next girl wanted to share her idea which was 5 dimes, then one nickel.  Again it was a wonderful opportunity for the group to be reminded of the associative property, not that they heard that big fancy word.  It means that I can add the same numbers in different order and still arrive at the same sum.
The minute this girl put down her coins, she said "Oh no!  I see what I forgot!  I needed 6 coins!"
Learning from our own mistakes, or those of others, really moves our own learning forward.  It was a great day in math and each of the students agreed, almost crawling over each other to be the next to share!  This new math is creating students who aren't afraid of numbers and don't say "I don't get it" quite as often!

1 comment:

  1. Mathematics is also a branch of science. It is used to calculate values with different methods. In the past, the calculation of the values ??with different things. In the above calculation method is too difficult, but due to the progress of science we can now calculate too large valleys with in a second.