Monday, January 2, 2017

Common Core - Unique Ways of Thinking

During a recent vacation visiting a friend, your blogger decided to go out with her one night to a PTA meeting. The topic at hand was Common Core math. The speaker, a math specialist at the school, acknowledged that helping kids with homework can be challenging and potentially frustrating for parents who were taught math in a different way. Borrowing and carrying the one, for example, may be the obvious way to solve a subtraction problem to a parent, but not to his/her child.

The speaker emphasized that students, such as my friend’s daughter (already a mathematician and doing fractions with Belgian waffles at breakfast), will be taught a variety of strategies for solving math problems, so they will be equipped with an arsenal from which they can select what works best for them. For example, without automatic recognition of the answer to 4x3, it could be solved by:
  • Adding 4 three times
  • Knowing that 4x2=8, and then adding 4 more
  • Drawing 4 circles, with 3 dots in each
  • Using graph paper, or a sketch with dots on regular paper, to make a rectangle with a length of 4 and width of 3, and finding the area
A problem such as 43-7 could be solved in various ways, such as:
  • Identifying that 40-7 is 33, and then adding 3 more
  • Mom and Dad’s good old fashioned borrowing and carrying method
  • Representing 43 by sketching bars-of-ten and the leftover ones
Then breaking a bar up into ones and crossing out the number of dots being subtracted

Clearly, some problem-solving methods will be more efficient than others, and efficiency is ultimately encouraged. However, the teaching of various strategies allows for:

a) options for students who are struggling with other methods

b) conceptual understanding rather than just rote memorization of procedures

c) foundations to turn to when thinking about more challenging problems in the future

For my friend’s daughter, and for breakfast enthusiasts such as myself, the world makes most sense in terms of waffles. For others, this might not be the best methodology. Exposure to various ways of viewing and analyzing problems creates doors where there might otherwise be walls. We may be entering from different angles, but it is important that we each enter in a place from which we can have the personally clearest view, while ultimately seeking out the most efficient route to get there.

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