Saturday, January 17, 2015

Confidence; the Forgotten CCSS Math Practice Standard

One of the interesting things about the Common Core State Standards for mathematics is that nowhere does the word 'confidence' appear. Yet it is, perhaps, the one thing that will help young children, and many adults too, develop their understanding and skills in the field of maths. All eight math practice standards, in some way, imply the development of confidence.

I'm always very aware of this concept at the beginning of the semester when I'm getting to know my new students. There are also activities I do in which I ask the students how confident they are in their responses. For example, we use a math manipulative called Unifix cubes which are colored plastic blocks that fit together. As they explore the materials I ask students to describe them so that they can get to know how to use them. I ask them how many different colors there are After a minute or two someone will say "ten" and I'll say "how confident are you". This seems to stop them in their tracks as if I am challenging their counting skills. They start looking through the box of cubes again to see if there are any more and after a few minutes they'll say they are sure there are ten.I then ask "on a scale of 1-10 how sure are you? The usual response is 9 or 9.5.
I then ask, How sure are you the sun will rise tomorrow morning?  "Aha 10" they say. So why not a 10 with the number of different colored Unifix cubes?  For some reason math seems to promote this lack of complete confidence.

I think confidence in maths comes from a variety of sources but primarily I think it comes from how well supported are the things we know and understand. If we can see something as part of a pattern, or part of a system, or part of a family, or part of a schema, or part of a series, or part of a predictable structure,  or related to something else we know or understand then our confidence ill be increased.
If we know or understand something in isolation, without these connections, then we have far less confidence.

So, taken together, the Common Core State Standards for Math Practices add up to the development  of a student's confidence on the content standards they are learning.       

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