Mathematically Speaking 2
by Roger Alcock (continues)
Meta-Cognition
Many teachers, myself included, have been at the “unconsciously competent” level. We work well with our students, we are successful teachers, but we don’t know why they are successful. (Depending on the subject matter, I have been at all of the levels on this chart!)
Unfortunately, there are teachers who are unconsciously incompetent. They don’t realize they don’t understand what they are doing. It’s our job to move them to the next level--- we want them to be consciously incompetent! Not really, but once you know that you don’t know, you can work on changing in a positive direction. The goal of Thinking Math is to help teachers and students reach the stage of “Conscious Competent.” If you are consciously competent, you know why something is working, and if you know why it is working, you can make it work over and over and over… almost to infinity! ( Sorry! I couldn’t help it! Have you ever wondered what one less than infinity would be??)
If you think about some of your students, you can see where they fit in this chart. Scary isn’t it! Our goal as teachers is to help all of our students become consciously competent. It’s a great feeling to know that we have helped some of our students move into that quadrant.
The “Ten Principles” of Thinking Math are:
* describe and justify,
* build from intuitive knowledge,
* develop a strong number sense,
* use a variety of teaching strategies,
* use situational story problems,
* use manipulatives,
* accept multiple correct solutions and sometimes multiple correct answers,
* balance conceptual and procedural knowledge,
* adjust the time line,
* use ongoing assessment
The principles are not ranked in order of importance because they are all important. (OK, be honest, how many of you counted to see if I actually listed ten principles?) The “ten principles” should be used at all grade levels, pre-k though college!
Describe and Justify
The first principle I would like to discuss is, “describe and justify.”
