1.2  Applying the LPM: Math and Metacognition
What Do You
Already Know?
Metacognitive Exploration Concept
Map
Hardest
Problem
Troubleshooting
Learning to Learn Mathematics Assessing Your Performance
             

Megacognition

One goal of every activity in this book is for you to learn to step back from just doing and THINK about what you’re doing (and why and how). Here’s an illustration of why that matters.

A mother was preparing a baked ham for dinner. Her 10-year old daughter was in the kitchen helping.

She watched as her mother prepared the ham, seasoning it and getting it ready for the baking pan. The last thing the mother did before putting the ham in the pan was to remove about two inches from one end.

She set this piece aside and then put the ham in the pan and into the oven.

Her daughter asked, “Mom, why did you cut that piece off?”

She replied, “That’s how my mother taught me to do it.”

She began to wonder why. Together, she and her daughter called Grandma and asked the bottom of the ham had to be removed before the ham was put in the pan. Grandma's reply was, “That’s how my mother taught me to do it. But I don’t know why...I’ll give her a call and let you know.”

A while later grandma called back. The answer, it seems, is that her mother’s only baking pan wasn’t large enough for a full-sized ham, and she had to trim off about 2-inches from the bottom in order to make it fit.

As amusing as the story may be, it truly does illustrate the way most of us tend to sleepwalk through our daily lives, rarely stopping to think about what we’re doing and why. Great-grandma was confronted with a problem and she used an effective and successful strategy to solve it. Grandma and Mom, on the other hand, merely learned to do what they were shown; they never thought about it more deeply until the daughter stopped everything, asking, “Why?”

This activity takes things further than previous activities in that you’re now ready to literally take your thinking to another level. After all, as you’ve learned by now, when we’re aware of our thinking, we can improve our thinking. In terms of learning skills, metacognition means that:

  • We can become aware of and improve our thinking (cognitive domain)

  • We can become aware of and consciously control our emotional reactions (affective domain)

  • We can become aware of and ever more successfully interact with others (social domain)

Additionally, to begin to put it all together,

  • We use reflection as a way to trigger awareness of who we are, what we’re doing, and why we’re doing it, at any given moment

  • When we are aware, we can use assessment as a way to systematically improve our performance in any of the domains

     
Model 2
Concept Map of "Concept Map"