Metacognition and Reflection

This is a post that I started pre-covid, but never finished.  I just came back to my blog, and saw it 'under drafts'.  Here it is, just for a record:  

Metacognition, the awareness of one’s own thinking processes, is something that some of my students lack. 

I saw it in my students from summer school.  There was a dearth of metacognition especially amongst my students who are weaker in mathematics.  

My fellow grade 10 academic colleague have tried to address this problem through a short series of assessment wrappers and assignments based on their most recent quiz/test.  

In the beginning of the year, we spent 3 days reviewing grade 9 mathematics and trying to look at the big picture of what was taught last year.  It is often easy when learning things for the first time to get lost looking at the tree when there's a whole forest to be discovered.  Looking at mathematics again a year later gives a chance to see the course as a whole. It also lets them reflect on what information they retained, and what was and wasn't so easy to recall.  We were able to discuss how the mind forgets, but can easily relearn what they learned well.  It is also worth reflecting on what concepts wasn't so easy to recall.  

We did a short half hour diagnostic of grade 9 material after the 3 days of learning.  As soon as a student finished, we completed something called an "assessment wrapper" - one of my favourite things I learned from my colleague 10 years my junior.  It comes in many forms (as you may google and find out), but the one I did was have students go to the side of the room where there were solutions and a red pen available and reflect.  

After a linear systems quiz, students were to make corrections and write a short comment for helpful feedback for themselves.  Then they need to choose one particular question they did wrong, and go into depth displaying some metacognition.  

Reflection is considered one of the core processes of being a mathematician.  I have to learn to emphasize it more.  And how do I emphasize it?  By evaluating what I value.