(This post is the second in a series based on metacognition as a way of improving classroom assessment and instruction)

In response to How Students Learn, a second book was written addressing discipline-specific strategies. How Students Learn: History, Mathematics and Science in the Classroom is an outstanding resource for those who want to dig deeper in to Bransford's key principles. The emphasis on metacognition continues as well:

"Ultimately, students need to develop metacognitive abilities - the habits of mind necessary to assess their own progress - rather than relying solely on external indicators" (Donovan & Bransford, 2005, p. 17)
The application of this idea seems to be natural from a theoretical point of view - learners must be able to tell themselves whether or not they are understanding a given concept. From a practitioners perspective, I am unsure how well this idea is accepted and applied in a typical mathematics classroom. Based on my experience and observations, a secondary math class looks something like this three day cycle:

DAY #1
8:20 - Teacher reads answers aloud; students check with a red pen
8:25 - Teacher asks if there are any questions; One student raises hand to ask what answer to #6 was as s/he was too busy writing the correct answer to problems 1-5 to hear the answer to #6
8:27 - Students hand in papers to teacher to be recorded in grade book
8:30 - Lesson ABC begins; students take notes
9:00 - Students work on homework, wondering if they have the "right answers"
9:15 - Bell rings; students leave not knowing if they understand lesson ABC

DAY #2: Students come back and cycle repeats itself. Students turn in homework for lesson ABC and are assigned homework for lesson XYZ
DAY #3: Students come back and receive "graded" lesson ABC homework that they started at 9:00 two days ago.

Two questions come to mind:
  1. What opportunities are we providing for our students to go back and learn from their mistakes when their mistakes are sitting in a folder on our desk "waiting to be recorded"?
  2. Even if we write detailed, diagnostic feedback on each students' assignment and give it back to them the next day, how many will take the time to go back and fix their mistakes?
I believe we're amusing ourselves if we think students will take the necessary time to learn from their mistakes after 48 hours have elapsed since they first started the assignment.

"Metacognitive functioning is also facilitated by shifting from a focus on answers to just right or wrong to a more detailed focus on 'debugging' a wrong answer, that is finding out where the error is, why it is an error, and correcting it." (Donovan & Bransford, 2005, p. 239)
The teacher-as-answer-holder system as we know it seems to be missing a valuable aspect of formative assessment - providing students with an opportunity to revise and improve their thinking. In my search for literature related to metacognition and assessment during the past few days, I stumbled across an ERIC article on student self-assessment. From the article:
"...students who assessed their own work were remarkably willing to revise it."
Sounds good to me. Perhaps we've never given our students enough opportunities to assess and revise their own work!

Possible Solution: Students must be trained how to assess and revise their own work.
Notice the key characteristics...trained....assess...revise.
I started out the semester working hard to train students to "check answers with a pen as I read the answers aloud and to not copy odd answers from the back of the book." I'm finding that this is a hard habit to break. For the past three weeks, I have not read the answers aloud, but instead encouraged students to check their answers against the key both during their work time as well as the next day when they come back to class. In general, students are simply not accustomed to the idea of checking their own work - they must be re-trained. There are the few who take full advantage of this new system and check their answers regularly. Others will check their work, but are unwilling to ask questions of their peers and/or me to overcome their misconceptions. The revision never takes place. I'm looking forward to the weeks to come as I develop strategies to break this habit that's been created by me and so many others in the "teacher-as-answer-holder system."

Just as we model positive group work behavior, passing in papers and appropriate use of technology modeling self assessment must be at the core of our daily practice. The image to the left is a sketch I wrote on the board for a student today as I was attempting to help him see the value of self-assessment.

The homework checking scheme I am currently piloting clearly encourages students to become "self-assessors" by eliminating the "teacher-as-answer-holder system," but I am unsure if it lives up to the revise key characteristic made above. Language arts instructors seem to have this characteristic down through the use of multiple drafts of an essay or research paper, but this seems like a relative weakness in the math education realm.

Looking towards the final post in this series, what strategies have you found to be useful in helping students revise their work through the lens of self-assessment?