One Teacher’s Attempt at Teaching Metacognition in her Math Class

In my classes, students have many opportunities to show what they know and make revisions on their work.  But more importantly, they think about their process of learning. 

In the revision process in the lovely room of 054, students receive their previous self-assessed work with each standard assessed and feedback given.  Students are then given the option to revise their work.  If they choose to, the little ones use the Revision Criteria for Success (see below) to improve their work and sentence starter (see student work) to reflect upon their changes.

The Revision Criteria for Success (CfS):

In order to revise your work for reassessment, follow the Criteria for Success.

Your successful revisions include:

  • New work shown on a separate sheet of paper;
  • New work stapled to original work;
  • An improvement statement for each standard you have improved (use the template);
  • (as applicable) a retake of the same objectives.

In my geometry sections, we recently finished a unit about classifying polygons in which we focused on standards in the strands of Problem Solving, Communicating Clearly, and Geometry.  Here’s the adventure of one student, Student K, towards her mastery of the standard and more importantly thinking about what she needs to continue to improve going forward.

Company Logo Project – Performance Task on January 23rd and 24th, revision on January 27th

Students created a logo of a known company using appropriate notation and relationships. 

K submitted her work after the two days of class and it needed major revisions to demonstrate mastery of many objectives.  She used the Revision CfS and submitted her improved work.  See the work below to read the sentences she wrote about each standard and how she improved each one.


This sentence frame encourages/forces students to think about how the improved project is lots of working pieces and different aspects of the product demonstrates mastery of different standards. 

Mystery Figure (Stage 4) – Original Performance task on February 11, revisions on February 12

In this multi-part, whole-year project, students show their ability to do the unit task with the same coordinates unit to unit and for Unit 4: Classify, students classified the polygon formed with their points.  K submitted her work, received feedback, and opted to make revisions on one standard (see work sample below).


K’s original work had the more traditional “math” work (Problem Solving and Geometry) fairly accurate.  However, she still needed to improve on writing a claim with mathematical evidence and reasoning (Communicating Clearly). In her revision, K made her mathematical facts become a strong statement.

Unit Assessment – MCAS problems.  Administered on February 12, revision on February 13.

After the guidance of their Mystery Figure project as a review, students independently attacked the MCAS practice problems, which served as our end of unit assessment.  The standards addressed on the assessment appear below.


Note that K somewhat accurately assessed her work in terms of the Problem Solving and Geometry standards above.  She opted to only revise one standard – solution.


As she submitted her revisions, she remarked “Ms. Always with the writing!”  She then began her portfolio, filled with writing.

Portfolio for Unit 4: Classify – End of Unit (February 13)

In this four-page template, students review their work from the unit, examine the unit objectives in multiple ways, reflect deeply about a product that demonstrates their mastery towards the unit goals, create and solve their own problem, describe and reflect on their growth, and assess themselves overall in terms of effort, achievement, independence, and community leadership.

On the bottom of page 3, students describe the other important skills involved in this unit.  K’s work is below.


After reviewing her work, K determined she needed to improve on writing up her work verbally (versus algebraically or pictorially).  She noticed that nearly all of the revisions in this unit involved a Communicating Clearly standard and she needed to focus on that for the next unit.

Unit 6 has just begun.  In the pre-assessment on February 25th, as K self-assessed her work, she realized she needed to describe her process in words as well as showing her calculation.  Huzzah! She is already consciously improving on the goal she set in the previous unit.


(Note for the concerned reader:  K’s process is inaccurate.  Fear not, this is just the pre-assessment.)

(Exercise for the eager reader: Identify why her math demonstrates a common misconception around proportional thinking.)

So that’s the story so far.  Please let me know if you have any questions/comments/concerns about the process I use to incorporate metacognition into mastery of Problem Solving, Communicating Clearly, and Geometry standards.    


Redo to actually learn

“We do not learn from experience…we learn from reflecting on experience.” -John Dewey

In my land of Standards-Based Grading, a chance to redo ANY assignment is available and encouraged. Even when a term closes, I let students redo their work to improve their year-long grade.  I know that many would argue that this system creates too much work to reassess multiple assignments throughout the unit/term/year and that only some assignments should be allowed to have additional amendments.

I feel that these experiences help a student actual learn and master the material and I tell the students that I don’t have a deadline on learning.  I stumbled upon a recent post about how the most important part of preparing for adulthood is redoing what is needed to be redone and how various educators think about and implement do overs.

I have a template that I give to students so they are able to reflect upon and correct their errors.  While I have been tweaking with the template to make it more “kid-friendly” for many moons, the content has essentially remained the same.  Students are required to talk frankly about and reflect upon the assessment as a whole.  Then they dive into specific questions that they want to try again: they record the problem number, redo the problem, explain their errors, and then create and solve a new similar problem.  Below are parts of the template.


At the beginning of the year, there are days dedicated to learning the template and then providing time for students to work on their own assessment.  As the year moves on, and I fell the pressure to “get through” material, fewer times in classes are given for students to confer with each other and teachers over their assessments.  Instead, they are encouraged to come after school if they want to have some sort guidance throughout their revisions; but then the students lose the time with their peers to debrief and reflect on their assignments.

I am hoping that with a revamping of the curriculum and its structure that there will be more time dedicated and available for students to conference with their peers and teachers to reflect and improve their work.



About three years ago, Kogut and I re-wrote an Algebra 1 project that happens at our school every year. (It’s called exhibition; the end-product includes students presenting their project to approximately 20 students and adults; it’s a long story; we’ll tell you more about it for sure sometime.) Basic background: our Algebra 1 exhibition involves students using linear regressions to analyze real data about worldwide or school issues. My senior math class (Advanced Mathematical Decision Making) exhibition involves a statistical analysis of data about a social issue (linked to the Civics class) and its prevalence in our school.

For several years, I’ve enjoyed the process of giving feedback on these projects. As a rule, I don’t grade the “first draft” of the math work, but rather solely give feedback in relation to the objectives. This feedback-giving barely feels like grading; rather, I get to look at students’ thinking without immediately evaluating it. I get to enjoy the hard work students have done and then offer suggestions for improvement and point out where students’ have skimped on certain parts. Students then have the opportunity to revise before I finally do evaluate their mastery of the objectives.

What I’ve noticed is that students do not miss the grade at all, but rather appreciate that I actually paid close attention to their work. This year, when I gave the seniors back their first drafts, only one person in the entire class asked about a grade. Everyone else (and that student too, once I explained) just started revising their work. The results were almost entirely high quality, and the process felt real, respectful, and meaningful. I look forward to shifting my classroom so that most of the work involves this process of genuine feedback and revision, and to including students as important feedback-givers.