Math Assessment Philosophy

Moving from “Getting Grades” to “Meeting Competencies”

This year, although we will occasionally be using “grades” for summative tasks such as unit tests, we are not recording these grades or using these grades in our evaluations. Instead, we are breaking down each math unit into a series of skills we are hoping to help the students achieve.

An Analogy

Each of my children starting walking at a different age. This did not cause me to label the “non-walker” as a slow learner or make excuses as to why they were not meeting the milestone of walking by 1 year. I didn’t “write them off” or “give up on them”. I couldn’t “just move on” because we had “so many other things to get through”.  From my quickest walker at 11 months to my slowest walker at 16 months, they all walk now and the fact that they learned this skill over different time periods is irrelevant.

Why can’t school be the same?

In professional sports, many athletes do not “play in the game” until they have demonstrated the required skills in practice. If math education was more like athletics in that the “coach” (teacher) constantly provided the “player” (student) with feedback in order to be ready for the game (test, assignment), then maybe students would be more willing to keep working toward mastery. With the current “grade-based” system, students can (too easily) accept that they got a “C” or “D” on a particular concept and then move on without obtaining that skill. Not only does this lack of mastery carry over to the next year but it also provides the student with an “out”; as the topic is not being “covered” anymore, they no longer need to concern themselves with it. Grading our students, in a way, stands in contrast to helping students develop the problem solving skills to persevere and reach goals. Furthermore, grades are a simplistic (and unhelpful) way to indicate achievement.


What would happen if students had to meet the objective before they moved on?

This philosophy is rooted in a “competency-based” approach to education and is something we are going to try to incorporate into our math class for the duration of the school year. Competency-based education is not a new concept; however, it is almost impossible to move to this model without completing overhauling the current one. I am enough of a realist to know that I shouldn’t hold my breath waiting for policy to change. We need to find creative solutions (within the current parameters) to ensure that students are obtaining the required skills before moving on.

A few years ago, I heard an episode of “The 180″ on CBC Radio entitled “Math without marks” that I found particularly intriguing. Listen here or below:

My favourite part of this is his comparison to grades with bridge building (skill). In school an 80% is an A but we would never want a bridge that only held 80% of the cars.

Ensuring assessment is rich, comprehensive and well-developed

I have taught math for 15 years and have experienced a major philosophy change over my career. My first few years were based on my own knowledge of what makes school “school”. The “math schooling” I knew was from when I was a student: desks in rows, no talking, completing textbook work, and answers that are either “right” or “wrong”. There was no written feedback other than the unhelpful “try again” or “good job”. It didn’t matter if I demonstrated I had some understanding of a concept during class time or if I could explain the concept orally if I was unable to duplicate that understanding on a written test.

I believe that in order for assessment to truly be indicative of a student’s understanding it needs to include products (such as tests and assignments), but also should include the conversations with and observations of students by the teacher.

Assessment of products is easy; it is the tracking and follow up of conversations and observations that is the real challenge.

How math assessment is changing in our classroom

Written tests, assignments and other “written products” will still exist in our classroom, as will conversations and observations; however, we plan to do three things differently:

  1. use a google form/sheet to track student mastery of essential skills
  2. target students who do not demonstrate proficiency with clearly defined next steps and anecdotal notes
  3. remove most numeric grades (once report card time comes up, I will sit down with each student to determine their “mark” and report card comment – hopefully that will make the “marks” more meaningful)

How we will use the assessment data

As data is collected in the spreadsheet, we can sort the categories to target those students who need a quick re-direct, those that can move on or require a greater challenge, and those that may need some 1 on 1 assistance to clarify major misconceptions. We can also group students who are struggling with a similar skills to ensure our time is as focused and efficient as possible. We also plan to use this form during observation time (e.g. when students are working to solve problems in teams) and conversational time (e.g. student conferencing). Also, since Google forms uses a timestamp, we will be able to see student progress over time.

Click HERE to see what the collected data looks like (student names and identifiers have been removed).

Our ultimate goal would be to set it up so that students (and parents) had access to their personal learning journey and therefore could also work at home to clarify concepts.

If you have any questions, concerns, or feedback, please feel free to email me or leave a comment below.

Here is hoping that at the end of the year, these math skills will be like walking: the acquisition of skills being paramount with the time taken to acquire the skills being completely irrelevant.