Personalized assessment

First, I want to make clear what my assumptions are about assessment.

• Each student learns at a different pace
• There should be no punitive action taken against a student who learns slower.
• Students are allowed as many times as they want to demonstrate learning.

Also, you must know of my story around abolishing grading in my calculus class.

Currently we are three quarters through the course and running out of outcomes to assess and master.  This week I have tried something different.  Personalized assessment!

Each student is given a test but it is drastically different than anything I ever given before.  On the front page, there are questions which assess their knowledge of an outcome we have been working on for a week.  On the next pages, each student's exam is different.

On some, the pages are blank.  These are for the students whom have already demonstrated understanding of all the outcomes up to this point.  The cool part is that these students can be enriched with an activity, as they will most likely finish the test first.  For the rest, their pages are filled with questions on the outcomes they have yet to demonstrate understanding of. (Up to a maximum of 2)

Example:  Susie hasn't demonstrated understanding of outcome 5 and 7 and therefore on her pages, there are questions around outcomes 5 and 7.  Jason, on the other hand, has demonstrated these two outcomes but has missed outcomes 1 and 6.  Consequently, on his test there are questions around outcomes 1 and 6.

Next, I will assess this test under the following scenarios.

1. It will be summative if the student correctly demonstrates all parts of the test. 
2. It will be part summative and part formative for those who can only demonstrate learning of certain outcomes. 
3. It will be entirely formative if a student can't demonstrate any understanding of any outcomes.

If I followed the philosophy that all assessment should be common, then all students would be writing a test around outcomes 1-10, which would take longer than a period, and be a complete waste of time for those who have already demonstrated learning.

Is this a lot of work?

Yes! However, it is worth it when I can say that this test is more about the needs of my students than it is to generate another "mark" in my gradebook.

Not every child can learn

Lets face the truth now.  It is about time we stop talking about that "every child can learn".

After 8 years of teaching, I have realized that it is true that not every child can learn....by Friday.

Not every child can learn....by me standing at the front talking.

Not every child can learn....by working alone.

Not every child can learn....by reading the textbook.

Not every child can learn....by worksheets.

Not every child can learn....by passively taking notes.


So if we aren't going to talk about "every child can learn", we can then start talking about "what do we do when they don't".

Not going to let a test decide my fate

Wow!! Great clip!!

What's wrong with Math Education?

"You can't teach that now, because then what am I going to teach next year!"

Ever heard this?  Ever said it?  Ever been a part of a conversation with this used?

I know I answered "Yes" to all three.  When curriculum is designed linearly, then we encounter such problems.  You have to know Y before I teach you X.  However, what if curriculum was designed around the questions student asked in class?

In two of my classes this year, I have eliminated "Units".  I can now demonstrate how math flows from one concept to another instead of teaching through 5 disjoint units, and no longer do I have to answer "You will learn that later"

Check out the clip below

How I abolished grading.

Here is the story of one teacher who abolished grading in a highschool calculus class.

I started teaching highschool Calculus at my school a couple of years ago.  When I started teaching the course, I used a traditional assessment strategy.  I would assign homework daily, end the week with a quiz, and then end the unit with a multiple choice/written exam.

My classes would start around 30 students, and by the end of the semester the class size would be 20.  What I did was "weed out the weak".  One day I realized that I wasn't weeding out the weak mathematicians, but instead weeding out the weak test writers.

This year, after many talks with first year University and College professors, administrators, teachers, students, and parents, I am proud to say that I have abolished grading.  We are currently in the middle of our semester and I have not graded a single item of student work.

Before you continue, I want to remind you that this does not mean I have not assessed, but not one student in my Calculus classes has received a grade at this point.  (Other than the report card mark which I must give).

How does it work?

First, I went through my outcomes, given to me by the government, and identified what the "Rocks" are.  These rocks are the outcomes which I expect the students to master above all other outcomes.  I chose these certain outcomes after my discussions with others and as well as what will be helpful for students to succeed in the future.

Next, these outcomes were rewritten in student friendly language and then provided to the students on the first day of class.

My teaching schedule did not change, nor did the speed on which I have taught the course, but what has changed is the speed at which the students can learn at.  Once I had taught 2 or 3 outcomes at a level where I felt that the class has mastered the outcome, I administered a summative assessment.  For this assessment, each child wrote it as a traditional exam, but it looked drastically different than a traditional exam.  Each assessment was entirely written, broken up by outcomes, and tested only the basics of the outcomes.  There were no "trick questions", just simple questions that would assess "Can the child demonstrate this outcome, on their own, as a basic level of understanding?"

When I assessed these assessments, I would write comments only on them, and either a "Outcome demonstrated" or "Need to learn" for each outcome assessed (Not on the overall assessment).   It is very important to understand that "Outcome demonstrated" is not a 100%, as a student could make a minor mistake and still achieve this, as I am assessing understanding the outcome, not perfection. 

Next, if the child received a "Need to learn" he/she must do the following:
1) Demonstrate the understanding of the questions given at a later date.  This usually occurs after a lunch session, a quick conversation, or multiple conversations with the child.
2) A conversation explaining how he/she made the mistake earlier and how their understanding has changed now
3) Write another assessment on the outcomes.

If after completing these 3 steps, he/she can demonstrate the outcomes then I would I count this as "Outcome demonstrated" just as if the child had done it the first time.  I do not deduct marks based on the number of tries needed.

If the child still does not demonstrate, (which is extremely unlikely as I have seen) then he/she must repeat the same 3 steps.

After 5-7 outcomes have been taught, then each child is assigned an open ended project.  This project consists of each student creating a problem around the math in the 5-7 outcomes and solving it.  The expectation is the problem is one which is deep, relevant, and for a purpose.  This part is not always easy! 

An example:  A student to demonstrate his understanding created a Call of Duty video and determined the rate of change of a ballistic knife falling in the video. 

These projects usually range from 3-5 pages and must be handed in individually, but can be worked on with assistance from others and/or textbooks.

To assess these projects, I follow the same pedagogy from above.  I use comments only, and give guidance towards any errors I see.  The projects are then handed back to each student, who can go back, make corrections, and rehand it in.  This process is repeated until the child receives perfection on the project.

I have even abolished the traditional final exam.  The expectation is the students must give me a 30-45 minute presentation around the rocks of the course, and demonstrate their understanding of all rocks. 

How do I get a final mark percentage?

I simply take the number of outcomes and projects completed (at the end of the course) and divide by the total number of outcomes and projects.  This is not the best strategy, but it seems to work for me at this moment.  I do weigh projects twice as much. (I have 20 outcomes, and 5 projects, so the total is (20+5x2=30)

Let me know if your thoughts

Student led in High School.

This now sparks the third pair of interviews where I didn't bring any grades into any conversations with parents.  I have been asked many times how I do it, below is one experience of how I did it.


Parent: How is my child doing in your class?

Me: He is a hardworking student, seems to really enjoy hockey, and how the statistics of it relates to the course. He has, however, struggled with relating the combinations of the way teams could be arranged in a tournament, to the ideas of the course..  I believe that he has demonstrated superior knowledge in how a graphical representation of the scores of team can be manipulated through transformational change.

Parent: How does he rank with the rest of class?

Me: Well he is at the top of the class, but honestly this is the weakest class I have ever taught.

Parent looked puzzled.

Me: I am not being entirely true.  When it comes to your son's interest of hockey he has demonstrated an understanding of it far superior than any other child in the class.  See, the rest of the class doesn't share this passion and interest of hockey and finds it hard to understand the applications of it.  Jim has demonstrated a keen ability to relate this passion to many assignments, and questions we have completed in class.

Parent: Ok, but on the report card his mark is XX%, and what can he do to increase it?

Me: What mark should Jim receive?

This is when Jim smiled and he said "100%".

Me: Awesome, now what have you done to demonstrate a full understanding of the material.

Jim: Well I completed a ---

I interrupted him and asked him not to tell me but his mother who originally asked the question.

Jim: ok... (now a little shy) mom I graphed a function which shows how the Calgary flames is not increasing over time (I laugh) Quiet Mr. Martin I am talking...

And then I listened to Jim explain to his mom about what he did, what he struggled with, and how he wants to go back and ensure mastery of all concepts. 

**I do have to give credit to another teacher, who minutes before messaged me about how she is giving student led conferences and I wanted to try one immediately**

The result was amazing.  The student took control, and marks were not the focus but his passions, interests and his own challenges were. 

I then explained that I am willing to reassess him if he does truly go back and learns the material for which he struggled on earlier.