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)

Here is my updated list of rocks.

Let me know if your thoughts

Can you post your list of "Rocks", things that need to be demonstrated?

ReplyDeleteI would like to see how general they are, ex: Derivatives of nested trig functions vs chain rule.

Would it be possible to see an example of a project hat is the 3-5 pages long? I am in Saskatchewan and have been toying with this idea but have been struggling with the "how" of structuring it.

ReplyDeleteKara here you go

ReplyDeletehttp://realteachingmeansreallearning.blogspot.ca/2011/09/da-with-derivatives.html

Sounds intriguing. working to modify my AP Calc class. What does that do with regards to prepping for AP Exam? The one part I like is that they are taking tests that mimic the exam so they get practice with the style. Guess that can be done without traditional grades too though.

ReplyDeleteDid you have to get special permission from admin to stop "grading". Why do they need a final percentage? Incorporate final student interview/self assessment into the final percent if it is required?

ReplyDeleteDo the students in this class take the AP exam in May or a final exam prepared by yourself. It certainly seems like a great AFL approach to teaching math - I'm just curious how well it prepares the students for the AP exam. Thank you for sharing!

ReplyDeleteThis is an important topic that needs to be shared.

ReplyDeleteThis is great - exactly what the principles of AfL are! I too would love to see your "rocks" and would be interested to know how this fits in with your school's assessment policy. Thanks for sharing!

ReplyDeleteI will be posting the rocks in a week. They have changed drastically to what I started with. Sorry

ReplyDeleteThe strategy sounds great for students who are planning on ending their mathematical career with high school calculus, or who are not planning on taking any AP exams. Students who go on to major in STEM fields in college need to be prepared to take traditional exams, as do AP students. What are the demographics of your class? How do your students end up performing on the AP exams?

ReplyDeleteDave, this is terrific. I think this demonstrates what is possible, even under the present grading accountability regime. Your focus on learning is evident with formative assessment providing the practice and feedback students need as well as permitting your students' choice in how they demonstrate their learning thru their projects. Bravo.

ReplyDeleteDave -- Great walk though of your approach. Really enjoyed it. I wonder (along the lines of Danny's, Suminder's, and Lindsey's comments) as to whether proficiency assessments could be incorporated into an approach like the one you've outlined here. We could have students take computerized timed drills that would make sure the student is able to get through problems accurately and quickly. But instead of giving a grade based on a single time score, on a specific day (like we do ordinarily do with standard grading) -- grade them based on attainment of proficiency: allow them to take the drill as many times as they need to achieve the required proficiency, then mark that "proficiency rock" as complete once they do. This might help assure that students planning to go on in math and/or take the AP exam are proficient in the content as well possess a good conceptual understanding of it.

ReplyDeleteInteresting how the comments eventually get around to the need to prepare students for 'traditional' tests. If your assessments are truly measure learning in a way that requires students to apply what they know (the rocks) to unique situations and present that knowledge to their peers in an authentic way (writing or presenting) then the AP exam or other traditional tests are just roadblocks to learning.

ReplyDeleteWhy keep things that are roadblocks to learning?

How many STEM majors take 'traditional tests' while they are working in their STEM field? None. How many are required to present knowledge to peers and communicate what they've learned? All of them... on a regular basis.

It's time for us to stop using demonstrably inferior instructional tools just because they may be wielded against our students in an equally inferior way in higher education.

Do you assess this way in your other classes (I.e. 10C, 30-1, etc.)

ReplyDeleteMr. Martin,

ReplyDelete1) do you use this approach in your Math 10C, 20-1/-2 and Math 30-1/2 class or just in Math 31 (Calculus)? I would be interested in the successs rate in your other classes.

2) Could you use the same approach in a classroom with 40 students?

Thanks.

I currently only teach Math 31 and AP Math, however I have a colleague who has taken this approach to her math 10C class. She has seen a great success with passion and interest.

DeleteAlso I did have a class once with 44 students and yes I still did this.

Dave do you think this would work at an elementary level where Math is reported in strands?

ReplyDeleteHow do you manage time and lessons with assessments in the classroom. Fascinating idea. Trying to get my mind around an implementation in grade 8.