I think in the everyday life of being a teacher, we often talk about the word “grading” instead of more specific terms like assessment or evaluation (these are very different things though). I often hear conversations about assessment level 2 or level 4… and this makes me wonder about how often we confuse “assessment” with “evaluation”?
Assessment comes from the Latin “assidere” which literally translates to “sit with” or “sit beside”. The process of assessment is about learning how our students think, how well they understand. To do this, we need to observe students as they are thinking… listen as they are working collaboratively… ask them questions to both push their thinking and learn more about their thoughts.
Evaluation, on the other hand, is the process where we attach a value to our students’ understanding or thinking. This can be done through levels, grades, or percents.
Personally, I believe we need to do far more assessing and far less evaluating if we want to make sure we are really helping our students learn mathematics, however, for this post I thought I would talk about evaluating and not assessing.
A group of teachers I work with were asked to create a rubric they would use if their students were making chocolate chip cookies as a little experiment. Think about this task for a second. If every student in your class were making chocolate chip cookies, and it was your responsibility to evaluate their cookies based on a rubric, what criteria would you use? What would the rubric look like?
Some of the rubrics looked like this:
What do you notice here? It becomes easy to judge a cookie when we make the diameters clear… or judge a cookie based on the number of chocolate chips… or set a specific thickness… or find an exact amount for its sugar content (this last one might be harder by looking at the final product).
While I am aware that setting clear standards are important, making sure we communicate our learning goals with students, co-creating success criteria… and that these have been shown to increase student achievement, I can’t help but wonder how often we take away our students’ thinking and decision making when we do this before students have had time to explore their own thoughts first.
What if we didn’t tell our students what a good chocolate chip cookie looked like before we began trying things out? Some might make things like this:
or this?
or this?
But what if we have students that want to make things like this:
or this?
or this?
Or this?
I think sometimes we want to explain everything SO CLEARLY so that everyone can be successful, but this can have the opposite effect. Being really clear can take away from the thinking of our students. Our rubrics need to allow for differences, but still hold high standards! Ambiguity is completely OK in a rubric as long as we have parameters (saying 1 chip per bite limits what I can do).
What about the rubric below? Is it helpful? While the first rubric above showed exact specs that the cookies might include, this one is very vague. So is this better or worse?
As we dig deeper into what quality math education looks like, we need to think deeper about the evidence we will accept for the word “understanding”!
…and by the way, are we evaluating the student’s ability to bake or their final product? If we are assessing baking skills, shouldn’t we include the process of baking? Is following a recipe indicative of a “level 4” or an “A”? Or should the student be baking, using trial and error and developing their own skills? Then co-creating success criteria from the samples made…
If we show students the exact thing our cookies should look like, then there really isn’t any thinking involved… students might be able to make a perfect batch of cookies, and then not make another batch until next year during the “cookie unit” and totally forget everything they did last year (I think this is currently what a lot of math classes looks like).
Learning isn’t about following rules though! It’s about figuring things out and making sense of it in your own way, hearing others’ ideas after you have already had a try at it, learning after trying, being motivated to continue to perfect the thing you are trying to do. We learn more from our failures, from constructing our understanding than we ever will from following directions!
Creativity happens in math when we give room for it. Many don’t see math as being creative though… I wish they did!
Thinking Mathematically 