Have you told your students how much you value honest attempts at solutions to a problem? Even incorrect solutions? Then you have to assess this way.
You can’t tell students that you value their incorrect attempts at solutions when you take off points when they get an answer wrong. Worse, you can’t say you value the process over the solution when you assess using a multiple choice or short answer examination. Students are too smart and they will see right through that facade, as well they should.
“Mr. Krall, you say you want us to be persistent problem solvers and you value our mathematical thinking, but you still took off half-credit for my solution attempt.”
“And you said the highest I can make on my re-test is a 70.”
I’m not suggesting an “everyone gets an A” or a “crocodile in Spelling” method of assessment, but just that one needs to put a grade where their mouth is.
Similar to Dan’s “What Do You Worship?” question, I’d ask what do you, the facilitator, value? Value, both in an ethereal “boy I sure would like this!” way and a “yes, this is what you will be assessed on” way.
You will be assessed on your growth. You will be assessed on your persistence. You will be assessed on your various methods of solutions. You will be assessed on your communication.
You will not be assessed on the correctness of your answer. You will not be assessed based on the boxed number on the right side of the page. You will not be assessed using rote tasks that are easily solvable using a formula chart.
Also, this goes beyond “I allow retakes.” Retakes is a way of saying that students have one more chance to get it right (usually accompanied by a significant numerical penalty). It’s not penalizing a student for a wrong answer whatsoever. Or at least honoring the solution attempt that isn’t actually a penalty in disguise (i.e. “partial credit”). This is a huge assessment shift, and requires a more sophisticated assessment tool than an answer key can provide (such as these).
It’s really difficult to switch gears like this in the middle of the year though. There’s a certain foundational work that needs to happen first. And frankly, it’ll probably take a few rounds of assessment before students even believe you. You’re probably not the first person to say they value honest – if incorrect – solution attempts, only to turn around and dock students in the name of “well, the SAT doesn’t allow redo’s”.