Today, we logged into Khan Academy in class and I introduced the site to the majority of my students. Since we were learning a new tool and not math, we checked out the K-2 mission. I had 5 students ask me for technical help on the same type of question. They were sure the answer they had was correct and the program just wasn’t letting them advance.
Here’s an example of the problem they were looking at.
5 = 2 + ?
The answer had to be seven, so why wasn’t the program letting them answer?
I asked one student if they’d ever seen a problem with the answer (I should have said “sum” instead) on the left rather than the right. “No.” They hadn’t. I wondered about how we present problems to students. If all addition problems are only ever shown as addend plus addend equals sum, then the student can stop even seeing the operation signs and stop thinking as well. It made me recall a lesson I learned in grad school about how we (teachers) need to be sure and show our students different forms and views of shapes that meet the definition. Students who have only ever seen a right triangle when being shown with one leg parallel to the bottom of the page may not recognize it as a right triangle when it is rotated. Similarly, they may not recognize a pentagon as a pentagon if it isn’t a regular pentagon.
Maybe this was a simple error and not a major lack of understanding, but it gave me pause. I want to be thoughtful in the problems I have my students tackle and growth their brain against. I need to make sure how I present problems to students adds to their understanding, enlarges their perspective and experience with numbers. My assessment should check their understanding and not offer things they can do with a superficial understanding of the math. Or worse, things that can be solved correctly with an incorrect understanding.