Something I’m working on with my students right now is the idea that subtraction is the same as a negative.

Here’s a question:

Combine like terms: 8x - 4 + 3x + 5.

Students get really confused by this! Many will say 11x + 9. That looks like it’s subtracting 4, not a negative 4. They’re more or less the same thing, and it’s a subtle idea that takes some getting used to.

I could name dozens of little things like this that confuse students in 7th grade. We often just kindof hope students figure this stuff out on their own. That creates a divide. Some students do figure it out. Others don’t and feel completely mystified. That can snowball.

One approach is for teachers to figure out all these little things and know how to teach them as they come up. They’re not quite full objectives (I don’t think teaching a full lesson on “Students will be able to understand that subtracting and negatives often mean the same thing” is the right way to tackle it). It’s also really easy to forget stuff like this because it’s so automatic for most teachers.