My sixth graders have a difficult time transitioning from expressions with one variable or one term to multi-term or multi-variable expressions, especially seeing, for example, 5x and 4 as two things that can’t be combined, and are really focused on just calling it 9x. I’ve followed my curriculum on introducing this topic, and it calls for the use of manipulatives, and takes a lot of time. I think my mistake has always been rushing through the concept because it is always so close to testing time that I feel pressure to cover, cover, cover. I think my students need the time to process, and actually use the manipulatives, then pictures, to represent different terms or variables using different things (which makes me see a big connection to coding).
I can’t get my students to slow down and think carefully about involved tasks. I see a lot of students rushing and just “trying to get it done”. I’ve tried to combat this by having them work a task, then using student samples of work and having a discussion that re-engages them in the task and thinking about what others were thinking. And bringing specific attention to instances where students just didn’t read carefully. I’ve incorporated the same techniques their reading teachers use for close reading lessons. students respond well in class but I don’t understand why for at least half of them, it still isn’t translating over to when they take a standardized test.
My students also struggle with seeing an equation as a statement that two things are equal, and when you solve an equation with a variable by using an inverse operation, you are really doing the same things to “both sides”. They are very step-oriented and I struggle with getting them to commit the mental energy it takes to understand the concepts behind what they’re doing. And again, I usually feel pressure to cut bait and power through anyways because of time constraints.