I was reading the comment thread in an old post of mine when I hit this gem by Bert Speelpenning:
Here is a short list of things that kids in math class routinely unlearn in their journey from K through 12:
* when you add something, it gets bigger
* when you see the symbol “+” you are supposed to add the numbers and come up with the answer
* the answer is the number written right after the “=” symbol
* you subtract from the bigger number
* a fraction is when you don’t have enough to make a whole
* a percentage can only go up to 100
* the axes on a graph look like an L
* straight lines fit the equation y=mx+b
* the values (labels) on the axes must be evenly spaced
* putting a “-” in front of something makes it negative
* a reciprocal is a fraction that has 1 on top.
What are some other things our students unlearn?
Which things are acceptable to teach initially in a way that will later be changed? When is unlearning problematic?
Which things are impossible to avoid having the unlearning effect? (For instance, even if the teacher avoids saying it explicitly, it’s hard for students to avoid assuming “when you add something, it gets bigger” before negative numbers get introduced.)