29-(10x2) = ?
Of course, you might realize that these parentheses are unnecessary given the order of operations, however they do not yet know this, and, until the introduction of parentheses, they simply approached equations left to right. They are coming to understand now, however, that parentheses mean that you do that operation first, so most looked at this question and found the 20; however, many then got stuck. "Ms. Rachel," they said, "this isn't possible! We can't do 20-29 that doesn't work" (they don't know anything about negatives yet). I was confused why so many of them were switching these numbers, something I had never seen them struggle with in subtraction previously. But then one student explained to me, "the number from the parentheses comes first," and I got it; we had told them that what happened in the parentheses came first, and they extended that beyond the initial operation to reverse the rest of the problem. I bring up this moment, because it really stood out to me as an example of a misconception that makes COMPLETE sense, but does not even occur to those of us who already understand a concept. Until my student talked me through it, I had no idea why they were switching things around, and therefore did not know what part of the procedure to re-teach. I believe that the accumulation of moments like these will make me a better teacher, such that I can guard against them (or at least know what to look for) in the future. It is so impressive to me when my Classroom Mentor can anticipate these challenges that students often have, and address them before they get confused or frustrated and I am grateful for a year of student teaching to begin to build up these experiences such that I, too, can begin to do this for my students.
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