Many of my students' go-to strategies are on the lower level of different types of problem solving. This is not to say that my students' strategies are less effective than those who use a sophisticated algorithm. I have seen this assumption, or the inference of this assumption, made by some General Education teachers when they make comments like, "I don't have time to pass out manipulatives" or "Letting them use the blocks takes so much time out of my instructional time". It's difficult not to sympathize with these teachers because they make some valid points; I struggle even offering wait time to 5 students in my 30 minute lessons. Teaching time is a precious gift, but fundamentally I can't deny a student their right to think the way they prefer. We have to stretch our minds to overcome the difficulties we face and differentiate our methods for our students. They are what truly matter, not our timetables.
I have a student who offers quite a different take on addition and subtraction-or does she? When I first met her I assumed she was just confused about which direction to start her computations. I observed her teachers shut down all discussion or communication about this apparent "mistake". However, I got to thinking...perhaps my student was using an inventive strategy to solve the problem. When I look back at her Brigance pre-test I notice that on a few of the problems that require difficult regrouping my student attempts to start the problem on the left and work right. Perhaps she was attempting to use mental math and known facts to work around the difficult regrouping? For example, given a problem like 32-19, the student could use her knowledge of 32-20=?, and then added 1 to even out the equation. I will never be sure of the truth because the talk moves exhibited by her teachers (which should be nicknamed "extinguish") have ceased all discussion. I feel as though I should ask the student to explain her thinking in my small group instruction, however I worry that by doing so my student will be singled out by her teacher as doing it "wrong" again. I suppose it comes down to feeling as though I lack the authority to so drastically change the model of instruction in another's classroom. Perhaps one day this lesson will prove fruitful for me and my class.
My student in the Problem Solving Interview did not have any invented strategies, but relied upon direct modeling or (for the easy numbers) recalled facts. I wish there was more relevant information I could write about my interview, but sadly there isn't.
