Last week, I blogged about how we decided to have students consistently access a resource that presents the algorithms for fraction operations so that students are practicing the algorithms with more accuracy. However, as I sent student after student back to their desk in search of their Fraction Notes, I realized we had another problem here: we needed to do some training to model for the students HOW to use this fraction resource. First, half of the kids didn’t even know that they should be using it. “What fraction sheet? We have a fraction sheet? What does it look like? Is this it?”
Once the students had copies of the fraction sheet, I realized we had another learning curve around how to use it, namely that there is cyclical process that most kids are not engaging with. I know that I need to start at the top of the list of steps and that I may need to do a step more than once…I understand the process as cyclical. As I watched the students, Fraction Notes in hand, I realized they often just sort throw mental darts at the list and start on any step that appeals to them, which undermines the value of the entire process.
On the math front, this is most problematic when we think about working with the Order of Operations. Of course, the biggest issue when working with Order of Operations is that the students work left to right, with no regard for the Order However, even when a student is trying to implement the Order, I often observe that they think that, once they have done a step once, they are done. For example, if they have computed one multiplication, they must be done….but that’s not true! There may be more than one in the problem. There might have been an exponent that was a grouping symbol that needs to be calculated after addition within parentheses. And so on. I see the students do a sort of mental check-off and then they walk away from the Operations, but the Order tells us to apply the Order to every new “version” of the steps as you work through them. It’s a cyclical process.
I was thinking about how this plays out in life. Every month, I sit down and write checks for all of my bills, written in advance, and then put the envelopes on my desk with the date for mailing in the corner where I’ll put a stamp. The envelopes go out at different times, until the pile is gone, AND THEN IT STARTS AGAIN. It’s never a one-and-done. As adults, I think little in our lives is one-and-done! We are constantly writing the next set of checks, paying the next round of bills, etc. We can start modeling that process for the kids when we are explicit about the cyclical nature of processes.
This is TIME CONSUMING. We need to value the time and be okay with setting it aside, knowing that it will pay off, knowing that we are building habits for the future. And, of course, this also means we have to be prepared to advocate for how we are spending the time when administration is questioning how we are spending our time.