Engaging in the Familiar: Independent Work
Once students get into my classroom I want them engaged in doing math for as many minutes of the period as possible. Entering class, students take 2 or 3 minutes to write that evening's video assignment in their daily planners. From the moment they finish putting their planners away, my sixth graders are "doing math" -- either working independently on a few problems as a warm-up exercise or working independently on a series of problems related to the previous day's lesson. These problems reflect the type of problems the students encountered in class with a partner the day before. So the first part of my math class is actually the last part of my lesson carried over from the previous day, the independent phase (see post on gradual release).
As they work on the sheet of problems (the difficulty level of which they self-select) for 20-30 minutes, I move from one student to another checking their work and asking them questions based on their level of understanding. I ask simple process questions of my strugglers (e.g. What do you put in the quotient before you even begin to divide a decimal by a whole number?). I may ask "higher order" questions of those secure with the concept (e.g. What does a remainder that is bigger than your divisor tell you about your calculation?) Many days I can move myself to most every student. Those that I don't catch initially I will make my way towards later during the period when they are engaged working through problems in the new lesson. My goal is to be able to have meaningful contact with every student everyday! By meaningful, I mean interaction that moves forward their mathematical understanding or corrects misconceptions.
As they complete their set of problems they will self-correct their answers against answer keys posted in a handful of locations around the classroom. The time following when a student corrects their sheet and awaits the rest of the class to correct their own is the time I need to structure differently to continue to have them engaged in doing math. Currently that time is anywhere from 5-10 minutes. I default to having them read in their "just-right" books for that short window of time, but feel compelled to have them continue to be engaged in doing math. Maybe a "problem of the day" projected on the board after they are finished correcting is a viable option -- a problem that can be wrestled by a student within a 5-10 minute window. That time chunk requires more scrutiny.
Engaging in the New: Interacting with the New Lesson
I tell the kids every day. "You are working on these problems in your partnerships not to finish all the problems, but to ensure that both of you know how to do the problems that you do encounter."
I want them to work cooperatively during these 20-25 minutes. I want them to gain confidence in their abilities. I want those who struggle with the concept to gain better understanding through the work of collaboration. I want those who readily understand the concept to become secure in it by asking guiding questions that would lead their partners to the correct answer. Checking in with each partnership, I listen to how they help each other. I clarify and correct.
When the 20-25 minutes have gone by, I will usually project the answers on the ActivBoard for them to self-correct. Then selecting a couple problems, I direct 2 or 3 pairs of students to show the class how they solved those problems. This allows for some accountability as well as validates the thinking and struggles going on in the classroom.
As the period comes to a close my students today have spent more time engaged in actually doing math than students in my classes before adopting a flipped model. My students will spend 60 to 70 minutes of the 80-minute period solving problems! In years past, students used to watch me model a lot of problems in class to teach a concept which took a ton of time. I would err on the side of modeling more problems to them to "ensure" my struggling learners had more chance to understand; yet, this grace given those students that struggled began to take a toll on those that already got it after the very first problem. Through flipping my classroom and adherence to the gradual release model. I have not only increased time spent with students doing math, I have increased the time I spend supporting kids -- and isn't that what what I came into teaching to do over 17 years ago?