Attending to Precision: INBs and group work (Interactive Notebooks)

I love new beginnings, but I am only so-so with early middles. Now that kids have started their INB journey, we've arrived at that crucial moment between the beginning and the first INB check. This, as the saying goes, is where the rubber meets the road.

I find that kids never understand at this stage why I insist on being so darned nit-picky about their notebooks. Every day someone new asks me why this or that HAS to go on the right-hand side or EXACTLY on page 5.

One of the many reasons why this is important, I have learned, is that it is all about teaching strategies for attending to precision — Mathematical Practice Standard #6, which is defined this way in the standards documents:

Mathematically proficient students try to communicate precisely to others.• They try to use clear definitions in discussion with others and in their own reasoning.When making mathematical arguments about a solution, strategy, or conjecture (see MP.3), mathematically proficient elementary students learn to craft careful explanations that communicate their reasoning by referring specifically to each important mathematical element, describing the relationships among them, and connecting their words clearly to their representations. They state the meaning of the symbols they choose, including us- ing the equal sign consistently and appropriately.• They are careful about specifying units of measure,• and labeling axes to clarify the correspondence with quantities in a problem.• They calculate ac- curately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. 

The problem, I find, is that this description of precision is precise only at the theoretical level. On the front lines, it's unrealistic because most kids never get to this level of precision.

And that is because their notes and their work are generally quite a mess.

A big part of teaching students to attend to precision is giving them a structure for being an impeccable warrior as a math student — that is to say, taking and keeping good notes, noticing and keeping track of your own progress as a learner, preserving your homework in a predictable place that is not, let us say, the very bottom of your backpack, crushed into a handful of loose raisins.

It means stepping up your game as a student of mathematics and presenting your work in a way that makes it possible for others to notice the care with which you are specifying units, crafting careful explanations, describing relationships, and so on. And it means presenting your work in this way ALWAYS — in all things, in all times, wherever you go.

INBs are an incredibly low-barrier-to-entry, accessible structure for teaching attention to precision. There are no students who cannot benefit from having a clear, common, and predictable structure for organizing their learning. INBs are also a great leveler. For those of us who are focused on creating equity in our classrooms, INBs offer all students a chance to prove both to themselves and others that they are indeed smart in mathematics. As I saw the other night at Back To School Night, my strongest note-keeping students are rarely the top students computationally speaking. But they are the ones who can always find what they are looking for — a major advantage on an open-notes test.

INBs are also a phenomenal formative assessment tool. Flipping through a students INB gives me an incredible snapshot of where and when they were truly attending to precision and where they were fuzzing out. Blank spaces and lack of color or highlighter on specific notes pages give me a targeted spot for further formative assessment. In my experience, it is exceedingly rare for a student who thoroughly understands a topic to write no notes or diagrams on that page. If anything, they are the ones who are most likely to appreciate the chance to consolidate their understanding.

So I am sticking with it and zooming in on some of the areas where kids' understanding fell apart last week. We'll be reviewing how to convert from percentages to decimals and how to document and analyze the iterative process of calculating compound interest because that is where my students' notes fell apart.

I'll be astonished — but will report back honestly — if these on-the-fly assessments prove to have been inaccurate.

SBG, Intrinsic Motivation, and the "Grading" of "Homework"

One of the surprising parts of this latest round of parent conferences was the number of parents who wanted to talk to me about why their child is suddenly interested and engaged in learning mathematics when — as I gathered — this was not previously always the case.

I teach in a district which places a very high value on school, teachers, and academic achievement, so this conversation in and of itself was not the surprising thing.

I explained about using Standards-Based Grading, frequent formative assessment, and the remediation and reassessment method I first stole learned about from Sam Shah and others in my Twitterverse/blogosphere orbit, but two things came up again and again during this round of conversations which really caught me by surprise: my emphasis on in-class autonomy as a mode of differentiation and my approach to grading homework.

In-Class Autonomy
My Algebra 1 classes are unusual for a middle school in that they contain a mixture of 7th and 8th graders. I find there are huge benefits to this kind of heterogeneous grouping. For one thing, the students in one grade tend not to have met the students in the other grade, so there are fewer preexisting status issues to contend with among math learners (for an excellent discussion of working with status issues in the math classroom, see Between the Numbers' presentation on this issue from the Creating Balance conference on Math & Social Justice in an Unjust World). For another, it creates a healthy competitive atmosphere in which neither age range wants to be shown up by the other. 8th graders do not want to have their clocks cleaned by a bunch of 7th-grade whippersnappers, and this is an excellent antidote to the problem of 8th grade "senioritis." At the same time, 7th graders are somewhat intimidated by being around the older kids, and that motivates them to bring their A game to class to help them compensate for any feelings of insecurity. The mixing of students encourages everybody to notice and value what others bring to the situation and to stay focused on their own work.

I am pretty much tied to the curriculum, our pacing guide, and the state testing schedule, with minor variations allowed to deal with large-group (or whole-group) lostness as need be. But that means that there are times when the most with-it students could get frustrated or bored if I did not provide them with some differentiated alternatives to keep them engaged while I work with the 75% of the class who are catching up to them.

So I allow students who are ahead of others to either "work ahead" or "dive deeper" during these times. I see no reason to bore them when I can challenge them and call them back to work with the whole group when I need everybody (or when there is a whole-class activity they do not wish to miss out on). I provide them with self-selectable options and I find that it works out really well.

This fits well with Dan Pink's thesis in his book Drive that intrinsic motivation arises from our basic human desires for autonomy, mastery, and purpose. Middle-schoolers do not have much autonomy in their own lives, so giving them a little bit in the classroom goes a long way towards both motivation and harmony (which is how I prefer to think of "classroom management").

Apparently this has been my unwitting secret to getting many of my students' cooperation. Students who would be bored or frustrated at being tethered to a whole-class pace that is either too fast or too slow feel happy and engaged because I try to make it possible for them to work at a pace and a depth that is meaningful for them. I did not realize this was such a giant change for so many of them.

The Grading of Homework
The other thing that seems to be working for my students is the change in emphasis on the "grading" of "homework," in that I do not actually grade their homework.

I was convinced long ago that Sam Shah's approach to Binder Checks is the best way to place an appropriate value on homework — namely, that homework is work one does at home to improve one's own learning. In an SBG world, mastery is measured by the student's performance on assessments — not by the teacher assessing each of 40 problems that one has worked on at home. The purpose of homework is to provide practice and investigation time, in addition to exposure to different kinds of problems and issues that may come up. The purpose of "assessing" homework is to assist the student in developing good study habits and organizational habits so that homework becomes a meaningful part of their school lives.

When I moved from high school to middle school, I discovered that the full binder check approach was a recipe for discouragement. It seems to be a developmental issue. So instead, I have modified the program into a system of "mini-binder checks," in which I check the corresponding homework "chunk" while they work on the test/assessment on that particular chapter/chunk. The "grade" or "score" they receive for "homework" is merely a completion score. It is not a problem-by-problem assessment of their thought process on each homework assignment.

Apparently it's a novel approach to trust motivated middle school students to do their homework and check it all at the assessment point in one fell swoop. At conferences this week, I heard some pretty upsetting stories about students staying up until midnight or one o'clock in the morning, trying to get all their math homework done so they would not get punished and graded down. I heard stories of students I think of as super-mathletes breaking down into tears and meltdowns because they couldn't get their homework all done and they got punished (and shamed) in class because of this failure. So I heard a lot of appreciation that I assign a reasonable amount of homework and expect them to take ownership of getting it all done in time for a reasonable assessment of completion.

It makes me kind of sad to hear these stories because I think of the students in my Algebra classes as pretty joyful learners. And it also saddens me because I do not see these practices as leading toward the "positive dispositions toward mathematics" that we are supposed to be building.