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.