Formalizing and its challenges

I've really been feeling the tension recently between emphasizing creativity, different ways of thinking, innate mathematical processes that are genuinely student-driven and the type of formal math notation and expression that are needed in order for us to have a common language and to be able to demonstrate our understanding to people outside of our community.

This is the first year in a long time that I'm working with students (7th graders) whose almost entire math learning experience has been rich and validating of the importance of expressing their thoughts and ideas in ways that made sense to them. They have done a lot of open projects and pattern investigations. As a result, they are exceedingly curious and creative in their approaches. They are not into answer-getting, they listen to the ideas of others, and they demonstrate really cool insights and ways of thinking. Having said that, their notation and formalizing of thoughts is ghastly. Their work is just numbers and symbols all over the place, a very personal record that somewhat makes sense to the student writing it, but is incomprehensible to anyone else. Equal signs are placed willy nilly, variables are used with little rhyme or reason to sometimes mean one stage and sometimes mean the previous/next stage, the progression of thought skips blithely around the page in seemingly random directions.

So I'm in a position where I know that I need to teach some formalization of process, some common notation and standardization of the way that we communicate our thinking and show our work. But I want to do this in a way that doesn't destroy the freedom of thought that has been carefully cultivated by their previous teachers, their ownership of mathematics as personal expression. Every time I ask a student to show their work in the very specific, standard way, just like all the other round pegs, I feel a little bit like I'm crushing something wild and pure and free.

It's a math fairy in its natural habitat! Let it run wild and free!

Help me out, teachers of younger students. How do you help students channel their approaches without crushing their spirit? How do I know how much to push formal notation? Our high school does not have an Algebra 1 class so by the end of 8th grade, they are supposed to have learned the equivalent of a standard Algebra 1 class. In my previous school, formal and precise approaches were held in very high regard and students bought in and didn't question it. I received my yearly package of students, some of who maybe weren't so amazing at formalizing their thinking, but were definitely aware that this was a goal for which to strive and gave a reasonably good effort to make it happen. Not so here. I feel like I need to be fully confident and able to justify to these students (and their parents) that what I'm doing is for their best development as students of mathematics. And clearly, I have some doubts at the moment. 

If you teach middle school math, I'd love your thoughts and feedback. How do you get buy in to formalization? My approach so far has been to first let them tackle problems intuitively and then try to demonstrate how to convert that into a more formal way, but their response so far has been a bit of

I feel like I can create some need and urgency to communicate more clearly by having them read and edit each others' work, but that won't likely get them to writing in the standard ways that the rest of the math world shows their thinking. And how to approach formal ways of writing without narrowing their thinking and reducing ownership? Or is that a conflict that's inevitable and just part and parcel of continuing in one's studies as a student of mathematics?

Digital workflow

In my previous post, I blogged about starting to use Google classroom with my 10th grade students this year. So far, I'm having not the easiest time with figuring out exactly how I want to use it. When you post to your classroom stream, you have the option of posting as an announcement or an assignment. Every time you post an assignment, Google classroom makes a folder with that assignment name and automatically drops work that students turn in into that folder on your Drive. However, students seem to be having a hard time using the "turn in" feature. For the assignment due today, they were supposed to make a spreadsheet of data (using a coin flipping simulator to flip coins and record the number of heads) as well as answer questions about their data. Apparently, Google classroom doesn't appreciate you trying to turn in two things for one assignment. I was told that there's an option to turn in one document and then add another, but I haven't tried this yet. Also, what to do for students who really want to answer the questions by hand?

This brings me to my second question... in the past, I have had students keep a very organized binder with sections. Not quite an Interactive Notebook, but something that could serve as a reference and be easily searchable and reflected upon. I had a great system for managing student workflow and feedback. Now that I'm using Google classroom, I'm trying to figure if I should go completely digital and have students create organized folders in Drive and scan/take pictures of their work or if I should try to maintain a hybrid system of some kind. My goal is for students to be able to compile and reflect on a portfolio of their work, as well as be able to turn in and receive back work in an organized manner. I'm a big fan of systems and right now, everyone is turning things in completely willy nilly and it's driving me crazy. I feel like I have this small window right now while the year is still in formation mode and students are eager to please to create an organized and simple system that makes sense for different types of Math work.

So please, clue me in to your wise ways. If your workflow system has a digital component, I would love to hear about it. How flexible are you? What's your take on helping students be organized? What do you do that you like or don't like? If you went all digital, how did it go? Tell me all of your things!!