Final journal entry for my current math course. Lots to think about looking back.

• Comment on our discussion of point gathering vs data gathering.

Short version: every teacher (in Peter’s words) is either doing one of these two things, or trying to mush them together. Point gathering is what it sounds like: a gradebook where everything gets points and you just add the points up at the end to get a grade. Data gathering is where you collect data that you can look over holistically and read a narrative from that tells you whether someone’s learned. That data narrative can then turn into a grade based on professional judgment and/or by translating it into scores to add up / average, but then you’re scoring based on learning, not based on specific assessment events.

This is more-or-less the idea behind Standards-Based Grading (SBG) which the math blog world already got on board with heavily around the time I was starting teaching. It’s also shown up in various other names, with different twists and spins on how it’s organized, from other assessment gurus and researchers. Whatever the specifics of the system, though, it’s fundamentally different than point-adding because we’re using assessment events as data to generate a measure of learning, rather than letting specific events (eg. old, early quizzes back when someone was just forming new ideas) dictate the grade.

So, yeah, I’m on board with this, no doubt.

• Re-respond to the following questions…

What is mathematics?

Mathematics is the practice of finding logical patterns and exploring them logically. It is the community of mathematics practitioners and their shared wealth of understanding of the world’s mathematical patterns. It is the language in which we communicate those ideas to each other.

How does someone best learn mathematics?

They best learn math by being given resources and an environment in which to do mathematics that are on the edge of their current understanding. Those resources can include peers, technological tools; the environment ought to be social, supportive, safe and guided.

How does someone best teach mathematics?

By providing an effective, efficient environment in which to think mathematically while also giving well-designed challenges to the learner that afford mathematically ‘flow’ in the direction of new ideas and understandings.

• Read your entire journal and comment on what has changed the most for you?

Mostly, I’ve gotten what I wanted to get, which was to be supported in implementing the Thinking Classroom approach to math class. I’m more ready to just dive in and do it; I’ve got a better theoretical and data-driven background in why these techniques work and what they’re meant to improve. I’ve got a much greater appreciation for the nuance and skills that this style of teaching requires, and know I’m both on the right track and also have a long road ahead to work on improving this for myself.

I also have more questions about designing good tasks than I had when I first started. I feel like there’s a lot of room to research and investigate how to design a good task, rather than stumble across one, and how to pass those design strategies on to teachers for their own work.