Doing Mathematics

I had a thought this morning biking home from school (our first day is next Thursday). What is the goal I have for my students? Well, to learn mathematics. In order for that to happen, I need to maximize the amount of time that students are actually doing mathematics. Everything I plan should be centered around this.

This begs the question, though - what is "doing mathematics"? First, it's easy to list a few things that it is not. Doing mathematics is not:

• taking notes
• listening to me talk
• drill & kill assignments
• taking tests

Already, so there is one guide post - minimize the amount of time doing these activities.

As for doing mathematics, I like the way that Keith Devlin describes it:

"Doing math" involves all kinds of mental capacities: numerical reasoning, quantitative reasoning, linguistic reasoning, symbolic reasoning, spatial reasoning, logical reasoning, diagrammatic reasoning, reasoning about causality, the ability to handle abstractions, and maybe some others I have overlooked. And for success, all those need to be topped off with a dose of raw creativity and a desire - for some of us an inner need - to pursue the subject and do well at it.

However, I'm having a difficult time describing exactly what "doing mathematics" means. In my mind, it's more of "I know it when I see it", so I need to work on clarifying what it means. Some activities that I think do fall under this umbrella:

• Solving novel problems
• Student-generated questions
• Investigations
• Cooperative groupwork
• Communicating reasoning and thinking
• Proving conjectures
• Finding patterns

This list could go on and on, but my takeaway has been this. All planning should be focused on maximizing the amount of time that my students are doing mathematics.

Making Assessment Part of Teaching

I spent the first part of the summer thinking about whether I should give standards-based grading a shot my first year or not. Actually, that's not true. I spent the first month of my summer in Germany and Spain. After that I started thinking about grading.

My wife and I hiking up to Schloss Neuschwanstein

Anyway, all it took was a little nudge from some teachers on Twitter along with support from my chair and administration. Over the past couple of weeks, I've been working on designing my grading system, and discovered a major reason to implement SBG: it actually gets me excited about assessment!

During my student teaching, I felt that assessment was one of the worst parts of teaching. A necessary evil. I loved teaching, but when it came to giving tests and passing out only vaguely meaningful grades, it was just something I had to make it through. And then I had to deal with students negotiating for another point or pleading for extra credit. We were never discussing their learning, we were discussing how many points they had and how many they needed. Ugh.

Now, when I'm working on designing my system and assessments, it feels more like teaching than test giving. The focus is specifically on what I want students to learn and their progress. Hopefully the conversations will mirror this.

I think this alone is a good enough reason to try SBG.