Tag Archives: asperations

Math Heroes

I want my students to have math heroes. This is another aspect of my commitment to consciously cultivating values in my classroom this year.

Lots of kids have sports heroes and music heroes. It’s not uncommon for them to have literary heroes or science heroes. But math heroes are something of a rarity.

Why? I’m not really sure. Is it because kids have little exposure to contemporary mathematicians? That the math that “famous” mathematicians do can be opaque, inaccessible, or unrelatable? Or because it can be hard to tell a good math “story” because mathematicians’ achievements are so abstract?

Whatever the reason, I know that if someone is going to have a personal connection to a subject or pursuit, it helps a lot if they have heroes—people to look up to, people to cheer for, people whose work and achievements they just can’t get enough of. People who are both very human and larger-than-life.

Sharing the work and human stories of mathematicians—present and past—is one part of what thrills me about co-writing Math Munch for my students and others. But in addition to this online locale, I find myself with the desire to share my own math heroes with my student in concrete, present-in-the-classroom kinds of way. Even further perhaps, I want to model how enthusiasm for a mathematician can be shown and shared.

For a while I’ve had the thought of setting aside a space on the wall of my classroom for the celebration of math heroes. I’ve tinkered with this thought just a little. Year before last I had a student who made a nice drawing of Augustus de Morgan during our 7th grade logic unit. But I realized that if this “math hero wall” was really going to take off, I’d have to put my money where my mouth is. So last summer, I sketched out this idea for a portrait of Felix Klein, who is one of my math heroes.

And then, of course, the school year started up.

Then two weeks ago, I was feeling like I needed a really concrete project to take on, and my mind went to my Klein sketch. After an initial couple of hours, and then some further detail work a few days ago, things now stand here.

I just need to add his name toward the bottom, and the names of the four objects that surround him. They’re all named after Klein. Clockwise from the bottom-left, they’re his quartic, his bottle, his model, and his four-group.

Hopefully my painting will serve as a good anchor for my room’s math hero wall. I’m looking forward to seeing what it helps to inspire my students to do this year. Drawings? Collages? Sculptures? And most of all, to have math heroes of their own?

Plus, I’m pretty pumped to have made a painting myself and to get to share it with you!

Read more of this week’s #made4math posts here!

SBG: Skills Mastery as the Beginning, Not the End

Ah, the interminable design cycles that we as teachers put ourselves through! Something that I often find challenging is how lengthy these cycles can be–I mean, if the day after you’ve shared a lesson with kids you have a great idea about how it could have been way better, it could be up to a year or more before you get a chance to try it out.  And that’s if you remember your idea.

The cycle that has thrown me for the biggest loop is the one I’ve been in about SBG (or Standards-Based Grading).  When I first got into this mathedtweetblogiverse two years ago, I was excited by the work Dan Meyer and others had done to make their expectations about skills clear to their students.  Until that point, my own assessment arc had not been going well.  From the start, it had been really hard to match up my previous experiences with assessment with Saint Ann’s culture and ideals.  Giving quizzes and tests in arbitrary and knee-jerky fashion after we had covered “enough” material fizzled in the face of not giving grades.  Also, neither the tests themselves nor the feedback and corrections I labored over seemed to improve anyone’s understanding.

When I pulled back from those traditional assessment methods, however, I found myself in something of a vacuum.  The fact that I’m in charge of my own curricula and evaluations with little to no constraint–coupled with the fact that I tend to spontaneity and disorganization–often meant that I did few formal assessments whatsoever.  I knew that my students were learning things from the work they were doing for my class.  I could make records about my observations of their activities to include in my anecdotal reports.  Still, I couldn’t help but to think something was missing–my students just weren’t being best served by the lack of clear expectations, a systematic way of pursuing them, and a feedback cycle.

Enter SBG.

Trying to bring Standards-Based Grading into a no-grades school was an interesting adventure.  Suffice it to say that after trying out several different formulations over the past two years, I’m really excited to try out my new approach very soon.  I’ve decided to go binary with respect to my skills quizzes, since trying to measure progress toward understanding numerically never felt fruitful to me in practice, and there’s no need for me to establish a final “average” for each kid.  (Shawn Cornally’s thoughts here also helped to get me there.)  I’ll continue to have skills lists for my kids and weekly quizzes for them to choose from in order to demonstrate their mastery.  I’ll be giving them copious feedback and letting them know if they nailed it or still have work to do, and we’ll both keep track of the skills they’ve mastered.

Still, I really wanted to find a way to encourage students to see that skills mastery is the beginning of the story, rather than the end.  Skills are tools that let you do new things, that empower you, that even give you a new bit of social capital.  With these thoughts in mind, I designed the following sheet to help kids to track their progress toward skills mastery and to inspire them to use their knowledge in fruitful ways.  I’ll be using the same document to track their progress.

That first column gets checked off once a kid aces a weekly skills quiz–that’s the binary got-it-or-don’t.  The space below is for me and students to keep track of feedback that I give them and reminders they might make for themselves.  The other three columns are by no means sequential and don’t represent “stages” past mastery.  Rather, they are suggested asperations and goals for the newly-minted master geometric-series-summer.  Would you like to try a non-routine problem that involves geometric series?  Just ask me for one.  Does someone you know–in our class or out of it–need help with this topic, or just curious about learning some new math?  Share your new knowledge and document it by journaling, snapping a photo, or making a video.  Did you recognize three months later that knowing how to sum geometric series opened up a route to solving a problem as you worked on a project?  Sweet!  Include it in your project write-up.

The point is that those other columns are an ever-present alert: You know things!  You can seek out ways to use your knowledge!  All three of the “choice prongs” are here–the suggested tasks are big and open-ended, the timeframe is as long as needed, and students can choose these for themselves as goals and record and reflect on their successes as they happen.

A final thought: it seems to me that something like this could be easily adapted to a grades environment.  I’m not well-practiced at designing grading schemes, but I’m thinking:

  • non-mastery of a skill in isolation is a high F
  • mastery of a skill in isolation is a high B or low A
  • mastery of a skill in isolation plus a further use of the skill is a high A

And then average them up.

Thoughts on the practicality of such a grading scheme?  Comments on the set-up I’m going to try out?  Ideas for other ways of building and sharing skills mastery beyond use in isolation?