Team Tests

I administered my skills tests for the week today, but instead of making students complete the tests individually, they were encouraged to work within their team (of 3 or 4 students total).  Each student turned in a separate piece of paper.  I picked problem 1 from student A, problem 2 from student B, problem 3 from student C, and so forth, to determine the grade that all group members would receive.  Interesting.  Overall, I recommend you try it.


  1. A different format.  The kids were really in to it.  Afterwards, every kid I asked said something between “I liked it” and “It was way better.”
  2. Easy to administer and grade.
  3. I felt like I could put tougher problems on the test.  In fact, all of the problems I put on it were harder than usual, and the scores on this test were 10.6% higher than the scores on the rest of my tests.
  4. Students got practice communicating in a “high stakes” environment.
  5. It didn’t feel like I was spending the whole class on assessment.  There was also learning going on.  I heard things like, “this is the way I’ve started to think about this,” and “can we check this [answer]?”


  1. Tension was high, particularly in one group, when there were disagreements.  There was some snapping and flustered rustling of papers.
  2. Probably at least one student earned a grade higher than his understanding should indicate.

The pros are great, here.  Compared to the atmosphere during individual tests, today’s vibe was much more collegiate and… educational.  How can I mitigate the cons?  I could alternate individual and team tests.  I could talk with the students about strategies to work under pressure.  Would more time alleviate the tension?

Anyone else have experience with team tests?

Train a teacher in one week? (!)

I run a summer camp and am charged with training my staff of 25 in one week, immediately before campers arrive.  I can’t tell them everything I know.  What are the most important pieces of being a good teacher?

  • Basic skills
    • Smile
    • Listen
    • Comfort
    • Support
    • Keep them safe
  • Advanced skills
    • Model
    • Challenge
    • Bond
    • Feedback
    • Cooperate
    • Improve
    • Let them be in danger1
  • Basic Knowledge
    • Safety policies
    • Fun activities
    • Hard skills: Cooking, pitching a tent, adjusting a pack (multiplying, dividing, solving a system of equations)
  • Advanced Knowledge
    • Edifying activities
    • Stages of child development
    • The bigger picture of skills: Where’s the best place for a tent?  (Why do we solve systems of equations?)

Anything else?  Look how much summer camp has in common with math ed!

The basic categories are easy enough to teach, but let’s look at some advanced topics in closer detail.  These are the skills we use in math class, too.


Praise should be specific and direct.  Criticism should be specific and direct.  All feedback should be timely: “see it, say it,” right?  How do you teach someone else to give good feedback?  We all struggle with giving more and better feedback in our classrooms, and my counselors have as many kids as we do.


Kids on a bedrock of support and success will learn best when they’re challenged.  We want them to feel comfortable most of the time, but acknowledge that most learning happens at some stage of discomfort (though we must avoid stages of panic).  How do good teachers move kids out of their comfort zones in a safe way?


We want our kids to improve themselves, and as their role models we must improve ourselves.  At camp, staff meet with supervisors once per week.  In school, my PLC meets 1 or 3 times per month.  How do you teach someone to improve?

Edifying Activities

At camp we have kickball, right?  And in school we have, for example, properties of exponents.  Both of these can be lead in a basic level 1 way or an advanced level 2 way.  At level 1 we have kicking, running, adding, multiplying.  At level 2 we have working as a team, changing the rules to make the game more fun, understanding why exponents are added, building on previous knowledge, verifying results.  How do you teach someone to build level 2 into their activities?  How do you convince them it’s important?

  1. a safe amount of danger, of course

An opportunity to spend the summer doing what you love best

I am the director of Shiloh Quaker Camp.  I use the camp as a medium for teaching subjects more important than math1: problem-solving, self-confidence, compassion, teamwork, and other “level 2” skills.  My goal is to lead my counselors (aged 17-22) in creating a community that fosters these skills, and it is a pursuit that brings a deep satisfaction to my daily life.

If you have dedicated your life to shaping the world by teaching, you might be interested in my camp.  There is a position available this summer for what we call “staff-staff,” the staff who train, support, and guide the cabin counselors.   These positions are normally filled from within our camping program, but I am interested in looking outside of our program for a fresh set of ideas.  The things I read in the math-ed-blogosphere have shown me that there are a ton of great ideas out there, and so many things can be brought to camp from the classroom.  Think of it like this: Shiloh is like teaching a class where 100% of the students are there to learn, everything you have to teach is personally rewarding (replace long division with leadership, and factoring with love), you have fun every day, and you get to be in a real community all summer long.

It runs for the 8 weeks between June 15 and August 12, and is based out of Virginia.  If you’re interested in helping to guide teenagers towards being better guides for campers (the campers are aged 9-14), please ask me for more information:

I was about to write something clever like “this blog will now return to its irregularly scheduled programming,” but I realized that writing about camp is really not different from writing about my math class.  Both are about helping kids find themselves.

  1. though I do try to teach all of these skills in my math class as well

What do you mean, “relevant?”

Do you try to make your lessons relevant to your students and their lives?  Do you struggle to find ways your students will actually use your math in the future?  I suggest a reframe: make lessons relevant to your students by immersing them in mathematical situations during class.  Don’t worry too much if you can’t find something in their life outside of class.

My text book refers to bank accounts to make exponential equations relevant, and so does yours, probably.  Some problems with this example are obvious: my account is compounded monthly instead of continuously, I put money in and take money out at weird intervals, etc, so this math actually does not apply without modification.  Some problems are more subtle: you don’t need to know about exponential equations to pick a bank account, you just pick the one with the highest interest rate.  My students have very little money and differences in interest are on the order of pennies per year.  My students don’t have bank accounts.  My students don’t care about bank accounts.

The most subtle problem (that I’ve found, anyway) is that even students who do care about bank accounts aren’t opening bank accounts at the moment I am trying to teach them about exponential functions.  Even if the example is relevant to their outside life, when they are in my class they are not in their outside life.  The best I can do is “imagine you’re choosing a bank account” or maybe “find three bank accounts online.”  What I want is a student faced with a problem that he wants to solve during our class.

Give up on outside relevance in favor of inside relevance.  Pass out super balls.

This idea is from CPM’s Algebra 2: Connections.  Ask students, “how high will your ball bounce?”  They will have a mental crisis as they think of all the reasons this question is unanswerable in its current form.  Already they are thinking about a problem during my class.  Better yet, they are pretty fluent in bouncing already – they have bounced a lot of things in their day, you know?  They have some vocabulary to describe what’s going to happen, and a framework in which to place guesses.

You get the idea: it turns out that the height of bounce x follows a path almost exactly exponential, and you can ask students how high the second bounce will be, and how high the tenth bounce will be.  Please note that this has nothing to do with anything that “matters” in “real life.”  This activity makes exponential functions relevant by showing kids how exponential functions can improve their fluency about bouncing.  Exponential functions give them the power to, with absurd accuracy, guess how high the fifth bounce will be – and everyone likes that.  Increased fluency about reality is relevant to everyone.

So I’ve traded outside relevance for inside relevance, and the biggest difference is that I am teaching during the problem-solving process instead of before the problem-solving process.  The kids who learn about bank accounts won’t use that math until they are opening a bank account, and at that point they can’t get help from me or from classmates.  The kids who learn about bouncy balls use the math at the same time they are learning the math, and so their ideas are immediately challenged and reinforced by results.  It’s better!

One more reason I want to be Bobby McFerrin

Here’s Bobby McFerrin effortlessly using his audience’s intuition to bring them from a simple idea to a complex one:

(if you can’t see the video, watch it on youtube)

Let’s talk about brilliant scaffolding, huh?  He is just so efficient at it.  I’ll write up my own thoughts soon (it’s the middle of the school day right now, tsk tsk), but I’m going to pose the question to the audience: what is Mr. McFerrin doing right?  And, for completeness: Is there any way he could improve?