Archives for the month of: August, 2011

This year I aim to model how someone can use SBG to improve. Students are going to assess me on eighteen standards based on the areas of performance from The Skillful Teacher*. No rich feedback on this assessment, just a chance to identify problem areas that will then get deeper conversation. So, students will just circle one choice for each standard: 4 (Always), 3 (Usually), 2 (Sometimes), 1 (Rarely), 0 (Never).

In this class:


I get help to stay focused on learning.


Class moves smoothly without wasted time.


I like being in the room, and I can see, hear, and work well.


We spend the right amount of time on each activity each day.


I know how we get stuff done (how we start class, how I get help, where and when to turn in work, etc.)


People behave well; when they don’t, it is handled well.


I understand the teacher, and I know what I’m supposed to be doing and why.

Principles of Learning

Lessons are interesting, connected to my goals, and long-lasting. I get help when I need it, and not when I don’t.

Models of Teaching

I am learning ways of thinking and working with others that will help me outside of math.


My teacher knows I am brilliant and expects me to show it.

Personal Relationship Building

My teacher knows me personally and cares about my success.

Class Climate

I am happy to share my ideas and questions even if I am completely lost or have a weird idea.

Curriculum Design

I know what the big idea of the course is and how each day connects to it.


I know what we’re learning each day, it’s the right level of challenge, and it’s worth doing.


What we do each day helps me achieve the day’s objective.

Learning Experiences

The things we do are a good match for my interests and the way I learn.


I know what things I can do well and what I need to work on next.

Overarching Objectives

Working hard and succeeding in this class makes me feel smart and free.

The concepts behind these standards are complex (each is treated with at least a chapter in TST) and I may have over-boiled. What I am going for is, for each area of performance, if I am performing ideally on that dimension, what will students say is “Always” true about class?

After each assessment, I’ll share with the class the distribution of responses for each standard, and get help from the class with making, then doing, my plan for improvement.

Word-smithing or other suggestions welcome!

*Jon Saphier, Mary Ann Haley-Speca and Robert Gower (2008) The Skillful Teacher: Building Your Teaching Skills (6th Ed.), Research for Better Teaching, Acton, MA, 544pp.

The Pure/Applied distinction is one that I loathe. It is the creative/mindless distinction that I care about. -Paul Lockhart

Many of my friends and family have asked me about today’s Op-Ed by Garfunkel and Mumford. I couldn’t get really excited about agreeing or disagreeing with it. In my very short experience, coming up with rich and engaging applications for teenagers isn’t any easier or harder than coming up with rich and engaging “pure” problems. MBP discussed part of the reason for this in his comment (“Let’s partition the world of course-spanning questions into the purely mathematical and applied mathematical questions…”). But to me, in the end, whether or not a student genuinely goes after a question comes down to whether or not the student makes the question her own. And I’m finding it slow going, as a beginner, to do what Lockhart describes in the same article cited above:

Look. A child will have only one real teacher in her life: herself! I see my role as not to train, but to inspire and to expose my students to a wide range of ideas and possibilities; to open up new windows. It is up to each of us to be students – to have zeal and interest, to practice, and to set and reach our own personal artistic and scientific goals. Children already know how to learn: you play around and have fun and struggle and figure it out for yourself. Grownups don’t need to hold infants up and move their legs for them to teach them to walk; kids walk when there is something interesting in the room that they want to get to. So a good teacher is someone who “puts interesting things in the room,” so to speak.

Whether the interesting things are mortgages or matrices doesn’t matter, if they are actually interesting.

Dan’s comment on this exchange got me thinking about procedures (the mathematical kind, like FOIL, not the general classroom kind, like how to turn in homework). The student in that exchange was a senior who had given up on ever learning to multiply polynomials. I said “Oh, no problem” and began to explain, and she literally covered her ears. She said the words don’t help. So I said “Ok. I’ll write on the board. You ask questions.” I did a silent, large-format, multi-color demo of FOIL, one step at a time. At each step she looked intently at the board for a minute and then I saw her make up a hand gesture for each step. I told her to go practice. The next day she came in for assessment and I put one on the board and left the room. When I returned she had done that one and three others that she’d made up on the spot, including one with huge coefficients, just for fun.

There’s a magic moment between hard and boring. FOIL is a rote procedure — anathema — that for this student had always been hard. When she constructed her own way of organizing it, it became fun. The success was fun. Knowing what to do was fun.

This year I taught few if any memorized formulas or procedures, and I downplayed the ones students presented. I am firmly in the “if you understand it, you don’t have to memorize it” camp. I think Dan’s comment describes precisely why that student finds math “boring or hard.” But, I experienced this student’s mastery of FOIL as a successful educational moment. Put these together and I am confused.

Maybe I need to examine my aversion to teaching rote procedures. Are they like sugar in the diet? Insubstantial and unhealthy as a main course, but in small amounts, an enjoyable and useful way to increase confidence and willingness for more serious inquiry? The hard-line anti-proceduralist in me says “That was a pyrrhic victory. If she hasn’t built up a solid mental model of what it means to multiply sums, it’s just another arbitrary algorithm.” But another part of me saw in her exuberance–finally learning to FOIL–a move from I Can’t to I Can, a step in the direction of smart and free.

So I am left with questions about rote procedures. Ever? When? Which ones? Why? How often? For whom?


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