So 2/3 of a master’s program completed, 2 years spent as a Learning Leader in my building, a year on mat leave to mull over where I am in my teaching, and a return to the classroom as a half-time teacher in a spectacular pilot program. This year I vowed I was going to walk the walk. My math classroom would be inquiry based. We would discover math together through interesting problems. On top of this we’d make interesting connections to ELA and Social Studies. It would be amazing.

My reality? Is not nearly so pretty or amazing. It’s actually just barely passable for organized chaos. My process looks a bit like this:

Plan pretty decent lessons that let students play with the ideas (thanks to awesome real-life and internet colleagues). Have chaotic, but really interesting discussions about math rules & conventions. Continually be impressed by the things students notice and observe and conclude about math. Be not so impressed with the general hormonal behaviour of 14 year old young people. Arrive at desired conclusions eventually; sometimes painfully, sometimes brilliantly. Transition into applying the rules we’ve discovered. Realize that many students need more time with the idea, but that curricular demands say there is no more time. Default to giving struggling students procedures to “get questions done correctly.” Feel horrible. Repeat.

Folks, I know what the research says. I know in the long run these conversations, inquiries and struggles are far more important for students than if they can find a common denominator and remember to reduce. But I’m asked to evaluate students on their ability to find that denominator. That and many many other things. I just don’t have faith that if I don’t tell them how that they will eventually get there on their own. Especially when they bring all sorts of crazy math baggage with them and are defeated before we even begin. (Seriously, I asked students to tell me the most fun they’ve had in math and 80% of kids couldn’t think of ANYTHING. 9 years. Nothing. Oy.) Showing them step by step procedures doesn’t feel right either though.

What do you do for these kids? How do we afford them more time but not lose them in the class? My units are less sequential/dependant on previous stuff than most, but still, some stuff is just plain ol’ important in a “curriculum” kind of way.

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I’m not nearly as dedicated as you are to applying inquiry to my Math classes, but it is hard! Out of 30 kids I have 3 who understand the lesson by reading the title of the lesson, 15-20 who understand after some inquiry and 7-10 who have no clue. Ahhh!

As for fun memories, please remember that these are the same children who have spent nine years going home every night telling their parents they do “nothing” at school. They had fun.

Michelle, reality may not be pretty but it is amazing. Thank-you for your dedication, determination, and unwavering commitment to doing what is right for these students.

I don’t think there is a single thing you should feel bad about here. You’re giving them the chance at inquiry, spending what sounds like a good amount of time to explore. It’s only when you’re running out of time that you resort to procedure, and that procedure isn’t empty with all of the exploration they’ve done. Not every student needs to be able to explain everything from top to bottom.

Keep in mind that by providing these explorations you’re providing a basis for the procedures in their brains. And at the end of the day you’re expected to teach them to learn a skill and duplicate. Between the absolute optimum pure inquiry and memorization is the compromise we must make. Compromise is a good thing. It keeps all parties invested.

I am finding myself increasingly compartmentalizing in order to find time for cooler things. There’s the time we spend learning rote procedures and then there’s the other time where we do real math.

I might be at the point now where I would support showing a kid every calculator trick in the book if it means a week or two to do something cooler. I used to cringe when a person would use the math>frac button or use a calculator program to find the roots of a quadratic. Now I’m thinking, who really cares? Want to find the solutions to a polynomial equation? Graph it and see where it crosses the x-axis. 30 minutes max in class as opposed to a week or two talking about the rational zero test, DeCartes’ rule of signs, synthetic division and the like. This is only one example, but there are many spots where we subject a kid to much more than she needs to know for the state tests.

This is becoming my philosophy for an at-grade-level or below-grade-level Algebra 2 or Geometry course. I still believe those who are advanced in high school are helped by deeper discussions of algebra. They appreciate the beauty of working within that world more and are more excited about pure math problems without the bother of context.