This blog post is my contribution to Mission #1 of Exploring the MathTwitterBlogosphere.
I already write a lot about what physically happens in my classroom, so today I am going to write about three values of my class that impact my students' experience and give it a stamp of uniqueness. They are what I consider core elements of my classroom culture.
The first: Each kid learns at a different rate, but what's non-negotiable is the quality of their efforts and the fact that each student needs to be challenged.
I think that a lot of teachers out there hold the same value, so I wouldn't say that it's uniquely mine when taken alone, but it has practical implications in my interaction with the kids.
The most important implication of this value is that in my class, deadlines are not strictly held. If I tell kids that they should bring me an assignment on Monday, then on Monday I would discuss it a bit, answer last questions, and then say, "Okay. Please hand it in to me if you've already done your best on this assignment and feel that you have understood everything. If you need to still take another day or two in order to bring me your best work, then please do that instead of giving it to me now. I don't want you to turn in something that is less than your best efforts, because it's not useful to either you or me."
The same holds for quizzes and tests. Last Friday, a kid was struggling with a quiz I gave in class. After class, I gave him a full period of extended time, but as I was looking over his shoulders, I could see that he was still making the same mistake over and over again with signs, which was causing more frustration further down the line when he realized that his answers wouldn't check against the equations. Eventually, I stopped him and just said, "Alright, look, I don't want you to keep spinning in place and to feel more frustrated. Why don't you give this to me, and we'll plan for a requiz next week after we look over your errors together?" A part of me really struggled with that recommendation, because I think persistance is such an excellent trait, and allowing a kid to persist in face of difficulty is very valuable. But, a bigger part of me believes that each kid has to learn at their own rate, and forcing this quiz upon this kid then was going to do more harm than good.
Another manifestation of this value is that in class, I always try to touch upon a higher-order application of what we are learning, in order to keep the interest of those kids who just yearn for a little more depth beyond what everyone else can grasp immediately. Inevitably, those higher-order applications will come back as bonus questions on the test, not because I love to give bonus points but because I want a way to assess which students are accessing that knowledge based on our brief discussion in class. The real, core assessment is still based on the lowest common denominator, the core skills that we have thoroughly developed and practiced as a class, but on each assessment there should be room for the upper-end kids to stretch their understanding. It is one way that I make room for kids to show me that they are acquiring knowledge at a different rate.
The second: Kids should have ways of verifying and monitoring their own correctness, beyond asking me.
This is a value that a lot of math teachers hold, but one that I really invest a lot of time to teach and to develop in my classes. Depending on the topic and what makes the most sense, I either expect them to check their results via the calculator or to check their results by hand.
At the beginning of the year, it can take me more class time to teach this and to ask kids to self-verify their work, than the time that it takes me to teach new algebra skills. This is why I don't think that other teachers really teach it; a lot of people value this skill, but when it comes down to it, they don't necessarily value it enough to put in the time to force every kid to develop this skill. But as time goes on, the time spent learning this skill shrinks rapidly, and kids get very used to doing this as part of learning and assessing any new topic. In fact, my current students have said to me, "You really force us to check every problem on a quiz!" ...And yes, I do! The time they spend completing a quiz should be roughly as follows: only 2/3 to 3/4 of the time spent on completing the quiz, and the rest of the time going through and gaining full confidence in all their answers. Ideally, they should be able to tell me after every quiz, "I know I got 100%."
I try to get away from being the source of verification, because I want my students to one day exceed me in their knowledge and understanding of math, and if I don't teach them how to verify their own answers, their knowledge will always be upper-bounded by what I know.
The third: Learning to learn immediately supports learning of the content, so time should be spent in class to explicit teach, discuss, and practice various learning strategies.
Again, I think all teachers believe that learning strategies are important and incorporate them into our daily lessons. But, we don't all teach them explicitly or discuss their usefulness. In fact, some of the best content-teachers can still overlook the importance of explicitly teaching and discussing strategies for review in the classroom. Teenagers need modeling for learning strategies as much as they need modeling for how to do a math procedure. I find that once my students and I practice a certain strategy in the class, they often come back to me to request more support in learning to learn. And, in the long run, it helps them greatly in building their confidence with math.
The three most popular strategies with my students are: creating their own concept flash cards; doing practice quizzes; and doing white-board procedural practice (while they take photos of the problems). These are tried-and-true methods that the kids find to be the most useful in terms of self-diagnosing their gaps, ironing out consistent procedural errors, and increasing mental focus.
As I think about content delivery in my classroom, I tend to think that it is inseparable from the learning culture that I set up around the content. These three elements are not unique by themselves, but together they do help to form a strong culture of high expectations when it comes to self-reliance, self-monitoring, and self-knowledge. The learners cannot be viewed as helpless and passive, but in order for them to become successful and self-reliant, we need to cultivate the tools that would help them reach those expectations.