Well guys, it's been fun.

Life calls us all in various directions, and such it is with me. Due to personal reasons, I won't be continuing the TEEMS program. Thank you everyone--Jermaine, Fetimah, Rachael, Charles, Millard, Brandi, Janet', Dr. Matthews, Dr. Daily, Desha, Ms. Turner, Winston, and all the people I forgot to mention. It was a challenging but profitable summer for me. Best of luck to all of you who are teaching for the first time ever--hang in there!

The end. No, wait, not yet.

Thus draws this summer session to a close, and it is approaching time to return to our schools and teach, some of us for the first time. Personally, I'm ready to take what I've learned here and apply it to the classroom. I've witnessed those moments of euphoria where students, after having spent a great deal of time and effort attempting to solve the problem, they finally arrive at the solution. It's extremely empowering for them to have done it on their own with little to no help. It will take us a great deal of work and planning to arrive at that point, but I think that once we get in there, it's actually pretty fun to let go and see what they're capable of. Heck, I think we all witnessed that at Sandtown last week!

Expectations re This Week's Teaching

To be very honest, I'm keeping my expectation list short. I do, however, expect myself to engage the students from the moment I walk into the classroom. The students and teacher will assess one another as soon as they first see one another. It is vital to capitalize on this short window of opportunity to capture their interest and imagination. I intend to do this by having a catchy, relevant introduction to the activity, and by maintaining good pedagogy and professionalism throughout the lesson. While I am in charge of the classroom, I will expect every student to engage in the activity, from the "high-achievers" to those who consider themselves to be struggling learners. All students can learn, and it will be my responsibility to transform that "can learn" into "will learn."

No pressure. :)

Teaching through problems

"Letting go" and letting the students take charge. I don't know of too many teachers that actually like the sound of this. Why? Because it's the way we've been taught that the classroom is supposed to work; it is our understated idea of its mechanism. And heaven forbid we let a kid go slip through the cracks--please, no child should be left behind. Yet that's one major obstacle that's keeping our students from truly learning.

So, then, what happens when they are wildly off track? At this point, they usually beg--I don't just mean ask, but beg--the teacher to supply the answer. Hints are good here. Give them only enough information to shift their line of thinking, just enough so that they have a better chance of taking the problem from here. One way I like to do this is with questions. "Remember when we had a problem that looked like ___? How did we solve that one?" Eventually that gets them going. And it's very empowering when they realize that they solved the problem on their own, and all the teacher did was just ask them questions. That's really the whole purpose of this: student empowerment. Remember, we have to prepare them for the day when they won't have us around to help them, and that day is coming soon.

One of the features that I introduced to one of my math courses last year was the concept of a "Closing" session--essentially the same thing as the After. The key principle was that the students had to explain the solutions to each other, and if they got it wrong, they had to rely on each other to correct it, not me. For much of the course, this drove the students nuts. Why do we have to go over a problem that we already know the answer to? Why can't we just say whether the answer is right or not? But I didn't cave into this, because I knew that they would learn a lot more effectively if they had to not just explain their mistakes but why they were mistakes. That has a lot more power than just hearing the teacher give the correct answer.

Something I'm planning on doing new next year is this idea of teaching the idea from problems. Have them understand why you need to learn FOIL--or do they need to learn it at all? Have them figure out what makes the Distributive Property so powerful. Reinforce their findings with multiple examples, but by all means, avoid skill-and-drill as the primary locus of teaching.

Mathematics in the real world

It's early in the morning--one minute before 6 a.m., to be exact. That the time is 5:59, is math. Your bedside clock receives a 120-volt current. That's math. So is the way your clock displays "5:59" on the front. Exactly 60 seconds after this, the clock sends a signal to change the digits to "6:00," and because that is the matching time to the previously-set alarm, the alarm goes off. There's all sorts of math going on there! Barely awake, your brain sends a signal to the muscles in your arm, which swings over and hits the snooze button. All of that is math. That clock registers 60 times however many minutes your clock's snooze is set for, and after that number of seconds, it goes off again. You guessed it.

You finally get up, whether a multiple of how long each snooze lasts, or if by chance a roommate or family member wakes you up for good. Those decisions involve math. You walk down the stairs, which support you all the way down. Guess what that is. And then you take a look at the cereal carton, and pour yourself what turns out to be 1.5 servings of cereal. That means you get 150% of all the vitamins and ingredients, good or bad. And that's not including the milk.

Folks, that's only the first half hour of the day, and look how much math there is. That doesn't include starting your car, having your car's engine run, the acceleration and aerodynamics on the car, and stopping at the traffic light. Heck, the traffic light cycle is a whole set of math in and of itself.

And you haven't even gotten to work or school yet! Look at all this math!

Now how come our students don't know this? Well, maybe we've forgotten to tell them. Perhaps we've let many of them become so satisfied in their phobia of math that we don't risk bursting their bubble, and make them realize that, Hey, this IS real-world stuff, and I AM going to have to bite the bullet and learn it for the sole reason that I can not only better understand the world, but perhaps change it as well.

You get students that start thinking like this...LOOK. OUT. WORLD. :)

"Limitations" in the classroom, and Engineering past those constraints

If you've ever taught a day in any classroom anywhere, you know the game. "This class has enough trouble behaving as-is, so how in the world can they manage themselves on their own?" "It's hard enough for them to solve problems with my help; how can they possibly do so without it?" "I have to go through the same exact type of problem over and over, and they still do not get it. I have presented the material as clearly as I know how, and they still act like they are lost." Such are the tricks we play with ourselves in an effort to convince ourselves that we alone understand the material. Therein lies the paradox: While we do indeed stand out as the unique bearers of particular information at the onset of a lesson, it is our role to get that knowledge across to the students. Placing the ball in their court may sound good in theory, but can we teachers convince ourselves that it can be done?

Consider the golfer who is on the green, lined up to make a long putt. His objective is straightforward: put the ball into the hole with as few additional strokes as possible, preferably no more than one putt. There are a number of ways to go wrong--he can hit it short or long, left or right, or break a rule that costs him strokes--but there is only one way to get it right: line up the shot exactly, and hit the ball with just the right touch. The great golfers, the Tiger Woodses and the Phil Mickelsons, do not concern themselves with the endless number of ways that they can do it wrong; they focus on the one way that they can do it right. If the green is hilly or the putt is long, do they give up and not attempt the putt? Absolutely not.

We can learn from pro golfers this way. In fact, we may have it better off, because unlike golfers, we teachers have a few more options of where we "putt." Once we properly "engineer" our lessons and work around obsticles instead of letting them get in the way, there isn't a whole lot that can stop us. We can show them via manipulatives, or via the whiteboard, or via technology. We can let them work under their own brainpower, or we can drop hints from time to time. We can be tough as nails, or we can loosen the reigns a little, or we can do both at the same time. We have options.

If we commit ourselves to getting it right, we won't have to worry about getting it wrong.

Just ask Tiger. http://www.youtube.com/watch?v=1nJfhUGM4Yc

Constructivism in the Math Classroom

When one student thinks entirely in the abstract, another thinks in terms of real-world applications, and yet another thinks in terms of the least possible work required to solve the problem, how do you teach an entire classroom full of such differing personalities? Simply put, IMO, you go for the mixed bag. Take the infamous case of multiplying (x+a)(x+b): Only the abstract student is going to be able to understand that. So you give an example of a room that measures, say, (x+5)(x+2) square feet. Have them draw out what that looks like. Then have them discover--don't show them yet, just have them discover that this can further be divided into four sections: x^2, 5x, 2x, and 5*2 piece. In other words, they come up with the FOIL method instead of having it taught straight-up.

For the student who doesn't want to go through all that work (but who really can, whether or not he or she knows it), have this student attempt to find an easier way and justify it. Pull this off properly and ironically, this student will do more work, but more important is that they will discover an important truth: there comes a point with some problems where certain steps have to be done. Granted there are often various paths that can be taken, but at some point, particular ways have to be followed.

My Experience in Math

From learning about Algebra equations in the 8th grade, to teaching those same equations now, working with math has always been something that I am accustomed to doing. I have always seen mathematics as more than just crunching numbers; it is a language, a world unto itself, yet a world linked with the everyday world that we know. This language is applied in the realm of computer design and operation, supply-chain management, statistical analysis, to name but a few fields. Having seen first-hand all of these applications, I have gained a real appreciation to those who devote themselves to it, and I can see what certain applications a particular math problem might have in the real world, for example.

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