Gwinnett County Public Schools is hiring…

They are looking for math, science, and special education teachers. 

I work with absolutely excellent educators! We need teachers who teach students the subject matter, not the subject matter to students. There is a difference, and it matters.

Our county has been the recipient of the Broad Prize for excellence, not once, but twice. We excel. We are Gwinnett. It’s what we do.

Please put my name in the comments of your resume to let them know you heard it from me!

Good Hunting! Your next job is out there.

Why do we teach math? This teacher’s honest answer.

A math teacher friend has been questioning his value in his classroom. In his honesty, he asks “why do we teach what we teach?” His plaint comes as children ask him “why do we need this stuff, why prove something you have told us to be true, when will we ever use this?”
His desire is to answer honestly, but brilliantly; to give an answer that will make the child stop, gaze at him in awe, and return to his/her studies with renewed vigor and purpose. I suspect he is not alone in his thinking. For him, and for all teachers who go to this place of doubt and fatigue and, perhaps, even frustration, I offer these words:

Children need the discipline of effort, of struggle. They need to try something new, to push themselves beyond their comfort zone. As all of us know, that comfort zone is, well, it’s comfortable!

Teachers push, encourage, cheer, exhort, challenge, and free students to step into the unknown and the new. It’s like the first taste of vegetables for a baby. Oh, that face! But we know it is good for them. We know what they do not– that there is a wider world out there for them, and that they will need ways of dealing with it. Math has a logical, beautiful order to it. There is a discipline of thought that is rich and worth learning. And that is the first part of my answer. The noble part.

Here is the second:
I teach for totally generous and totally selfish reasons: I generously want children to find the wonder and excitement of knowing something beautiful. I want them to feel and own discovery of patterns and trails that numbers make; how they loop back upon themselves; how they start at one place and end up in another. I want them to see the magic of numbers. I want them to feel the satisfaction of revealing the secrets behind the magic – the elated rush of struggling with and conquering a numerical puzzle. It is Alice finding a key to a door and then choosing the correct potion to become the right size to fit through the door. (And for many children, math is as confusing as wonderland was to Alice!)
And selfishly: to see that most elusive of creatures – the excited spark when a student makes that connection to something learned. That spark is my adrenaline, my satisfaction. It creates a pride in me about that student that is like no other feeling in the world.

There are many comments about how students don’t care; how testing is killing the learning; how teachers’ hands are tied by administration. Still we teach. We teach because we know in our hearts that it is right and important. We want to be in the classroom. We want a better future for our students than they can possibly envision. We hope, eternally. We hope. That’s why we teach.

Our hope is stubborn and sure. Our hope does not back down. Our hope transcends the newest strategy, policy, or curriculum. Our hope spurs us to persevere with every child.

We must not, cannot assume that we have no impact. No one comes up at the end of each period with a trophy or a plaque. Children rarely write thank you notes (or parents for that matter). As teachers we may never see any result, we may feel we are simply parroting what other, greater teachers have already said. We cannot let that stop us. It is persevering into the dark, shadowy night, not knowing what we will meet along the way, with people telling us to go back, to beware, calling us foolish. Hope. What a powerful thing. Our students are the beneficiaries of this conviction, this hope. They may neither appreciate nor value it, now. But someday, ahhh someday, we know they will. There will be that moment, although we won’t be there to see it, when a child will silently thank a teacher for not giving up. And since we don’t know which child in our care that will be, we must place that unopened hope with each child we teach. And we will, because we must teach as surely as we must breathe. No matter what.

Subtraction or Adding a Negative: Tracking change

In response to a recent article about the state of teaching of subtraction in schools vs teaching children to add the inverse or the negative: Mathematical computation is about change, movement. (Link at the bottom of the post.)
To move along the number line, in whatever direction, or plot one point to another on the Cartesian or imaginary planes, is to chart change. The direction, positive or negative depends on the starting place.
The example: Jonathan has two apples, but if you subtract one, how many does he have, is not about a negative apple (there us no such thing!) but about the change with respect to possessions; the movement from one amount to another. It is relational, depending on who holds the apples and who is receiving the apple.
Astronomy led to expression because of the movement of the heavenly bodies. Calculus is the expression of movement of all sorts of actions. The “rules” of math; why 2 acts the way it does, set definition, the differences of movement in a Euclidean world vs a spherical one- all of the rules are predicated on understanding and defining observed change, or predicting future change.
Somewhere along the way, the vision of math, the way we share this lovely process with our children, has been turned into some cookie cutter process. We lose the observation of this movement by disconnecting it from change and giving children math problems with no relationships to anything but counting. Showing that numbers can be broken apart and recombined, that they are fluid and can show change, (number sense we call it) is critical to math knowledge.
Subtraction is movement away from the center of one person or place- addition is movement toward a person or place. It is relative to the location of center.
As we get older, more mature, we begin to understand that we are not the center of the universe. Until then (and this is the teacher in me) we believe we are the center, that movement away from us is loss- subtraction, if you will. Take-away is a valid way to teach movement away from (possessions like apples moving from one position to another, or reducing numbers by other numbers, or defining the distance from ground to sub-basement, or of one planet’s orbit around the sun), especially to younger students.
As students get older, we can continue with the idea of movement: the concept of adding a negative number works well on a number line. It serves to explain the process of movement – in the multiplication of negative and positive, or negative and negative, numbers. It is a difficult idea for students who do not grasp the true nature of numbers. The words used to describe what is happening in math and the ensuing confusion are understandable- perhaps as suggested by a colleague who creates mathematical texts, we can simplify the terminology. Until then, we need to teach and talk about mathematics in as many ways as we can. There are so many ways to get to the accurate answer, one of them is sure to resonate with our students, or with each other as mathematicians, and each can be the correct way, no matter the language.