It seems that many school districts are having a hard time attracting qualified math teachers. Gee, I wonder why that is? Could it be that those potential educators are having a hard time turning down the six figure salaries that Google or AT&T are offering them? I seriously doubt there's nearly that kind of disparity between professional historians and social studies teachers.
I can't even count the number of times I have advocated raising teachers salaries. All teachers need to be paid more for what they do, but we ought to bear in mind the realities of the situation. Marquee players bring in a larger chunk of revenue and so they get paid a larger salary. Well in the world of education, STEM grads are the marquee players. I'm not saying this is fair; I'm saying "fair" is irrelevant. If the goal is to better educate young people, then those kids deserve to get the best teacher money can buy.
In the case of math teachers, that price may just have to be a bit higher.
Friday, July 25, 2008
Thursday, June 5, 2008
Tuesday, March 25, 2008
Exceptions and Higher Standards
I'm not quite sure how I feel about this. An art teacher in Florida is in danger of losing his certification because he cannot pass the minimum general skills requirements due to diagnosed discalcula. His argument is that he doesn't see what math skills have to do with art.
I guess it depends on your perspective. I certainly feel bad for him, but truly, all things being equal, wouldn't you rather have an art teacher who is good at math? I know I would.
I guess it depends on your perspective. I certainly feel bad for him, but truly, all things being equal, wouldn't you rather have an art teacher who is good at math? I know I would.
Wednesday, March 19, 2008
Classroom Etiquette
I have heard it said that there are no stupid questions, and while this may be true, I think it deserves some clarification. A well crafted question designed to invoke a particular response can never be stupid, and nor can the person asking it. The very fact that the question was raised implies that the student has identified a specific gap in knowledge and wishes that hole to be filled. A stupid person doesn't even know what they don't know. Even broad questions like "Can you explain that again?" or implied questions like "I don't understand" can be helpful in determining where the explanation ought to begin. As a teacher, I will strive to maintain patience, addressing all questions no matter how outlandish or repetitive.
However...
There are certainly inappropriate questions. I believe that students ought to keep the following things in mind when asking a question in class.
1. Determine how specific your question needs to be. If you know the specific point that you need explained, feel free to cut to the chase. If you are completely baffled, just say so.
2. Remember that in most cases, you are not the only person in the class. If you feel that you are monopolizing the teachers class time, perhaps you should seek help outside of the regularly scheduled class.
3. Attempt to gauge your needs against those of your peers. If you feel that others are likely to have similar queries, then the question will benefit the whole class. If your are the only one who is confused, save the question for another time.
4. If you know for a fact that the question has been asked before, it should probably be held until after class.
5. Remember that good teachers have a prepared lesson plan that includes not only topics to be presented but the order in which they are to be presented. Do not ask questions about a topic that has not yet been covered. This disrupts the flow of the lesson and can negatively affect the ability of your peers to learn.
Most importantly.
6. Remember when I said there were no stupid questions? Well I lied. There are. There are really, really stupid questions. You should desperately fear being the person who mistakenly asks one of these questions. Before you even think of raising your hand or uttering a single syllable, ask yourself what your classmates will think of you. Will they be grateful that you share their confusion and that you have bravely stuck your neck out to obtain clarification? Or will they scoff, roll their eyes, or berate you.
These simple guidelines ought to ensure that your questions improve the overall quality of the class, rather than detracting from it. Teachers desperately want participation, but there comes a point when enough is enough. And as a student, you ought to know where that point is.
However...
There are certainly inappropriate questions. I believe that students ought to keep the following things in mind when asking a question in class.
1. Determine how specific your question needs to be. If you know the specific point that you need explained, feel free to cut to the chase. If you are completely baffled, just say so.
2. Remember that in most cases, you are not the only person in the class. If you feel that you are monopolizing the teachers class time, perhaps you should seek help outside of the regularly scheduled class.
3. Attempt to gauge your needs against those of your peers. If you feel that others are likely to have similar queries, then the question will benefit the whole class. If your are the only one who is confused, save the question for another time.
4. If you know for a fact that the question has been asked before, it should probably be held until after class.
5. Remember that good teachers have a prepared lesson plan that includes not only topics to be presented but the order in which they are to be presented. Do not ask questions about a topic that has not yet been covered. This disrupts the flow of the lesson and can negatively affect the ability of your peers to learn.
Most importantly.
6. Remember when I said there were no stupid questions? Well I lied. There are. There are really, really stupid questions. You should desperately fear being the person who mistakenly asks one of these questions. Before you even think of raising your hand or uttering a single syllable, ask yourself what your classmates will think of you. Will they be grateful that you share their confusion and that you have bravely stuck your neck out to obtain clarification? Or will they scoff, roll their eyes, or berate you.
These simple guidelines ought to ensure that your questions improve the overall quality of the class, rather than detracting from it. Teachers desperately want participation, but there comes a point when enough is enough. And as a student, you ought to know where that point is.
Tuesday, February 19, 2008
AYTMTB
Recently, I was forced to add a text messaging package to my cell phone plan. My incoming texts have skyrocketed in the last few months, as more and more of my loved ones rediscover the joys of the telegraph. I must admit, there are situations where I find the technology useful. Perhaps I'm sitting in class and I can't talk or I'm at work and I shouldn't talk. Yet even as I send my conveniently packaged alphanumeric messages sailing through the stratosphere, I am not a real texter.
I write my messages in plain English. Occasionally, I will exchange 2 for to or too, or 4 for for. (That was fun to write.) But that's pretty much it. I never LOL or talk to my BFF. It isn't that I look down on the abbreviation process. Far from it, actually. I admire its speed and efficiency. Fluent texters can condense essays into a few acronyms. Despite what many language mavens or old fogies might think, there is nothing inherently wrong with streamlining communication. Oh, and if you currently find yourself disagreeing with me, I'm going to go ahead and point out your hypocrisy. Laser, robot, sonar, scuba, TGIF, snafu, RSVP. If you have ever used any of these words, heck, if you've ever used a contraction, you too are butchering the Queen's English.
If you are a mathematician, you certainly have no room to talk. Imagine what math would be like without all the symbols and notation. (This isn't rhetorical, I actually want you to imagine it.) There was a time when symbolic algebra didn't exist. There was an era when quadratic equations were expressed plainly in words. For example, I could ask you to draw a square such that the magnitude of its area added to the magnitude of a single side is equal to six. That is equivalent to saying x squared plus x minus 6 equals zero or x^2 +x-6=0. (The square would be 2x2.) In recent years, we've taken to calling these word problems. There are no symbols to manipulate or mathematical abbreviations to remember. It's simply a question written out in our language of choice. Ironically, these simple problems cause math students the greatest trouble.
The difficulty stems from the down side to abbreviation. Sure it's fast and efficient, but you do lose a certain something in the process. Imagine reading a Shakespearean sonnet in text messaging. It probably wouldn't carry the same meaning. Actually, it would probably never happen. The commonly used texting lexicon, while great for casual conversation, is not designed for expressing new or interesting ideas. Symbolic math suffers from the same problem.
Last semester, my most challenging class turned out to be Intro to Statistics. My professor was Egyptian, and there were hidden language difficulties. You wouldn't notice it at first. His accent was thick, but not impenetrable. He was perfectly fluent, at least when it came to his discipline. After awhile, I noticed something. He was essentially reading the math straight from the board, simply pronouncing the rhetorical equivalent to the symbols he was writing. There were no metaphors or personal anecdotes. No stories or comparisons. Because of this, I struggled when it came time to apply what I was allegedly learning. I grasped the equations, but not the math behind them. In effect, I was struggling with the word problems.
And you're telling me this because? (Refer to title of post for irony.) I'm simply saying that the same breakthroughs that made long division and calculus possible, also make math too easy to compartmentalize. It becomes an oversimplified model, so efficiently streamlined that it no longer represents the real world, which is exactly what students complain about. Of course, they complain about the word problems, too, but then those little buggers are never going to be completely happy.
So what's the point of all this? Simply that we have been the architects of our own demise. And the only solution is this. More word problems. Less symbols. And for god's sake, if you have something to tell me, quit doing calisthenics with your thumbs and just talk to me on the phone.
I write my messages in plain English. Occasionally, I will exchange 2 for to or too, or 4 for for. (That was fun to write.) But that's pretty much it. I never LOL or talk to my BFF. It isn't that I look down on the abbreviation process. Far from it, actually. I admire its speed and efficiency. Fluent texters can condense essays into a few acronyms. Despite what many language mavens or old fogies might think, there is nothing inherently wrong with streamlining communication. Oh, and if you currently find yourself disagreeing with me, I'm going to go ahead and point out your hypocrisy. Laser, robot, sonar, scuba, TGIF, snafu, RSVP. If you have ever used any of these words, heck, if you've ever used a contraction, you too are butchering the Queen's English.
If you are a mathematician, you certainly have no room to talk. Imagine what math would be like without all the symbols and notation. (This isn't rhetorical, I actually want you to imagine it.) There was a time when symbolic algebra didn't exist. There was an era when quadratic equations were expressed plainly in words. For example, I could ask you to draw a square such that the magnitude of its area added to the magnitude of a single side is equal to six. That is equivalent to saying x squared plus x minus 6 equals zero or x^2 +x-6=0. (The square would be 2x2.) In recent years, we've taken to calling these word problems. There are no symbols to manipulate or mathematical abbreviations to remember. It's simply a question written out in our language of choice. Ironically, these simple problems cause math students the greatest trouble.
The difficulty stems from the down side to abbreviation. Sure it's fast and efficient, but you do lose a certain something in the process. Imagine reading a Shakespearean sonnet in text messaging. It probably wouldn't carry the same meaning. Actually, it would probably never happen. The commonly used texting lexicon, while great for casual conversation, is not designed for expressing new or interesting ideas. Symbolic math suffers from the same problem.
Last semester, my most challenging class turned out to be Intro to Statistics. My professor was Egyptian, and there were hidden language difficulties. You wouldn't notice it at first. His accent was thick, but not impenetrable. He was perfectly fluent, at least when it came to his discipline. After awhile, I noticed something. He was essentially reading the math straight from the board, simply pronouncing the rhetorical equivalent to the symbols he was writing. There were no metaphors or personal anecdotes. No stories or comparisons. Because of this, I struggled when it came time to apply what I was allegedly learning. I grasped the equations, but not the math behind them. In effect, I was struggling with the word problems.
And you're telling me this because? (Refer to title of post for irony.) I'm simply saying that the same breakthroughs that made long division and calculus possible, also make math too easy to compartmentalize. It becomes an oversimplified model, so efficiently streamlined that it no longer represents the real world, which is exactly what students complain about. Of course, they complain about the word problems, too, but then those little buggers are never going to be completely happy.
So what's the point of all this? Simply that we have been the architects of our own demise. And the only solution is this. More word problems. Less symbols. And for god's sake, if you have something to tell me, quit doing calisthenics with your thumbs and just talk to me on the phone.
Wednesday, January 30, 2008
Practice Makes Perfect
When I volunteered to lead a study group for my physics class, I wasn't reallly expecting anyone to show up. Not a single person asked me for help last semester, even though it was obvious by my test scores that I was significantly ahead of the curve. So I was planning on essentially having a study hall after class each day where I could get other work done. Surprisingly, I have had several customers and at least one new person each day.
I am becoming more and more certain that I love teaching. It gives me such a high when a student leaves the room feeling more confident about the material than when they arrived. In many ways, they are helping me more than I'm helping them.
I am becoming more and more certain that I love teaching. It gives me such a high when a student leaves the room feeling more confident about the material than when they arrived. In many ways, they are helping me more than I'm helping them.
Wednesday, January 23, 2008
The Joy of Cooking
While on your bi-weekly excursion to your local grocer, you notice that there is a new species of mushroom in stock. You've never seen it before, and you're not sure how to prepare it or what exactly it will taste like, but something about it's aroma appeals to you. You place it in your cart an continue on your way.
You run to Target for some personal items, and as you scurry around a child screaming in the center of an aisle, your eyes fall on a birthday card with a curious drawing. You open it, read, and chuckle. Though no one close to you has an upcoming birthday, you buy it and save for an appropriate occasion.
Realizing that your couch desperately needs to be either reupholstered or thrown away, you embark on a trip to the fabric discount store. You find the shade of red that you are looking for, but you also find a bolt of green that you can't resist. It's a real bargain, and it finds it's way home with you.
What do all of these stories have in common? Well, for starters, I know people who regularly do these things, and I'll bet you do, too. People who buy a dress without having anywhere to wear it or squirrel away the styrofoam packing from a computer purchase. These aren't packrats that I'm portraying. They don't save everything indiscriminately. Rather, these are people whose life experience allows them to judge the potential usefulness of a brand new item with reasonable accuracy. They are experienced cooks with a new ingredient, accomplished seamsters with a new cloth, and stylish socialites with closets full of perfect ensembles.
These characters are to their area of expertise what mathematicians are to mathematics. Why do these spmetimes bespectacled bookworms play around with formulas and numbers and patterns, seemingly without purpose? Why do they care about things that don't relate to the "real world?" They play for the same reason we all play. Because it's fun. They care because the shelf life of a piece of mathematics is a whole lot longer than a mushroom. It is not uncommon for a discovery to collect dust for centuries before someone makes a connection or draws a comparison, and suddenly that dusty function springs to life, providing just the thing needed to complete the recipe.
I can't cook. I wouldn't know a porcini from a shitake. But I love to eat, and I appreciate the experienced chefs who are willing to try new ingredients and new combinations. Nor will I ever gain fame as a mathematician, but I still love what it is they do. And you should, too.
You run to Target for some personal items, and as you scurry around a child screaming in the center of an aisle, your eyes fall on a birthday card with a curious drawing. You open it, read, and chuckle. Though no one close to you has an upcoming birthday, you buy it and save for an appropriate occasion.
Realizing that your couch desperately needs to be either reupholstered or thrown away, you embark on a trip to the fabric discount store. You find the shade of red that you are looking for, but you also find a bolt of green that you can't resist. It's a real bargain, and it finds it's way home with you.
What do all of these stories have in common? Well, for starters, I know people who regularly do these things, and I'll bet you do, too. People who buy a dress without having anywhere to wear it or squirrel away the styrofoam packing from a computer purchase. These aren't packrats that I'm portraying. They don't save everything indiscriminately. Rather, these are people whose life experience allows them to judge the potential usefulness of a brand new item with reasonable accuracy. They are experienced cooks with a new ingredient, accomplished seamsters with a new cloth, and stylish socialites with closets full of perfect ensembles.
These characters are to their area of expertise what mathematicians are to mathematics. Why do these spmetimes bespectacled bookworms play around with formulas and numbers and patterns, seemingly without purpose? Why do they care about things that don't relate to the "real world?" They play for the same reason we all play. Because it's fun. They care because the shelf life of a piece of mathematics is a whole lot longer than a mushroom. It is not uncommon for a discovery to collect dust for centuries before someone makes a connection or draws a comparison, and suddenly that dusty function springs to life, providing just the thing needed to complete the recipe.
I can't cook. I wouldn't know a porcini from a shitake. But I love to eat, and I appreciate the experienced chefs who are willing to try new ingredients and new combinations. Nor will I ever gain fame as a mathematician, but I still love what it is they do. And you should, too.
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