At a recent professional development meeting of gifted coordinators, one of the attendees said something to the effect that, although each of us have different methods and strategies operating in our schools, we all had the same goal: a year's growth for each of our students.

I respectfully disagree. If we are setting our sights for gifted students on a year's growth, we are aiming too low. As I have written before, if average students can learn 10 things in a given amount of time, our gifted students should be able to learn 13 or more things in that amount of time. This is, of course, a gross oversimplification, but I believe that, as a goal, it should hold up pretty well.

In fact, I would assert that, if we are doing things right in our classrooms, the gap between the highly able students and the less able students should get larger and larger each year. It is fine to talk about getting rid of the gaps among various ethnic groups, the gaps among different socioeconomic classes, and gaps between genders, but it is different altogether when we talk about the gaps between students of different abilities. The only way to close that gap is to hold down the top, while boosting the bottom.

As educators interested in gifted students, we should aim for more than a year's growth every year and an increase of the gap between the achievement levels of average students and gifted students.

Of course, this brings us to the problem of assessment. In general, I would say we know very little about gifted students' levels of ability or the change in that ability from year to year. Most of the tests just don't go high enough for proper baselines. I see great potential in the use of computerized adaptive testing, but I must admit, I haven't had much direct experience with it.

## Tuesday, April 24, 2012

## Friday, April 20, 2012

### High School Today

I frequently sub for math classes at the high school level. I am decent at math, though it has been a very long time since I had calculus, so that is a bit of a struggle. Thursday, I was teaching two calculus classes and two pre-calc classes (block scheduled) and today, Friday, I was in a different school district, teaching three algebra II classes and two intermediate algebra classes (and one study hall) (non-block scheduled).

Two things are relatively noteworthy: what's with the eating all day? Kids come into class with candy, breakfast, snacks, lunch, and drinks, no matter what time of day the class meets. Evidently the regular teachers permit this, but it completely astounds me. The kids have 30 minutes for lunch, but evidently they don't like to eat lunch at lunch time.

The other thing that I notice is that, with the exception of the calculus classes, most of the students are confused and not interested in even trying to find out why they don't understand their math. If I explain something on the board, even in response to a question, I have the feeling that I might as well be talking to the walls. No one is paying the least bit of attention - even the person who asked the question. I KNOW I am not that bad at explaining things. Over the years I have gotten enough direct feedback to know that I am actually reasonably good at it. But only if I am talking to students who are actually paying attention. It is impossible when they are shielding their faces so much that you can't tell whether they get it or not. I usually assume they are not getting it, but I leave feeling very confused myself: what is going on in their heads? Given that 80% of them are hooked up constantly to their electronics [why do teachers permit iPods all day? iPods that morph into iPhones and cell phones and electronics of any sort], my guess is that they aren't really there.

Two things are relatively noteworthy: what's with the eating all day? Kids come into class with candy, breakfast, snacks, lunch, and drinks, no matter what time of day the class meets. Evidently the regular teachers permit this, but it completely astounds me. The kids have 30 minutes for lunch, but evidently they don't like to eat lunch at lunch time.

The other thing that I notice is that, with the exception of the calculus classes, most of the students are confused and not interested in even trying to find out why they don't understand their math. If I explain something on the board, even in response to a question, I have the feeling that I might as well be talking to the walls. No one is paying the least bit of attention - even the person who asked the question. I KNOW I am not that bad at explaining things. Over the years I have gotten enough direct feedback to know that I am actually reasonably good at it. But only if I am talking to students who are actually paying attention. It is impossible when they are shielding their faces so much that you can't tell whether they get it or not. I usually assume they are not getting it, but I leave feeling very confused myself: what is going on in their heads? Given that 80% of them are hooked up constantly to their electronics [why do teachers permit iPods all day? iPods that morph into iPhones and cell phones and electronics of any sort], my guess is that they aren't really there.

### Which Is Worth More? and/or Multi-Potentiality

On Thursday, I was subbing at a high school not too far from where I live and after the class was done with the lesson, I got to talking with the students. The subject of after school jobs came up and how much money the students had to spend on various things. One girl said that she made a bit over $11.00 an hour at her job, which was a fairly easy one, according to her. Most of the time she just got to sit and play games on her phone, while occasionally helping customers.

Of course, then I got to thinking: How much do I get paid an hour? The subbing jobs vary in length, even the ones that are supposedly for a "full day". I get paid either for a full day or a half day. Full days, depending on the school district pay $90.00, $94.50, or $95.00. The job that day was for 7.5 hours, with 30 minutes for lunch. So, 7.0 hours @ $94.50 per day. So I get $13.50 per hour. After 4 years of undergraduate education, two master's degrees, and virtually all of a Ph.D., except the final signature, I am making barely more than a high school kid. And, by no stretch of the imagination would I characterize subbing as "easy".

Why don't I get a "real" job? Part of it has to do with multi-potentiality. I am good at a lot of things. I am especially good at learning stuff, so I kept wanting to go back to schools to learn more. And, as I did, I also tried out jobs that followed from the things I studied in schools. But each time, the thing that fascinated me was the learning process itself. So each time, in some way, I returned to teaching. I have taught everything from pre-school through grad school, from beginning swimming through computer modelling of proteins. But now, I am virtually unemployable. I am too old, I have too many degrees, my experiences are all different from what would be expected of someone who is looking for the positions I seek, and I don't exactly have a dedicated career path.

I enjoy subbing, actually. It is terribly hard some days, boring some days, but I like the variety and the challenge. But most of all, I enjoy analyzing all of the parameters of the job. How does this school compare to that school? What difference does socio-economics make? What about the linguistic background of the students? Why are the teachers friendly at one school and completely stand-offish at another school? Which curricula do I like? Which seem to work better for the students?

Years ago, my own children complained that I "had to analyze everything". I guess, yes, they are right. And subbing gives me a chance to analyze a lot of things. I just wish I made more money than a clerk in a pet store.

Of course, then I got to thinking: How much do I get paid an hour? The subbing jobs vary in length, even the ones that are supposedly for a "full day". I get paid either for a full day or a half day. Full days, depending on the school district pay $90.00, $94.50, or $95.00. The job that day was for 7.5 hours, with 30 minutes for lunch. So, 7.0 hours @ $94.50 per day. So I get $13.50 per hour. After 4 years of undergraduate education, two master's degrees, and virtually all of a Ph.D., except the final signature, I am making barely more than a high school kid. And, by no stretch of the imagination would I characterize subbing as "easy".

Why don't I get a "real" job? Part of it has to do with multi-potentiality. I am good at a lot of things. I am especially good at learning stuff, so I kept wanting to go back to schools to learn more. And, as I did, I also tried out jobs that followed from the things I studied in schools. But each time, the thing that fascinated me was the learning process itself. So each time, in some way, I returned to teaching. I have taught everything from pre-school through grad school, from beginning swimming through computer modelling of proteins. But now, I am virtually unemployable. I am too old, I have too many degrees, my experiences are all different from what would be expected of someone who is looking for the positions I seek, and I don't exactly have a dedicated career path.

I enjoy subbing, actually. It is terribly hard some days, boring some days, but I like the variety and the challenge. But most of all, I enjoy analyzing all of the parameters of the job. How does this school compare to that school? What difference does socio-economics make? What about the linguistic background of the students? Why are the teachers friendly at one school and completely stand-offish at another school? Which curricula do I like? Which seem to work better for the students?

Years ago, my own children complained that I "had to analyze everything". I guess, yes, they are right. And subbing gives me a chance to analyze a lot of things. I just wish I made more money than a clerk in a pet store.

## Wednesday, April 18, 2012

### The Great Raccoon Saga

A couple of days ago, my neighbor, whose house is connected to ours came over and told me that he thought there were squirrels in our attic. He pointed to a small hole in the siding and to a pile of insulation that he had swept up on his porch. He said that they had some bait for squirrels that made them kind of crazy and would make them leave; then he would board up the hole for me.

When I got home that evening, the hole was boarded up, but that night, I still heard scratching, as if the squirrels were still inside. I then started worrying that the squirrel(s) were trapped in the attic and would die of starvation. But then, a couple of mornings later, I noticed that the cats were really skittish. I went downstairs and found that all of the metal covers on the heater vents had been pulled up (4 different heater vents), my office area was ransacked, and the kitchen was messed up. The cat food was all gone.

I figured a burglar wouldn't bother with heater vents, but I couldn't figure out how (or why) a squirrel would pry up heater vents. So I looked around and spotted a bushy tail behind one of the chairs in the living room. I thought it might be Hobbes, my Maine Coon, until I noticed that Hobbes was right next to me. Hobbes is really big, but this raccoon was even bigger.

After panicking a bit, I tried calling Animal Control, and they said they would come right out, until they found out that the raccoon was INSIDE the house - they evidently don't deal with animals inside the house. So I called a company called Critter Control, but they wanted $199 just to come to the house.

That seemed like too much to me, so I took the car out of the garage, and coaxed Calvin (my other cat) downstairs and put both cats in the garage. I left one door open and put a trail of cat food leading to the door. Then I went to school (my one day a week job).

When I got home, my neighbor was outside, so I told him that he had been wrong - it wasn't squirrels, it was a big raccoon. He came in and we tried to find the raccoon. It was hiding under the bed in the south bedroom. He stuck a broom under the bed and managed to scare the raccoon out, and it ran downstairs. It avoided all of the open doors, however, and instead headed for the kitchen. When we tried to herd it toward a door, it slipped by us and ran back upstairs. This time, after we found it (in the middle bedroom), we closed all of the other doors and herded it downstairs, but again it avoided all of the open doors and hid in the bathroom.

I blockaded the way upstairs, but again, it squeezed by and ran upstairs. This time, though, there was no place to hide, so when we chased it downstairs again, it hid behind the chair again. Finally, with nowhere else to go, it went out the open door, climbed over the fence, and left.

The only problem is that I don't know if it was male or female. If it was a female, there could be babies in the attic. So we went to look to see if we could get up in the attic. But my neighbor had to leave, so I still haven't gotten up in the attic to check. But, next to the attic access is an air conditioning air return vent, with several bent metal slats. I am guessing that that is how the raccoon got out of the attic.

And now, the thing that amazes me is that I managed to sleep through all of this destruction the night before.

When I got home that evening, the hole was boarded up, but that night, I still heard scratching, as if the squirrels were still inside. I then started worrying that the squirrel(s) were trapped in the attic and would die of starvation. But then, a couple of mornings later, I noticed that the cats were really skittish. I went downstairs and found that all of the metal covers on the heater vents had been pulled up (4 different heater vents), my office area was ransacked, and the kitchen was messed up. The cat food was all gone.

I figured a burglar wouldn't bother with heater vents, but I couldn't figure out how (or why) a squirrel would pry up heater vents. So I looked around and spotted a bushy tail behind one of the chairs in the living room. I thought it might be Hobbes, my Maine Coon, until I noticed that Hobbes was right next to me. Hobbes is really big, but this raccoon was even bigger.

After panicking a bit, I tried calling Animal Control, and they said they would come right out, until they found out that the raccoon was INSIDE the house - they evidently don't deal with animals inside the house. So I called a company called Critter Control, but they wanted $199 just to come to the house.

That seemed like too much to me, so I took the car out of the garage, and coaxed Calvin (my other cat) downstairs and put both cats in the garage. I left one door open and put a trail of cat food leading to the door. Then I went to school (my one day a week job).

When I got home, my neighbor was outside, so I told him that he had been wrong - it wasn't squirrels, it was a big raccoon. He came in and we tried to find the raccoon. It was hiding under the bed in the south bedroom. He stuck a broom under the bed and managed to scare the raccoon out, and it ran downstairs. It avoided all of the open doors, however, and instead headed for the kitchen. When we tried to herd it toward a door, it slipped by us and ran back upstairs. This time, after we found it (in the middle bedroom), we closed all of the other doors and herded it downstairs, but again it avoided all of the open doors and hid in the bathroom.

I blockaded the way upstairs, but again, it squeezed by and ran upstairs. This time, though, there was no place to hide, so when we chased it downstairs again, it hid behind the chair again. Finally, with nowhere else to go, it went out the open door, climbed over the fence, and left.

The only problem is that I don't know if it was male or female. If it was a female, there could be babies in the attic. So we went to look to see if we could get up in the attic. But my neighbor had to leave, so I still haven't gotten up in the attic to check. But, next to the attic access is an air conditioning air return vent, with several bent metal slats. I am guessing that that is how the raccoon got out of the attic.

And now, the thing that amazes me is that I managed to sleep through all of this destruction the night before.

## Thursday, April 05, 2012

### Unclear on the Concept

I was subbing in a 6th grade recently and the warm-up question for the math lesson (directly from the teacher's manual) was something like this: A certain state has chosen to use the following format for their license plates: a single letter, followed by 5 digits. How many different license plates could they make that start with the letter A? The students were supposed to write their answers on their individual white boards and then show them to me to verify their answers.

The first answer I got was 28. I was completely baffled. Then came the other answers 15, 59, 25, etc., etc. NONE of the answers was even above 100, let alone near the correct answer. When I told the class (of 29 students) that their answers were all way too low, they started guessing above 100. But their guesses were completely (to me) random.

I decided to give them a hint: if they could use only 1 number after the A, you would have license plates A0, A1, A2, A3, ..., A9 - for 10 license plates. With two digits, you would have A00, A01, A02, ... A99 - giving you 100 license plates. They still didn't get it.

Pedagogically, I was so baffled by their lack of understanding, that I missed a golden opportunity to ask them what their reasoning was. I wish I had asked. "My bad", as they say. But now I am left wondering how they could possibly have thought that 28, 15, 59, or 25 could be anywhere near reasonable. This was a charter school, where the kids had to be delivered to the building in cars by their parents every day and picked up at the close of the day. How could they possibly think that 28 license plates starting with A, 28 starting with B, etc., would be enough? There are nearly that many cars at that one school in one day.

I was left thinking that the thinking habits of those kids were pretty bad.

Then came the lesson. It was on the number of degrees in specific turns. Though this wasn't in the teacher's manual, I had them stand up and demonstrate turning clockwise and counterclockwise. That isn't nearly as intuitive was it was in the days of all analog clocks. Our digital kids nowadays don't seem to have quite as much familiarity with the rotation of the hands on clocks. So I had them practice. First we established that a full turn, either CW or CCW was 360 degrees. Then that a quarter turn was 90 degrees and a half turn 180.

As I expected, a lot of the students mixed up CW and CCW, until we had practiced quite a bit. What surprised me a little was that several students refused to participate at all. This is a fairly strict and structured charter school and the non-compliance was unexpected. I didn't make a big deal of it, however, since it was an unplanned part of the lesson. I was more interested in the fact that this was actually a fairly difficult exercise for 6th graders.

That was just about the whole lesson - that and a few word problems. I was not terribly impressed with the curriculum, but this is a curriculum that I am not terribly fond of, anyway, so I am not going to name it. I was more interested in the seeming lack of comprehension of the students. They could do the rote problems, but the applications seemed to baffle them.

I would love to blame it on the curriculum, but I am not so sure that that is the problem. I have seen similar things with other curricula. What seems to me to be more evident is that kids are not particularly interested in making sense of things. They are willing to learn the arithmetic procedures - essentially just memorizing "how to do the problems", but they have very little (no?) interest in understanding why things work as they do. How have we gotten such disinterested kids? Was it always this way?

I remember hundreds of years ago, when I was a child, that I wasn't particularly interested in math. I could do the problems reasonably well, but the mathematics behind the arithmetic wasn't compelling to me. I don't remember if it was taught. I just remember that I was good at math, but, to me, that meant that I was good at arithmetic.

Then came my own 6th grade. The math teacher taught us about number bases - the reason behind carrying and borrowing when you get to the number of the base. It was, for me, a whole new ball game. Math became much more interesting. But that kind of enlightenment was sporadic. I remember asking several times in calculus classes how calculus was used, but I usually got either completely useless answers (It is used in everything!) or vague answers (In physics it is used to derive the laws of motion).

So now, I am wondering: it is counterproductive to try to explain mathematical reasoning to young children? Perhaps they just need to learn to do arithmetic very well. Then, in middle school or high school, with a bit more mature brains, they should take a class called number theory - and learn the reasoning behind the algorithms.

It is scary, though, to think that kids have so little practical understanding of math that they can't see the unreasonableness of the answer 28 for the number of license plates starting with A and having 5 numbers following the A.

The first answer I got was 28. I was completely baffled. Then came the other answers 15, 59, 25, etc., etc. NONE of the answers was even above 100, let alone near the correct answer. When I told the class (of 29 students) that their answers were all way too low, they started guessing above 100. But their guesses were completely (to me) random.

I decided to give them a hint: if they could use only 1 number after the A, you would have license plates A0, A1, A2, A3, ..., A9 - for 10 license plates. With two digits, you would have A00, A01, A02, ... A99 - giving you 100 license plates. They still didn't get it.

Pedagogically, I was so baffled by their lack of understanding, that I missed a golden opportunity to ask them what their reasoning was. I wish I had asked. "My bad", as they say. But now I am left wondering how they could possibly have thought that 28, 15, 59, or 25 could be anywhere near reasonable. This was a charter school, where the kids had to be delivered to the building in cars by their parents every day and picked up at the close of the day. How could they possibly think that 28 license plates starting with A, 28 starting with B, etc., would be enough? There are nearly that many cars at that one school in one day.

I was left thinking that the thinking habits of those kids were pretty bad.

Then came the lesson. It was on the number of degrees in specific turns. Though this wasn't in the teacher's manual, I had them stand up and demonstrate turning clockwise and counterclockwise. That isn't nearly as intuitive was it was in the days of all analog clocks. Our digital kids nowadays don't seem to have quite as much familiarity with the rotation of the hands on clocks. So I had them practice. First we established that a full turn, either CW or CCW was 360 degrees. Then that a quarter turn was 90 degrees and a half turn 180.

As I expected, a lot of the students mixed up CW and CCW, until we had practiced quite a bit. What surprised me a little was that several students refused to participate at all. This is a fairly strict and structured charter school and the non-compliance was unexpected. I didn't make a big deal of it, however, since it was an unplanned part of the lesson. I was more interested in the fact that this was actually a fairly difficult exercise for 6th graders.

That was just about the whole lesson - that and a few word problems. I was not terribly impressed with the curriculum, but this is a curriculum that I am not terribly fond of, anyway, so I am not going to name it. I was more interested in the seeming lack of comprehension of the students. They could do the rote problems, but the applications seemed to baffle them.

I would love to blame it on the curriculum, but I am not so sure that that is the problem. I have seen similar things with other curricula. What seems to me to be more evident is that kids are not particularly interested in making sense of things. They are willing to learn the arithmetic procedures - essentially just memorizing "how to do the problems", but they have very little (no?) interest in understanding why things work as they do. How have we gotten such disinterested kids? Was it always this way?

I remember hundreds of years ago, when I was a child, that I wasn't particularly interested in math. I could do the problems reasonably well, but the mathematics behind the arithmetic wasn't compelling to me. I don't remember if it was taught. I just remember that I was good at math, but, to me, that meant that I was good at arithmetic.

Then came my own 6th grade. The math teacher taught us about number bases - the reason behind carrying and borrowing when you get to the number of the base. It was, for me, a whole new ball game. Math became much more interesting. But that kind of enlightenment was sporadic. I remember asking several times in calculus classes how calculus was used, but I usually got either completely useless answers (It is used in everything!) or vague answers (In physics it is used to derive the laws of motion).

So now, I am wondering: it is counterproductive to try to explain mathematical reasoning to young children? Perhaps they just need to learn to do arithmetic very well. Then, in middle school or high school, with a bit more mature brains, they should take a class called number theory - and learn the reasoning behind the algorithms.

It is scary, though, to think that kids have so little practical understanding of math that they can't see the unreasonableness of the answer 28 for the number of license plates starting with A and having 5 numbers following the A.

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