### Tuesday, June 20, 2006

## spontaneity

I taught my last lesson of the summer today, and while I’m glad to be done, I do enjoy teaching. The topic was absolute value, something I had done well during the year. I tried to plan for it last night, but was more or less useless when it came to doing any work, so I gave up until this morning. (I also didn’t blog last night, so this post is a bit late. Did you highlight my name, Ben?)

Dave Molina let me borrow Radical Equations, a book by Bob Moses, describing the Algebra Project – a movement akin to the Civil Rights Movement pushing for mathematical fluency among minorities. To summarize, algebra is the new enfranchisement. Anyway, Moses’ whole idea is to teach algebra on field trips, specifically, on the T in Boston. There are obvious links to distance, displacement, direction, and the like.

This morning I decided we would take a trip down the halls. Our “field trip” consisted of three stops. First we stopped at a poster with the word “equality” written on it. My students discussed the idea of equality in mathematical terms. We then jumped off to the more general meaning of equality. They came up with examples, counterexamples, and explanations of various situations in which equality a central issue. Next, we walked to the trophy case and talked about the many ways in which basketball relates to math. They had to read some old newspaper clippings to ask questions of mine and, of course, we talked about the Dallas-Miami game that is on tonight. Our last stop was a poster with the word “inequality.” We had the same discussion about inequality that we did about equality.

One student was asked to write down anything interesting he saw or heard, while another student was counting the number of steps we took in each direction. Other than these two students, nobody else was required to do anything but take part in the discussions.

When we came back to the room, I drew a one-dimensional (line) picture of the trip we took. I labeled each stop on the trip and we briefly summarized what we talked about at each one. The step-counter filled in the number of steps in each direction on the picture, and I proceeded to ask a few questions leading in to absolute value.

How far was our end point from our starting point?

What was the distance we all walked during the trip?

Why are these answers not the same?

In all, the trip idea was successful. Math students need to move around and do things, even if the teacher is a good lecturer. And this got them thinking about distances in very real terms. After that, the link to absolute value was easy.

Dave Molina let me borrow Radical Equations, a book by Bob Moses, describing the Algebra Project – a movement akin to the Civil Rights Movement pushing for mathematical fluency among minorities. To summarize, algebra is the new enfranchisement. Anyway, Moses’ whole idea is to teach algebra on field trips, specifically, on the T in Boston. There are obvious links to distance, displacement, direction, and the like.

This morning I decided we would take a trip down the halls. Our “field trip” consisted of three stops. First we stopped at a poster with the word “equality” written on it. My students discussed the idea of equality in mathematical terms. We then jumped off to the more general meaning of equality. They came up with examples, counterexamples, and explanations of various situations in which equality a central issue. Next, we walked to the trophy case and talked about the many ways in which basketball relates to math. They had to read some old newspaper clippings to ask questions of mine and, of course, we talked about the Dallas-Miami game that is on tonight. Our last stop was a poster with the word “inequality.” We had the same discussion about inequality that we did about equality.

One student was asked to write down anything interesting he saw or heard, while another student was counting the number of steps we took in each direction. Other than these two students, nobody else was required to do anything but take part in the discussions.

When we came back to the room, I drew a one-dimensional (line) picture of the trip we took. I labeled each stop on the trip and we briefly summarized what we talked about at each one. The step-counter filled in the number of steps in each direction on the picture, and I proceeded to ask a few questions leading in to absolute value.

How far was our end point from our starting point?

What was the distance we all walked during the trip?

Why are these answers not the same?

In all, the trip idea was successful. Math students need to move around and do things, even if the teacher is a good lecturer. And this got them thinking about distances in very real terms. After that, the link to absolute value was easy.

### Monday, June 19, 2006

## wik-ed

Between two metanodes is a vectortext.

## Palindromic Plants

With the exception of Dr. Mullins’ class, an overwhelming majority of the hours we’ve spent in the “graduate” program at Ole Miss have been less than unproductive. That’s right, I said less than UNproductive. Professors don’t know how to handle the new Teacher Corps. It’s a problem with differentiation. Our strong academic, and in many cases personal, backgrounds make us a different animal entirely than traditional School of Education students. And this is exactly why the MTC exists: to recruit college graduates with exceptional content knowledge that have not yet suffered the lobotomy of education classes. But our professors are having a problem with differentiation – teaching to a wide range of ability levels. To some extent, this is understandable. Differentiation, in my opinion, is the single most difficult task as a teacher. It is my biggest failure. But I had zero years of experience. Our professors, however, ought to be able to differentiate between Teacher Corps members and everyone else.

Let me briefly state that this is not an attack on the program, nor am I venting my frustrations. I’m not ready to burn those bridges yet. This is also not a personal attack on our current professor (though I cringe at calling him by such a distinguished title).

We are currently enrolled in an online class. The actual title has slipped my mind, but please allow me to paraphrase: “The Internet: It’s Good and You Should Use It.” Granted, not all the higher ups were keen on requiring this class, but the fact remains we are responsible for completing the assignments. In theory, I have no problem with online classes. But let me outline the absurdity we have thus encountered.

1. Our professor refuses to meet with us and has not given us sufficient methods of contact. We must e-mail him, and if he gets back to us (he doesn’t always) it is certainly not in a timely manner. It’s as if this guy doesn’t exist, except to scold (not criticize, more on that below) our attempts at adding substance to very unsubstantial content.

2. Take a look at the rubric for one of the weekly assignments (below). Notice that there are no explanations for the assigning of points, nor is it clear where the cutoff for acceptable work lies. Based on my rudimentary knowledge of rubrics, this is a pathetic attempt at objectivity. And I think grading objectively (let’s assume it can even be done) is misguided! Okay, so five is the best and one is the worst. How do I get a five? A one? If you are claiming to be objective when grading (and this is the point of a rubric) than the rubric needs to be crystal clear. If you grade subjectively – and let’s be honest, this is the only way we grade – your expectations of good work also need to be lucid. This rubric fails on both accounts.

3. Our professor has personally attacked us. Part of the course requirements is to maintain an online discussion forum amongst each other. We post our comments on the reading and discuss various issues that are raised. A number of us pursued a liberal arts education in which the process of learning is often more highly regarded than the material actually learned. Thus, we are predisposed to engage in philosophical discourse by using a given text as a jumping off point. In our “community of learning” (our professor’s language) we would rather hash out the overarching concepts. But our professor claims that our discussion is a waste of time and contains no substance. Here is one of his comments:

“Nice philisophical [sic] ranting but can you get to your point?”

Our professor claims we are missing the point, not actually saying anything substantive. But the real problem is that the curriculum thus far has no substance! We’re doing our best to discuss the reading, but in order to do so we have to transcend the jargon and inane statements such as “experts have expertise.” Our professor is suppressing intellectual discourse…

“Okay, guys, you sure are loading the website up without saying anything. So is that what you do in your classes with your students? Have these great philisophical [sic] discussions and say nothing of any real substance. If any of you have bothered to look, the reading material comes from classroom research done by the National Academies of Science. I’d like to think that they weren’t just a committee of folks posting philosophical rants like I’ve been reading.”

“But the rest of you miss the point whether on purpose or not. […] Life is not about being automotrons [sic] popping out the correct answer, it’s about facing fluid problems and having the skills to think for yourself and solve them.”

Thanks, professor, for ensuring future teachers learn to think for themselves and are not scolded for metapedagogy!

Let me briefly state that this is not an attack on the program, nor am I venting my frustrations. I’m not ready to burn those bridges yet. This is also not a personal attack on our current professor (though I cringe at calling him by such a distinguished title).

We are currently enrolled in an online class. The actual title has slipped my mind, but please allow me to paraphrase: “The Internet: It’s Good and You Should Use It.” Granted, not all the higher ups were keen on requiring this class, but the fact remains we are responsible for completing the assignments. In theory, I have no problem with online classes. But let me outline the absurdity we have thus encountered.

1. Our professor refuses to meet with us and has not given us sufficient methods of contact. We must e-mail him, and if he gets back to us (he doesn’t always) it is certainly not in a timely manner. It’s as if this guy doesn’t exist, except to scold (not criticize, more on that below) our attempts at adding substance to very unsubstantial content.

2. Take a look at the rubric for one of the weekly assignments (below). Notice that there are no explanations for the assigning of points, nor is it clear where the cutoff for acceptable work lies. Based on my rudimentary knowledge of rubrics, this is a pathetic attempt at objectivity. And I think grading objectively (let’s assume it can even be done) is misguided! Okay, so five is the best and one is the worst. How do I get a five? A one? If you are claiming to be objective when grading (and this is the point of a rubric) than the rubric needs to be crystal clear. If you grade subjectively – and let’s be honest, this is the only way we grade – your expectations of good work also need to be lucid. This rubric fails on both accounts.

3. Our professor has personally attacked us. Part of the course requirements is to maintain an online discussion forum amongst each other. We post our comments on the reading and discuss various issues that are raised. A number of us pursued a liberal arts education in which the process of learning is often more highly regarded than the material actually learned. Thus, we are predisposed to engage in philosophical discourse by using a given text as a jumping off point. In our “community of learning” (our professor’s language) we would rather hash out the overarching concepts. But our professor claims that our discussion is a waste of time and contains no substance. Here is one of his comments:

“Nice philisophical [sic] ranting but can you get to your point?”

Our professor claims we are missing the point, not actually saying anything substantive. But the real problem is that the curriculum thus far has no substance! We’re doing our best to discuss the reading, but in order to do so we have to transcend the jargon and inane statements such as “experts have expertise.” Our professor is suppressing intellectual discourse…

“Okay, guys, you sure are loading the website up without saying anything. So is that what you do in your classes with your students? Have these great philisophical [sic] discussions and say nothing of any real substance. If any of you have bothered to look, the reading material comes from classroom research done by the National Academies of Science. I’d like to think that they weren’t just a committee of folks posting philosophical rants like I’ve been reading.”

“But the rest of you miss the point whether on purpose or not. […] Life is not about being automotrons [sic] popping out the correct answer, it’s about facing fluid problems and having the skills to think for yourself and solve them.”

Thanks, professor, for ensuring future teachers learn to think for themselves and are not scolded for metapedagogy!

### Thursday, June 08, 2006

## changes

This year I am restructuring the curriculum. After spending the better part of a year attempting to fill in knowledge gaps in my 7th grade students, I have come to the conclusion that the major problem isn’t lack of knowledge. My students knew rules and steps to solving problems, however the information was never presented in a way that emphasizes connections and continuity between units. Specifically, fractions, decimals, and percents were all more or less understood in isolation. Lacking, though, was comprehension of the equality of these concepts.

My plan is to first ground my students with a solid introduction to the number line. We will explore questions such as: How many numbers are there? Are all numbers greater than zero? Are there different types of numbers? How do we know when one number is greater than another? Is there a way of organizing numbers? Asking these questions to my summer school students was an excellent introduction to the concepts I expect to cover.

After developing the foundation of numbers and the number line I will introduce each concept one at a time. First decimals, then fractions and mixed numbers, followed by percents. The idea is to first include decimals on the number line. After students understand that decimal numbers fit in between the integers we will move onto fractions. Fractions will be introduced as a new concept and students will learn to manipulate and operate on fractions. Then they too will be incorporated on the number line. I will guide my students to connect locations of common fractions and their equivalent decimal numbers on the number line. My hope is that students will be able to apply the continuity between fractions, decimals, and percents to word problems and real world scenarios.

I failed to introduce the number line until the last nine weeks when my pacing guide said I was supposed to teach integers and negative numbers. It was an invaluable tool for comparing, adding, and subtracting negative integers and I believe it will prove quite useful for connecting basic concepts as well.

My plan is to first ground my students with a solid introduction to the number line. We will explore questions such as: How many numbers are there? Are all numbers greater than zero? Are there different types of numbers? How do we know when one number is greater than another? Is there a way of organizing numbers? Asking these questions to my summer school students was an excellent introduction to the concepts I expect to cover.

After developing the foundation of numbers and the number line I will introduce each concept one at a time. First decimals, then fractions and mixed numbers, followed by percents. The idea is to first include decimals on the number line. After students understand that decimal numbers fit in between the integers we will move onto fractions. Fractions will be introduced as a new concept and students will learn to manipulate and operate on fractions. Then they too will be incorporated on the number line. I will guide my students to connect locations of common fractions and their equivalent decimal numbers on the number line. My hope is that students will be able to apply the continuity between fractions, decimals, and percents to word problems and real world scenarios.

I failed to introduce the number line until the last nine weeks when my pacing guide said I was supposed to teach integers and negative numbers. It was an invaluable tool for comparing, adding, and subtracting negative integers and I believe it will prove quite useful for connecting basic concepts as well.

### Thursday, June 01, 2006

## student

In and out of psychiatric wards; completely dysfunctional family life; behavioral problems. These are not qualities one would expect from a young math genius…or maybe they are. Time and again, individuals who are able to wrestle with the complexities of math independent of a tutor have progressed mathematical thinking to a higher plane. Often, they are misfits – socially unable to adapt or interact with their environment. Some believe it is the level of abstraction necessary to advance ideas in math that prevent them from normal psychological development. Whatever the reason, the fact remains that genius and social ability do not often go hand in hand.

A student of mine fits the description above. He has been tested often for mental illness and psychological disorders. His family is a wreck. And he has spent more days at home suspended from school for fighting than he has in my class. Nobody teaches this kid math, yet somehow he just gets it. His test scores are among the highest in his grade and on the rare occasion that he graces my class with his presence he is able to figure out and understand some pretty high level mathematics.

In no small way, I wish the education system would get out of his way so that he can give real thinking a try. Administrators, teachers, and students are always pushing his buttons (of which there are many) and, being a loose cannon, he loses it. One of his teachers even refers to him as “Columbine.” Clearly, he is unstable. Through no fault of his own, he doesn’t know how to interact with other people. But it is also a terrible waste to keep him in a system set up for students like him to fail.

The tragedy of it all is that nobody has told him what a gift he has. Rather than nurturing his intellect and working with his needs, schools send him home or keep him in the office – apart from the very people that are able to cultivate his intellect.

And with this last sentence I should meet the word requirement.

A student of mine fits the description above. He has been tested often for mental illness and psychological disorders. His family is a wreck. And he has spent more days at home suspended from school for fighting than he has in my class. Nobody teaches this kid math, yet somehow he just gets it. His test scores are among the highest in his grade and on the rare occasion that he graces my class with his presence he is able to figure out and understand some pretty high level mathematics.

In no small way, I wish the education system would get out of his way so that he can give real thinking a try. Administrators, teachers, and students are always pushing his buttons (of which there are many) and, being a loose cannon, he loses it. One of his teachers even refers to him as “Columbine.” Clearly, he is unstable. Through no fault of his own, he doesn’t know how to interact with other people. But it is also a terrible waste to keep him in a system set up for students like him to fail.

The tragedy of it all is that nobody has told him what a gift he has. Rather than nurturing his intellect and working with his needs, schools send him home or keep him in the office – apart from the very people that are able to cultivate his intellect.

And with this last sentence I should meet the word requirement.