I know some of our math teachers at the high school level (mostly for algebra 1) are urged to do what they can to make sure a student passes. So if a kid has a 68%, .... "well, can't they just come in and do some make-up work and make it a 70% (which is passing in TX)?"
Now, teachers I know help the students in any way they can, and it's REALLY possible to pass class if you do your work and turn in homework and ask for help and get tutoring if you need it and pay attention in class. So I'm guessing that if the student has a 68%, then more often than not, it's because the student just REALLY doesn't get it (content) or REALLY doesn't get it (work ethic). Passing this kid along to the next level is not doing ANYONE any good: the student, the next teacher, the students in the next class this student would go to.
Then I was thinking about the students that were coming to us from the middle school. There are some kids that REALLY struggle with the math. They should not have passed their middle school classes. And in fact, this was supposed to be the first year that if they didn't pass the mandated NCLB test, then they would be retained. Hmmph.
We have a new teacher at our high school that taught at the middle school last year. This is what she relayed to me. All year long the teachers told the kids that they needed to pass the test, or they'd be retained. They drilled it into them. Then kids failed. Then the administration put them in extra tutoring and let them test again. Then if they failed, they had to take summer school and take the test again. Then MAGICALLY, all the kids passed. Poof. Let's move them on to high school and continue their struggles in harder classes when they haven't mastered the basics. Grrrrrrr.
Okay, just a big vent. I don't know what could stop this "passing along". Maybe we need to track the students in high school who are not successful and probe them about their middle school experience and see how many of those were passed along and how they're doing now. Maybe we could take that data to the middle school pass-along-ers. Would that help? I don't know.
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Monday, October 27, 2008
Wednesday, October 22, 2008
Algebra 1 Skills
I'm loving teaching (a 1 year course of ) Algebra 1 for the first time. It's fun to be the first person to show the kids all the stuff I take for granted they know later on.
Recently, we started solving one-step then two-step equations. Maybe everyone does this, but I found it helpful to start with a goofy story. I told them I bought them a special present (it was just some random object in the room), and I wanted to give it to them, but I first had to wrap it up. So I put it in a box, then I put the lid on the box (some plastic tub I had laying around), then since it was see-through, I wanted to wrap it up (I had an old sheet laying around), and then I had to put a bow on it (some random string I cut up). Then I asked them what were the steps to what I had just done. They repeated them. Then I asked them, if they wanted to get the present out, what specifically did they have to do and in what order. So we went through untieing the bow, unwrapping, opening the lid, and taking the present out of the box.
Then I linked this to a 2 step equation on how you have to undo what's being done to x and in the opposite order that you had "wrapped up" x. This seemed to work (so far).
A few days later we worked on combining like terms and "challenging" distributive property types like:
5 - 2(3x - 4) = 20. YEESH! That distributing the negative was a challenge. I explained it 3 different ways, and different ways seemed to work for different kids. One kid was okay with: okay, cover up the "5" and just look at the "-2(3x-4)", what would it become? Then it's just "adding 5 in front of that operation".
I'll see how they did on homework tomorrow.
Recently, we started solving one-step then two-step equations. Maybe everyone does this, but I found it helpful to start with a goofy story. I told them I bought them a special present (it was just some random object in the room), and I wanted to give it to them, but I first had to wrap it up. So I put it in a box, then I put the lid on the box (some plastic tub I had laying around), then since it was see-through, I wanted to wrap it up (I had an old sheet laying around), and then I had to put a bow on it (some random string I cut up). Then I asked them what were the steps to what I had just done. They repeated them. Then I asked them, if they wanted to get the present out, what specifically did they have to do and in what order. So we went through untieing the bow, unwrapping, opening the lid, and taking the present out of the box.
Then I linked this to a 2 step equation on how you have to undo what's being done to x and in the opposite order that you had "wrapped up" x. This seemed to work (so far).
A few days later we worked on combining like terms and "challenging" distributive property types like:
5 - 2(3x - 4) = 20. YEESH! That distributing the negative was a challenge. I explained it 3 different ways, and different ways seemed to work for different kids. One kid was okay with: okay, cover up the "5" and just look at the "-2(3x-4)", what would it become? Then it's just "adding 5 in front of that operation".
I'll see how they did on homework tomorrow.
Friday, October 17, 2008
Teaching a Class vs Tutoring one Student
In precalculus we recently learned how to solve triangles. This involved such equations as sin 20 = 5/x, or tan 35 = x/7, or cos (theta) = 6/11. From past experience I know there are students that forget how to solve things. Once you throw "sin 20" or "tan (theta)" into the mix, all their algebra knowledge goes out the window. So I carefully walk through and remind them of how to isolate variables, and assure them that "sin 20" is JUST a number, and warn them that, "no, you are not multiplying 'sin' by '20', you must keep them as a unit". And then, WHOA, stop the presses, x is in the denominator?? Well, why don't I just take 'sin 20 = 5/x, and divide by 5 and POOF, an x is left in the numerator on the right hand side.
Anyhow, we walk through this, and most kids get it. But then I see one student struggling and struggling and getting more frustrated when I'm going through the different types of examples because he doesn't know why things change up and why I'm "solving differently" for the different situations. Well, he came in for tutoring this past morning, and by probing his mind, I see that he never internalized the algebra steps: what's being done to x? how do you undo it? do the same thing to both sides of the equation.
He would look at an equation like 3x - 7 = 5, and reason it out in his head: well, something minus 7 is 5, so that something must be 12. Then 3 times something is 12, so that something, or x, must be 4. Great reasoning, but then he never had to learn or practice: add 7 to both sides. divide both sides by 3. And now when he sees: sin x - 7 = 11/3 (or something like that), his old methods don't serve him well. I believe we got him to the point where now he can do it. I'm so glad he came in for tutoring, so I could take the time to probe deeper as to where his difficulties lie (lay/laid/???). I don't have that luxury in class with 33 other students of all levels waiting for "teaching".
Anyhow, we walk through this, and most kids get it. But then I see one student struggling and struggling and getting more frustrated when I'm going through the different types of examples because he doesn't know why things change up and why I'm "solving differently" for the different situations. Well, he came in for tutoring this past morning, and by probing his mind, I see that he never internalized the algebra steps: what's being done to x? how do you undo it? do the same thing to both sides of the equation.
He would look at an equation like 3x - 7 = 5, and reason it out in his head: well, something minus 7 is 5, so that something must be 12. Then 3 times something is 12, so that something, or x, must be 4. Great reasoning, but then he never had to learn or practice: add 7 to both sides. divide both sides by 3. And now when he sees: sin x - 7 = 11/3 (or something like that), his old methods don't serve him well. I believe we got him to the point where now he can do it. I'm so glad he came in for tutoring, so I could take the time to probe deeper as to where his difficulties lie (lay/laid/???). I don't have that luxury in class with 33 other students of all levels waiting for "teaching".
Sunday, October 12, 2008
Graph Savvy
I've had former students come back to visit lately and they talked about the expectations of their college professors. One student who's in calculus says that the professor expects them to have a solid, quick-recall grasp of basic graphs (what does the sine graph look like? the square root function? the tangent graph?, etc). Yeesh, note to self on not just teaching that for one week but reinforcing and recalling it periodically.
Then that reminded me of a dream I had the other night. I like memory tools, and I dreamt that one way for the kids to remember the square root of x graphs is that, "SEE, the graph LOOKS like the square root symbol". Nerd alert. I'm going to try that this year.
Then I also started thinking of how to make all these graphs become second nature to the kids. Maybe periodically, and consistently, I can pull out "cards" with (say) pink cards graphs and yellow cards the functions, and maybe they can have a running contest with themselves and keep track of the time it takes them to match them up, and eventually (months? weeks?) we can have a "beat the clock or teacher" contest of a match up game.
I also want them to have the quickness of thought as to, "okay, I don't remember this shape, but hey! let me quickly make a table and plot the points to help myself (without the teacher prompting me or just sitting there and not doing anything)". Hmmmm, how to teach this skill. ... Maybe also a periodic and consistent "game" of "here's a weird function on the board, quick like a bunny, find 5 points on the graph or plot 5 points or something".
Then that reminded me of a dream I had the other night. I like memory tools, and I dreamt that one way for the kids to remember the square root of x graphs is that, "SEE, the graph LOOKS like the square root symbol". Nerd alert. I'm going to try that this year.
Then I also started thinking of how to make all these graphs become second nature to the kids. Maybe periodically, and consistently, I can pull out "cards" with (say) pink cards graphs and yellow cards the functions, and maybe they can have a running contest with themselves and keep track of the time it takes them to match them up, and eventually (months? weeks?) we can have a "beat the clock or teacher" contest of a match up game.
I also want them to have the quickness of thought as to, "okay, I don't remember this shape, but hey! let me quickly make a table and plot the points to help myself (without the teacher prompting me or just sitting there and not doing anything)". Hmmmm, how to teach this skill. ... Maybe also a periodic and consistent "game" of "here's a weird function on the board, quick like a bunny, find 5 points on the graph or plot 5 points or something".
Wednesday, October 08, 2008
Burning Questions
What is it with high school boys, the insides of their noses, and their index fingers?
How fast does a teacher shudder at night when they see a full moon, wondering how the next day will go?
Why do I get less work done when my last period is a prep period as opposed to periods when I'm rushing to be ready for my next class?
Who is the hobgoblin that comes and strews papers to be graded and dealt with and sorted all over my classroom the very next day after I clean up the last mess?
When is the timing right to drink large amounts of water (to stay healthy) during the school day?
How fast does a teacher shudder at night when they see a full moon, wondering how the next day will go?
Why do I get less work done when my last period is a prep period as opposed to periods when I'm rushing to be ready for my next class?
Who is the hobgoblin that comes and strews papers to be graded and dealt with and sorted all over my classroom the very next day after I clean up the last mess?
When is the timing right to drink large amounts of water (to stay healthy) during the school day?
Saturday, October 04, 2008
Out of School Etiquette
This Saturday my husband and I went to "the fields" to watch our school's rocket science class students launch their first-attempt rockets. There were a mix of students and teachers there, and I introduced my husband to the 2 teachers, but then while I was talking to the students (many that are also mine), I didn't introduce my husband. I always feel goofy (and maybe not quite adult even though I'm in my 40's) and the words don't seem right:
"Student A, this is my husband Mr. ___" (seems stuffy) or
"Student A, this is my husband _____ _____" (I guess this would have been the best option: first name last name) or
"Student A, this is my husband ____" (first name only seems "wrong")
So like any goofball, I just didn't introduce him at all to any students. Then that feels wrong now, like he's just this shadow following me around while I talk with the students. Okay. In the future, first name last name. Do It!
"Student A, this is my husband Mr. ___" (seems stuffy) or
"Student A, this is my husband _____ _____" (I guess this would have been the best option: first name last name) or
"Student A, this is my husband ____" (first name only seems "wrong")
So like any goofball, I just didn't introduce him at all to any students. Then that feels wrong now, like he's just this shadow following me around while I talk with the students. Okay. In the future, first name last name. Do It!