We've recently worked through those laws in precalculus. This is my 5th year teaching them at this school, and I think I've finally settled on a way to present the "ambiguous ... A.S.S. case" for the Law of Sines.
This I've done before and this year: I present a sheet that has 3 situations drawn in which I have a partially made ASS case but ask them to use their rulers to complete the triangle with the last "S". For example, for triangle ABC. I've drawn a long line for the "base" of the triangle representing side b. I've measured and drawn in angle A of 31 degrees and side c of 5 cm. B is at the top of the triangle, and they're to draw segment BC of length 3 cm to complete the triangle. I eventually get them to see that there are 2 triangles they could draw. Then we see how this plays out without drawing and why there are 2 triangles mathematically.
I also do this for the cases where there is one and zero triangles.
In the past, I used to make a big case of how you could tell there was a 2nd triangle by looking at the given information and if the 2nd "S" in ASS info given is longer or shorter than the 1st "S" then you make some decisions. Hmmm, made sense to me, and that's how I still do it myself, but the students weren't always successful.
This year, I just said: after you solve for your 1st angle, try for the 2nd option of that same angle and "see if it works" (you can add up to 180). That seemed to work for more students.
We also just did Law of Cosines. I had everyone create their own scalene, non right triangles and measure all sides and angles. Then we plugged into the formula to see why it may work (instead of just proving it to them or just showing them the formula). I always hesitate with this measuring thing because the numbers never work out EXACTLY. But I figure, it's a good opportunity to discuss human error and measurement tools and degrees of accuracy and such. I make a game out of it and make my own triangle and ask if they can beat my "closeness". Depending on the class, I was off by anywhere from 0.3 to 1.5 units when the 2 sides should have been equal. I blamed my aging eyes (cough cough).
Friday, November 28, 2008
Sunday, November 23, 2008
Cheating
Ackh! It's a few weeks until the students have to start thinking about and studying for (cough cough) finals. For the past couple of class periods in precalculus I haven't really gone over new material since they were getting ready for a test on graphing all the trigonometric functions. Instead of not assigning homework, I decided to assign OLD topics and grade on accuracy instead of just completion like I normally do.
The first assignment was on function notation, and the current one is on function composition. I gave them the stern teacher face of "don't show up and say you don't know how to do it. Look at your old notes and look at the book examples and look at the web, but LOOK and recall and do something for yourself." Gee. My face is expressive.
Anyway. I was giving the graphing test on Friday, and the homework was due, but I didn't collect it until after the test. Some students finished early and were doing various things. Two friends started to look suspicious. I saw one pass back a paper to the other. Then I saw the other surreptitiously copying her paper. Crap. I walked over and quietly said, "do not do that! That is a zero for both of you. Do your own work.". I was so mad. First for her doing it, and equally for thinking that I'm so oblivious, that I can't notice what's going on.
I debated talking to both after class (I didn't). I had the whole speech prepared in my head about how once you lose someone's trust, it's very hard to gain it back. But I settled for the unhappy glances their way and the ignoring of them and a total change of my demeanor towards them after the test was over, and we were going over other concepts. I'd had a hard enough week, and I didn't want to deal with more stress.
The first assignment was on function notation, and the current one is on function composition. I gave them the stern teacher face of "don't show up and say you don't know how to do it. Look at your old notes and look at the book examples and look at the web, but LOOK and recall and do something for yourself." Gee. My face is expressive.
Anyway. I was giving the graphing test on Friday, and the homework was due, but I didn't collect it until after the test. Some students finished early and were doing various things. Two friends started to look suspicious. I saw one pass back a paper to the other. Then I saw the other surreptitiously copying her paper. Crap. I walked over and quietly said, "do not do that! That is a zero for both of you. Do your own work.". I was so mad. First for her doing it, and equally for thinking that I'm so oblivious, that I can't notice what's going on.
I debated talking to both after class (I didn't). I had the whole speech prepared in my head about how once you lose someone's trust, it's very hard to gain it back. But I settled for the unhappy glances their way and the ignoring of them and a total change of my demeanor towards them after the test was over, and we were going over other concepts. I'd had a hard enough week, and I didn't want to deal with more stress.
Tuesday, November 18, 2008
November Slump
Sheesh. I forget this happens every year. I get super depressed and down on various kid behavior and teaching and the stress and all the whole bundle every year at about this time. I think I should make a cross-stitch sampler to remind myself that this will pass, and things do get better SOON.
It's been especially bad this year. We are mandated from above to have meetings up the wazoo that suck the life out of our planning periods. Then we are dictated to teach to the "exit exam" in a specified way and eat into our regular curriculum to do this. Then .... then .... then.
I think I have enough seniority to say "phhhphflt" and do what I think is best for the students: a type of don't-ask-don't-tell policy. My rationalization is that if questioned, I'll have a valid reason for why I think what I'm doing is the best for my kids.
On a positive note. My students are mostly great. Highlights:
One shared with me her way of remembering the sine and cosine graphs. She's Hispanic, and "sin" in Spanish means "without", so that's the one that is zero at zero. And "con" in Spanish means "with", so that's the one that has a value at zero.
A day or so ago we were doing the ambiguous case of "Law of Sines", and for the "no triangle case". I wanted to show them that in the A.S.S. case when they're first solving for the angle, the ratio of sides is 1._____. So I asked what happened on their calculators when they tried to solve sin x = 1._____. They said, "ERROR". Then I said, okay, close your eyes and picture the graph of y = sin x. My goal was to get them to see that the largest it could be was 1. So I asked, after they were thinking for a while on what the graph looks like, "what do you see?". One kid answered, "ERROR".
Anyway. Some of us got together tonight as a math department and went out for a drink after work and destressed and laughed and such. That will go a long way to making the rest of the 6 weeks livable.
It's been especially bad this year. We are mandated from above to have meetings up the wazoo that suck the life out of our planning periods. Then we are dictated to teach to the "exit exam" in a specified way and eat into our regular curriculum to do this. Then .... then .... then.
I think I have enough seniority to say "phhhphflt" and do what I think is best for the students: a type of don't-ask-don't-tell policy. My rationalization is that if questioned, I'll have a valid reason for why I think what I'm doing is the best for my kids.
On a positive note. My students are mostly great. Highlights:
One shared with me her way of remembering the sine and cosine graphs. She's Hispanic, and "sin" in Spanish means "without", so that's the one that is zero at zero. And "con" in Spanish means "with", so that's the one that has a value at zero.
A day or so ago we were doing the ambiguous case of "Law of Sines", and for the "no triangle case". I wanted to show them that in the A.S.S. case when they're first solving for the angle, the ratio of sides is 1._____. So I asked what happened on their calculators when they tried to solve sin x = 1._____. They said, "ERROR". Then I said, okay, close your eyes and picture the graph of y = sin x. My goal was to get them to see that the largest it could be was 1. So I asked, after they were thinking for a while on what the graph looks like, "what do you see?". One kid answered, "ERROR".
Anyway. Some of us got together tonight as a math department and went out for a drink after work and destressed and laughed and such. That will go a long way to making the rest of the 6 weeks livable.
Sunday, November 16, 2008
The Power of Off-The-Cuff Words
Just recently, my memory was refreshed as to how seriously students take what we say. Things I just sort of blurt out because I think they're the right thing to say seem to make a difference.
For example, I have this incredibly smart and hard-working student in BC Calculus this year. Last year I had her for precalculus preAP. Back then she was talking about her math choices for the next year, and I mentioned that she should definitely take BC calculus as opposed to AB because she had such a great work ethic and cared about really understanding topics and such. I think I also said something to the effect that it would be a waste of her time to take AB which would not challenge her as much. I did truly believe this, but I didn't know how much weight this would carry. Well, several times this year as she's bemoaning the fact of how hard it is (in a good-natured I'll-still-muddle-through sort of way), she kept mentioning the fact that I made her take BC calculus. Hmph.
I have another student in AB Calculus. I also had him in precalculus preAP last year. He's an interesting, intense, strange, slow-working, self-stressing type of person. I really did not think he could manage the pace of calculus with how much he frets over EVERYTHING. He asked last year if he should take calculus, and I hate to discourage students/people, because, really, what do I know, maybe they will surprise themselves and me and if not, then the experience will be a learning one one way or another. So here he is in AB calculus this year. He is struggling and stressing and such all along. He came to me after school one day and said he wanted to drop out of the class. I said that well, the decision was his, but I think it would be a shame if he did because then if anything hard came up in the future then his first idea would be just to quit because it was too hard. I also said that he was smart enough to handle it, and personally I would stick it out. (inside, I think he can do it, and he just has to approach it in a different way, but I DEFINITELY know that if he dropped, he'd be WAY less stressed than he is now). Well, anyway, he decided to stay, and later wrote me a note thanking me for believing in him and in his ability.
I guess the point of all this is to err on the side of pushing the kids to do their best and to do things they don't think they could do or think possible. Maybe it will open up opportunities for them and make them think of themselves in ways they didn't in the past.
For example, I have this incredibly smart and hard-working student in BC Calculus this year. Last year I had her for precalculus preAP. Back then she was talking about her math choices for the next year, and I mentioned that she should definitely take BC calculus as opposed to AB because she had such a great work ethic and cared about really understanding topics and such. I think I also said something to the effect that it would be a waste of her time to take AB which would not challenge her as much. I did truly believe this, but I didn't know how much weight this would carry. Well, several times this year as she's bemoaning the fact of how hard it is (in a good-natured I'll-still-muddle-through sort of way), she kept mentioning the fact that I made her take BC calculus. Hmph.
I have another student in AB Calculus. I also had him in precalculus preAP last year. He's an interesting, intense, strange, slow-working, self-stressing type of person. I really did not think he could manage the pace of calculus with how much he frets over EVERYTHING. He asked last year if he should take calculus, and I hate to discourage students/people, because, really, what do I know, maybe they will surprise themselves and me and if not, then the experience will be a learning one one way or another. So here he is in AB calculus this year. He is struggling and stressing and such all along. He came to me after school one day and said he wanted to drop out of the class. I said that well, the decision was his, but I think it would be a shame if he did because then if anything hard came up in the future then his first idea would be just to quit because it was too hard. I also said that he was smart enough to handle it, and personally I would stick it out. (inside, I think he can do it, and he just has to approach it in a different way, but I DEFINITELY know that if he dropped, he'd be WAY less stressed than he is now). Well, anyway, he decided to stay, and later wrote me a note thanking me for believing in him and in his ability.
I guess the point of all this is to err on the side of pushing the kids to do their best and to do things they don't think they could do or think possible. Maybe it will open up opportunities for them and make them think of themselves in ways they didn't in the past.
Saturday, November 08, 2008
Foreign Exchange Students
At my school we seem to get a lot of foreign exchange students. Every year I've had at least one; always from Germany; and last year I had 3. Phew! This year I again have 2 girls from Germany, and lo and behold one boy from China.
Well, a while into the school year, I saw that he wasn't interacting with the other students, and they weren't talking to them. I don't think it was a rudeness thing on either part. My sense is, that the girls (and boy) from Germany in the past and present were so cute and approachable and maybe "looked more like them", that they naturally talked to them and became friends. That's my guess, and now that I put it down in words, it seems kind of wrong somehow (the situation). Why hasn't anyone struck up a friendship with this boy? Maybe I'm just misreading the situation, and it's only in my class that this phenomenon occurs.
Just yesterday I asked the boy from China (He's cute: when he first arrived, he said, "My American name is Eric" ... I finally asked him his real name, and he mentioned it, and I've been practicing it, so now I use it when I talk with him). Anyway, I asked him to talk to the class about how school differs in China from our school. Sheesh. That was a cultural wake-up call for my kids.
He said they start school at 7am, and have 4 classes until 12pm. Then they have a 2 hour lunch break, and at 2pm until 7pm, they have 4 more classes. Then they have 2 hours of studying. They have a month off in the spring for a sports festival. Every year (?) they take off one week for each of the following activities (?) working in the factories, farms, and army. The sports they play are tennis, running, ping-pong, and badmington (for some reason, that got a titter from my students). I guess I was surprised there was no soccer.
Anyway, hopefully, he's getting a chance to interact with students and such and not having a lonely existence of a day.
Well, a while into the school year, I saw that he wasn't interacting with the other students, and they weren't talking to them. I don't think it was a rudeness thing on either part. My sense is, that the girls (and boy) from Germany in the past and present were so cute and approachable and maybe "looked more like them", that they naturally talked to them and became friends. That's my guess, and now that I put it down in words, it seems kind of wrong somehow (the situation). Why hasn't anyone struck up a friendship with this boy? Maybe I'm just misreading the situation, and it's only in my class that this phenomenon occurs.
Just yesterday I asked the boy from China (He's cute: when he first arrived, he said, "My American name is Eric" ... I finally asked him his real name, and he mentioned it, and I've been practicing it, so now I use it when I talk with him). Anyway, I asked him to talk to the class about how school differs in China from our school. Sheesh. That was a cultural wake-up call for my kids.
He said they start school at 7am, and have 4 classes until 12pm. Then they have a 2 hour lunch break, and at 2pm until 7pm, they have 4 more classes. Then they have 2 hours of studying. They have a month off in the spring for a sports festival. Every year (?) they take off one week for each of the following activities (?) working in the factories, farms, and army. The sports they play are tennis, running, ping-pong, and badmington (for some reason, that got a titter from my students). I guess I was surprised there was no soccer.
Anyway, hopefully, he's getting a chance to interact with students and such and not having a lonely existence of a day.
Sunday, November 02, 2008
9th graders
I'm teaching one section of algebra 1 preAP this year, and I feel like I take extra care of them ... because they're "young uns", and they're learning the foundation for everything else that comes, and they're just so darned cute most of the times. With that said, there are still some "young uns" issues.
There's one whiney child that grates on my last nerve, and I have to work extra hard to not show it. Everything we do, her response is (insert whine), "I don't get it. I don't get anything." She needs to be hand-held through every step. It got to the point where she snapped back at me in class one day because I told her to get to work when she was chatting (because she JUST didn't get it and was waiting for me to do things as opposed to getting help from her more capable group mates).
I was super frustrated last week, so I sent e-mail to her other teachers to explain the situation and to see if it was just me and my class or if these issues came up elsewhere. Two other teachers responded and mimicked what I said about her neediness. They mentioned that she either has a capable friend sitting by her to help or the teacher literally DOES break things down into baby steps. This made me feel better and gave me an idea of copying extra "reteach" sheets for each topic so that she'll have extra practice to look at while the rest of the class is "zooming" along.
She was better in class this last time, but had to leave, so I didn't get to test out my extra-sheet idea yet.
I'm also dealing with a large portion of the class (4-6 out of 28) not turning in ANY homework. I think they're still used to middle school where you magically pass no matter what. I've made some calls home, so hopefully that will produce some late work this coming week.
There's one whiney child that grates on my last nerve, and I have to work extra hard to not show it. Everything we do, her response is (insert whine), "I don't get it. I don't get anything." She needs to be hand-held through every step. It got to the point where she snapped back at me in class one day because I told her to get to work when she was chatting (because she JUST didn't get it and was waiting for me to do things as opposed to getting help from her more capable group mates).
I was super frustrated last week, so I sent e-mail to her other teachers to explain the situation and to see if it was just me and my class or if these issues came up elsewhere. Two other teachers responded and mimicked what I said about her neediness. They mentioned that she either has a capable friend sitting by her to help or the teacher literally DOES break things down into baby steps. This made me feel better and gave me an idea of copying extra "reteach" sheets for each topic so that she'll have extra practice to look at while the rest of the class is "zooming" along.
She was better in class this last time, but had to leave, so I didn't get to test out my extra-sheet idea yet.
I'm also dealing with a large portion of the class (4-6 out of 28) not turning in ANY homework. I think they're still used to middle school where you magically pass no matter what. I've made some calls home, so hopefully that will produce some late work this coming week.
Monday, October 27, 2008
Passing Kids Along
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.
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.
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!
Saturday, September 27, 2008
Piecewise Function Success
Every year as I teach piecewise functions in precalculus, there are students who get it and can successfully graph and understand them, but there are too many students that struggle. I've tried various things, but nothing with consistent success. Well. Last week after school I was helping a struggling student, and as I was looking over her old test, I saw that the mistake she seemed to make on the "3 piece" piecewise function was that to graph it, she made a big table with the same x values and used the same x values for all 3 pieces. I started to say what her mistake was, but then it struck me that if she reworked the idea, it could be very useful.
It worked for all the struggling students I had a chance to try it on, so I think this is how I'll start next year, and then show them the "other" way for those that "get it" and don't want to make such a big table.
It worked for all the struggling students I had a chance to try it on, so I think this is how I'll start next year, and then show them the "other" way for those that "get it" and don't want to make such a big table. Saturday, September 20, 2008
The Week, The Wiki-stix, & The Web
I went to another workshop this Thursday, and the algebra 1 information was very useful. What was NOT useful was the handful of people sitting at my table blatantly grading huge stacks of tests and totally disregarding the presenter and going so far as to discuss with each other about how to allocate points. Oh my.
What was ALSO not useful was my understanding of just how broken our "mentoring system" for new teachers is. One of our new teachers is TOTALLY struggling and crying and breaking down in class and being overwhelmed. I've heard from her mentor that she went in and gave her tips on what to do (do warmups, here are some activities, ...), and said the girl did not take her advice, and then the mentor thinks that's the end of it. Well, I sat in on the girl's class. Warm Ups are the least of her problem. There are some easy fixes that just need to be addressed and monitored and modeled and reinforced.
Anyway! After many deep breaths, I decompressed with some of my favorite "feel good" websites. Here are 2 examples:
DarynKagan.com (here are some old good ones)
http://darynkagan.com/heroism/stories/he_080324_computerfairygodmother.html
http://darynkagan.com/kids/stories/ki_080414_oneboyandaredwagon.html
smittenkitchen.com (yummy looking recipes) ... for example:
http://smittenkitchen.com/2008/08/chocolate-peanut-butter-cake/
Also, I found yet another use for the wiki stix. We started radians in precal today, and my first question was how many radii did they think fit around a circle. They drew circles and the radius, and then with a small piece of a wiki stix (stick?) they marked out the radius along the circle. It was easy to manipulate and curve.
And the funny joke I read in a book this week:
knock knock
who's there
little old lady
little old lady who
I didn't know you could yodel.
What was ALSO not useful was my understanding of just how broken our "mentoring system" for new teachers is. One of our new teachers is TOTALLY struggling and crying and breaking down in class and being overwhelmed. I've heard from her mentor that she went in and gave her tips on what to do (do warmups, here are some activities, ...), and said the girl did not take her advice, and then the mentor thinks that's the end of it. Well, I sat in on the girl's class. Warm Ups are the least of her problem. There are some easy fixes that just need to be addressed and monitored and modeled and reinforced.
Anyway! After many deep breaths, I decompressed with some of my favorite "feel good" websites. Here are 2 examples:
DarynKagan.com (here are some old good ones)
http://darynkagan.com/heroism/stories/he_080324_computerfairygodmother.html
http://darynkagan.com/kids/stories/ki_080414_oneboyandaredwagon.html
smittenkitchen.com (yummy looking recipes) ... for example:
http://smittenkitchen.com/2008/08/chocolate-peanut-butter-cake/
Also, I found yet another use for the wiki stix. We started radians in precal today, and my first question was how many radii did they think fit around a circle. They drew circles and the radius, and then with a small piece of a wiki stix (stick?) they marked out the radius along the circle. It was easy to manipulate and curve.
And the funny joke I read in a book this week:
knock knock
who's there
little old lady
little old lady who
I didn't know you could yodel.
Saturday, September 13, 2008
Life's Surprise Pop Quizzes
We are being judged and evaluated all the time, and we may not realize it. In fact sometimes we may think we're getting away with things when really we're not. This past week seemed to be full of those "pop quizzes", and now my outlook on a variety of people has altered.
test1: I gave my first test in precalculus this week. As I walked around the room, I noticed the continuously wandering eye of one boy. I stood near him after that and asked him to keep his knees forward (instead of turned towards a "smart" student). Then he turns in his test early indicating he had troubles with one problem (he left blank). Trying to promote his perseverence, I said, "you're a smart kid, keep looking at it and maybe you can work something out". I realized my mistake once he picked his test off the pile of "done" tests, when he walked back to his desk and I saw him erase another problem's answer immediately and put down what I'm guessing he saw on the pile. Now none of this was provable, so I didn't snatch his test up, but this was the 1st "life quiz" he failed. Even though he thinks he got away with things, I will no longer see him in the same way, and he will forever more be the "cheater" to me.
test2: For the nth and (n+1)st time one of our math teachers was basically bad-mouthing other people. In the first instance she was talking about a new teacher that was struggling, and after she recounted the struggles, she mentioned that this person was ONLY hired because we were desperate, and the new teacher must not have had strong interviews because she was not snatched up by other schools in the district. Her second mouthing incident was about a teacher at another school that our new AP wants to hire. She recounted 2 or 3 bad things about her personality and her teaching ability. I wasn't part of the 1st conversation (came in on the tail end), and for the second, I tried to say something nice about the other teacher, and basically I didn't say anything to this lady. BUT now I think of her as the bad-mouther. I wonder what she may say about me or about other people even though she's nice to me/others to their face.
test3: I park a ways away from the grocery store entrance in order to get some free exercise. I was walking back to my car and it looked like someone else with a cart had the same idea. After she was finished unloading into her trunk, I wondered if she would make the uphill trek to return the cart to the right place or just leave it willy nilly to bang into other cars. I was betting on the latter, but she surprised me and restored a bit of my faith in people by conscientiously walking it back to the "right" place.
test4: I walked my (cute little puppies) algebra 1 9th graders over to get textbooks this past week ... after I discussed hallway behavior and such. I also walked my precal and calculus classes over (older kiddies). When we got to the book room, the "manager" seemed surprised I was trusting the 9th graders with textbooks since apparently they don't have good reputations of caring for them and returning them. He even added an extra spiel that he didn't for my older kids about the cost of the books and such. Well, after they went through the checking out process, he told them all they were the best behaved 9th graders he'd ever seen. And I have to agree since out of my 6 classes, they were the best behaved through the whole process. Go Them!
test1: I gave my first test in precalculus this week. As I walked around the room, I noticed the continuously wandering eye of one boy. I stood near him after that and asked him to keep his knees forward (instead of turned towards a "smart" student). Then he turns in his test early indicating he had troubles with one problem (he left blank). Trying to promote his perseverence, I said, "you're a smart kid, keep looking at it and maybe you can work something out". I realized my mistake once he picked his test off the pile of "done" tests, when he walked back to his desk and I saw him erase another problem's answer immediately and put down what I'm guessing he saw on the pile. Now none of this was provable, so I didn't snatch his test up, but this was the 1st "life quiz" he failed. Even though he thinks he got away with things, I will no longer see him in the same way, and he will forever more be the "cheater" to me.
test2: For the nth and (n+1)st time one of our math teachers was basically bad-mouthing other people. In the first instance she was talking about a new teacher that was struggling, and after she recounted the struggles, she mentioned that this person was ONLY hired because we were desperate, and the new teacher must not have had strong interviews because she was not snatched up by other schools in the district. Her second mouthing incident was about a teacher at another school that our new AP wants to hire. She recounted 2 or 3 bad things about her personality and her teaching ability. I wasn't part of the 1st conversation (came in on the tail end), and for the second, I tried to say something nice about the other teacher, and basically I didn't say anything to this lady. BUT now I think of her as the bad-mouther. I wonder what she may say about me or about other people even though she's nice to me/others to their face.
test3: I park a ways away from the grocery store entrance in order to get some free exercise. I was walking back to my car and it looked like someone else with a cart had the same idea. After she was finished unloading into her trunk, I wondered if she would make the uphill trek to return the cart to the right place or just leave it willy nilly to bang into other cars. I was betting on the latter, but she surprised me and restored a bit of my faith in people by conscientiously walking it back to the "right" place.
test4: I walked my (cute little puppies) algebra 1 9th graders over to get textbooks this past week ... after I discussed hallway behavior and such. I also walked my precal and calculus classes over (older kiddies). When we got to the book room, the "manager" seemed surprised I was trusting the 9th graders with textbooks since apparently they don't have good reputations of caring for them and returning them. He even added an extra spiel that he didn't for my older kids about the cost of the books and such. Well, after they went through the checking out process, he told them all they were the best behaved 9th graders he'd ever seen. And I have to agree since out of my 6 classes, they were the best behaved through the whole process. Go Them!
Sunday, September 07, 2008
Math Workshop Already!
During the 2nd week of school I had to get a sub for Friday to attend a 2-day math workshop. Oh my, whine, whine, whine: too early in the school year, too hard to leave students with meaningful work when we just started, sets a bad precedent, .....
Okay. It was a great workshop. I learned so many things that will be BIG payoffs in the long run, so can I take back my whining? (except for the fact that now in 2 weeks time I'm basically mandated to miss another day to go to another workshop).
Here are some things I learned:
* a way one teacher gets her kids to remember the divide by zero and zero divided by something rule: 0/K = 0 means it's "okay to have a zero in the numerator". N/0 = undefined means "NO! you cannot have a zero in the denominator".
* which reminded me of the way I learned a long time ago to help kids remember the no slope and the zero slope of vertical and horizontal lines: "No" starts with a capital "n" and when you're writing "N", the first line is a vertical line, so vertical lines have "no slope". "Zero" starts with a capital "z" and when you're writing "Z", the first line is a horizontal line, so horizontal lines have "zero slope".
* with calculator usage for calculus and showing a function and its derivative function at the same time ..... put one in y1 and one in y2 and in MODE change the graph style to "simultaneous", and then you can start and stop the graphs at will and have a rich discussion about positive and negative slopes and + & - derivative values throughout the whole graph.
* I never remember which one of the "ON" or "ENTER" buttons on the TI=84 stops or pauses the graph, so I always end up pushing both. Well! The "ON" button stops the graph, so you can get "ON" with your life.
* Which reminds me of what I shared in the same session regarding calculators and limits to infinity. I have my kids look at just one of the polynomials of the numerator or the denominator in a rational function, say 4x^3 - 2x^2 + 100. I ask if you plug in larger and larger numbers, will that evaluate to basically the same or different value than if you plugged in the same large number to 4x^3 (the dominant term). They are convinced they'll be different. So we put 4x^3 - 2x^2 + 100 into y1, and in the main window do "function notation" of y1(5) and compare it to 4(5)^3. Then we start comparing the 2 things by typing in larger and larger numbers. They're eventually the "same" on the calculator. I tell them that the highest power term is like the ocean and all the other stuff is like spit, and if you spit in the ocean, it doesn't change the volume much, so you can basically ignore it when you are calculating limits at infinity.
Okay. It was a great workshop. I learned so many things that will be BIG payoffs in the long run, so can I take back my whining? (except for the fact that now in 2 weeks time I'm basically mandated to miss another day to go to another workshop).
Here are some things I learned:
* a way one teacher gets her kids to remember the divide by zero and zero divided by something rule: 0/K = 0 means it's "okay to have a zero in the numerator". N/0 = undefined means "NO! you cannot have a zero in the denominator".
* which reminded me of the way I learned a long time ago to help kids remember the no slope and the zero slope of vertical and horizontal lines: "No" starts with a capital "n" and when you're writing "N", the first line is a vertical line, so vertical lines have "no slope". "Zero" starts with a capital "z" and when you're writing "Z", the first line is a horizontal line, so horizontal lines have "zero slope".
* with calculator usage for calculus and showing a function and its derivative function at the same time ..... put one in y1 and one in y2 and in MODE change the graph style to "simultaneous", and then you can start and stop the graphs at will and have a rich discussion about positive and negative slopes and + & - derivative values throughout the whole graph.
* I never remember which one of the "ON" or "ENTER" buttons on the TI=84 stops or pauses the graph, so I always end up pushing both. Well! The "ON" button stops the graph, so you can get "ON" with your life.
* Which reminds me of what I shared in the same session regarding calculators and limits to infinity. I have my kids look at just one of the polynomials of the numerator or the denominator in a rational function, say 4x^3 - 2x^2 + 100. I ask if you plug in larger and larger numbers, will that evaluate to basically the same or different value than if you plugged in the same large number to 4x^3 (the dominant term). They are convinced they'll be different. So we put 4x^3 - 2x^2 + 100 into y1, and in the main window do "function notation" of y1(5) and compare it to 4(5)^3. Then we start comparing the 2 things by typing in larger and larger numbers. They're eventually the "same" on the calculator. I tell them that the highest power term is like the ocean and all the other stuff is like spit, and if you spit in the ocean, it doesn't change the volume much, so you can basically ignore it when you are calculating limits at infinity.
Monday, September 01, 2008
More Games and Such
I decided to add 2 new links to my homework website for games since these are ones I love love love. The first is ABC pureisu. Basically you place the letters A, B, & C (and sometimes D) so that every row and every column has exactly 1 of each. You can click around the buttons to get different sizes and difficulties of puzzles. By clicking in the box, you can place your letter.
The second is a "squiggly" sudoku site. I love the different variations of sudoku, and this one also has different difficulty levels. A different puzzle appears every day. This one you have to print out.
I had put a "notes" section on my website, but ultimately knew I wouldn't keep up the copying of the notes, and I didn't know how helpful it would be. So I decided just to sum up the topics of the day/week and mention what would be important to know how to do, and then I will provide web links to various sites that show/quiz/video/tutor/etc the same topic. That way the students have a different way of learning the same thing, and maybe a different explanation will make things click for them or just let them review more. It also gets them in the habit of searching the Internet using the topic name, and they can find other help.
The second is a "squiggly" sudoku site. I love the different variations of sudoku, and this one also has different difficulty levels. A different puzzle appears every day. This one you have to print out.
I had put a "notes" section on my website, but ultimately knew I wouldn't keep up the copying of the notes, and I didn't know how helpful it would be. So I decided just to sum up the topics of the day/week and mention what would be important to know how to do, and then I will provide web links to various sites that show/quiz/video/tutor/etc the same topic. That way the students have a different way of learning the same thing, and maybe a different explanation will make things click for them or just let them review more. It also gets them in the habit of searching the Internet using the topic name, and they can find other help.
Thursday, August 28, 2008
Testing Scribd
I gave the following quiz today in Algebra 1, and I've had "Scribd" on my radar for some time, and then I saw it used on the "f(t)" blog, so I thought I'd test it out here to see what's what.
http://www.scribd.com/doc/5267432/graphing-points-quiz
http://www.scribd.com/doc/5267432/graphing-points-quiz
Hmmm, not exactly perfect, but I'll work on it.
Wednesday, August 27, 2008
My Book Love Affair
I have passionate feelings for this resource and turn to it whenever I need great ways to ask questions or great real-life examples. I got my copy at an NCTM workshop, and am doing the happy dance ever since. For example, in precalculus today we were talking about function notation, and after we did some "math" graph and table and equation examples, I pulled 2 context examples from the book. One was a table having to do with NFL revenue for a number of recent years, and one was a velocity vs. time graph for a man going to the store.
They both generated discussion about the amount of money NFL made (billions!) and interpretations of the velocity graph and why it may be so "wiggly" going up and down and such and how you knew when he reached the store. The questions were worded such as: find v(24) and interpret the meaning. So they had to think about what "24" meant in this problem and what the "y" value meant and put it all in a coherent sentence.
We also started a discussion on graphs such as y = abs(f(x)). We first refreshed our memory on abs(x) (much needed for some folks). Then I had them make a table for f(x) = x*x - 2 and graph it. Then I had them hold up their hands in the shape they thought y=abs(f(x)) would be .... some, of course, held up "V" hands. So we made the table values and graphed JUST the points, and then I showed them the visual of "flipping" all the negatives "up". Ooh, ahh. That was a good segue into doing the same table/graph thing with f(x) = x ..... then doing y = abs(f(x)).
On a whiny note, my 6 class sizes so far are: 31, 22, 17, 26, 39, 34.
I'm just saying. .... but maybe that's the norm in other schools. BUT, I rember my math teacher friend in another state complaining that she had LARGE classes one year .... "26".
They both generated discussion about the amount of money NFL made (billions!) and interpretations of the velocity graph and why it may be so "wiggly" going up and down and such and how you knew when he reached the store. The questions were worded such as: find v(24) and interpret the meaning. So they had to think about what "24" meant in this problem and what the "y" value meant and put it all in a coherent sentence.
We also started a discussion on graphs such as y = abs(f(x)). We first refreshed our memory on abs(x) (much needed for some folks). Then I had them make a table for f(x) = x*x - 2 and graph it. Then I had them hold up their hands in the shape they thought y=abs(f(x)) would be .... some, of course, held up "V" hands. So we made the table values and graphed JUST the points, and then I showed them the visual of "flipping" all the negatives "up". Ooh, ahh. That was a good segue into doing the same table/graph thing with f(x) = x ..... then doing y = abs(f(x)).
On a whiny note, my 6 class sizes so far are: 31, 22, 17, 26, 39, 34.
I'm just saying. .... but maybe that's the norm in other schools. BUT, I rember my math teacher friend in another state complaining that she had LARGE classes one year .... "26".
Saturday, August 23, 2008
Wikki Stix & Me
A while back I was first introduced to Wikki Stix at a calculus workshop where the presenter showed how she taught slope fields by having large pieces of graph paper around the room, and each group had a differential equation and each person in the group had a point or 2 or 3, and they were to calculate the slope and stick the piece of wikki stix on that point in the appropriate slope. Super cool.
I was at a teacher supply store the other day, and found 48 for $5.95, and bought them thinking I could find some use for them. Well, now I have 2 things so far. On the first day of school, I will review functions and lead to function notation and how to read f(x) and find f(3) and find x such that f(x) = 6, etc, by first handing out premade graphs/grids/coordinate planes to each student and one wikki stix (stick?) to each kid. I'll first instruct them to plop down a "graph", and maybe have them decide if they're functions or not and maybe have themselves walk with their graphs and separate into 2 camps of functions and non functions. They can then self correct by glancing at others and discussing it amongst themselves. Then I'll say find your f(3), and separate yourselves into like groups (how to deal with non integers .....???). Anyway, you get the idea. I could do more.
My second idea is what I think is an improvement on an old activity I've done with precal in the past regarding learning the sine and cosine graphs. But my teacher friend (who I first learned to teach with/from) in another state basically does the same activity but with Wikki Stix. She has them do the measuring of the angles and the heights, not with a string, but with the Stix. Also, once they measure the "height", they snip the Stix into that length and "stick" it down on their graph. So ultimately, later on you have a Wikki Stix sine curve graph. Way cool and something I'll try this year .... though with 3 precal classes of (current sizes) 37, 32, 30ish, how much will that cost?
I was at a teacher supply store the other day, and found 48 for $5.95, and bought them thinking I could find some use for them. Well, now I have 2 things so far. On the first day of school, I will review functions and lead to function notation and how to read f(x) and find f(3) and find x such that f(x) = 6, etc, by first handing out premade graphs/grids/coordinate planes to each student and one wikki stix (stick?) to each kid. I'll first instruct them to plop down a "graph", and maybe have them decide if they're functions or not and maybe have themselves walk with their graphs and separate into 2 camps of functions and non functions. They can then self correct by glancing at others and discussing it amongst themselves. Then I'll say find your f(3), and separate yourselves into like groups (how to deal with non integers .....???). Anyway, you get the idea. I could do more.
My second idea is what I think is an improvement on an old activity I've done with precal in the past regarding learning the sine and cosine graphs. But my teacher friend (who I first learned to teach with/from) in another state basically does the same activity but with Wikki Stix. She has them do the measuring of the angles and the heights, not with a string, but with the Stix. Also, once they measure the "height", they snip the Stix into that length and "stick" it down on their graph. So ultimately, later on you have a Wikki Stix sine curve graph. Way cool and something I'll try this year .... though with 3 precal classes of (current sizes) 37, 32, 30ish, how much will that cost?
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