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.
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!
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?
Wednesday, August 20, 2008
New Skills
I was at a math workshop today, and from a participant I learned a great calculator skill that left me saying, "where have you been all my TI-83/4/silver edition/titanium life?".
Suppose you're graphing, and suppose you simultaneously want to see the graph and the table screens. Well: mode > G-T, and poof, when you hit graph, voila, split screen. Then you can toggle between the 2 parts by hitting the "table" or "graph" button, and then you can do whatever you want on that part of the screen.
Also, you can split the screen horizontally (mode > horiz ...) and then you can show the graph and either the main window or the lists or a table, etc.
Ooh, aah.
Suppose you're graphing, and suppose you simultaneously want to see the graph and the table screens. Well: mode > G-T, and poof, when you hit graph, voila, split screen. Then you can toggle between the 2 parts by hitting the "table" or "graph" button, and then you can do whatever you want on that part of the screen.
Also, you can split the screen horizontally (mode > horiz ...) and then you can show the graph and either the main window or the lists or a table, etc.
Ooh, aah.
Sunday, August 17, 2008
Saturday, August 16, 2008
Addiction
Ackh! In the process of updating my homework website further, I thought I'd add a "games" link that showed some fun thinking/math/logic games. Well, of course I had to try them out to see what I was linking. .... Too many hours later, I'm addicted to 2 I found at http://www.coolmath-games.com/ : "walls logic" and "bloxorz". The first has you building diagonal walls on each of the tiles in a grid, and you can't form loops, and you have to follow "# of walls rules" for certain intersections. The second has 33 levels, and you basically move a brick around to get it in a hole. ... Okay, must stop playing and go do other things.
On a side note, as I was trying the new games, I found myself getting blurry eyed just reading all the instructions, and I just wanted to jump in and test the waters instead of reading about it. Hmmmm, sounds familiar. So now I'll try to think of each school lesson in a new way: how can the students get started right away doing something and then learning what they need to know about it at various stages of the class.
On a side note, as I was trying the new games, I found myself getting blurry eyed just reading all the instructions, and I just wanted to jump in and test the waters instead of reading about it. Hmmmm, sounds familiar. So now I'll try to think of each school lesson in a new way: how can the students get started right away doing something and then learning what they need to know about it at various stages of the class.
Thursday, August 14, 2008
First Day Algebra Activity
It looks like on 8/25 we're starting right away with 1.5 hour block classes when school starts (as opposed to meeting all classes and having an "alpha" period with about 40 minute classes). I need about 40 minutes to call roll and ask for pronunciation corrections, have them fill out a seating chart (I like them to sit where they want the first time, so I see who can/can't sit together when I soon make a seating chart), take pictures of groups (so I can memorize names), and talk about the syllabus. While all this is going on, I like them to be doing something. Here's my something:
They'll work on it quietly while I'm calling roll, and then I'll prompt them to check and work with their group and meet everyone in the group while I'm snapping pictures. Section "A" prompts them about "PEMDAS". Section "B" has orders-of-operation problems with 2 answers to circle, one for the common mistake and one correct answer. Section "C" has a fraction/decimal/percent table with one column filled out where they fill in the other 2 with equivalent expressions. Section "D" has four "4"s and an answer, and they're to fill in operations to get the right answer.
Here's part of their first assignment (and parent homework):
This is a math autobiography and asks questions about past classes and school experiences and such. It also asks their parents to indicate "I am proud of my child because" ....
This will tell me many things about the student: if they do work on time, if they are neat/verbose/last-minute/thoughtful. They also get to see their parent's bragging comments (and sometimes if there are no comments, I'm sad for the kid). I also have a good opportunity to get their parents' e-mail address for future grade sending.
Then I have about 50 minutes left. I'm thinking of a "box plot" activity and a "meet and greet" activity. ... still in the planning stages, though.
Whew! Two tasks done.
Tuesday, August 12, 2008
My Summer Vacation
Just last week I went to an aerobatics contest my husband was in. It's small, so EVERYONE is wrangled into volunteering somehow.
I got to be a boundary judge and learn the skills of how to read a sequence card and how to call the ins and outs and how to survive blistering heat and curious cows and carcas sightings. First my partner and I (another wrangled wife) had to drive 10 minutes to the location.
Here is an actual corner boundary that the pilots would see from the air.
This is the other wife sitting in position ready to call outs/ins. The contraption is uber cool and thought up by an engineer/pilot who used a compass and his brains. AND there's math involved (what else).
There are 2 sets of 2 strings lined up perpendicular to the other set, and you line up the strings of one set with your eye and .... since 2 lines form a plane, you can determine when the aerobatic planes cross the boundary or not. We were at the "southeast" boundary, so our job was to call "out south", "in south", "out east", "in east".
Boy were we stressed about doing it right. We're not pilots, and we had to figure out what squiggly lines on the cards matched what things the pilots were doing in the air. Eventually, we mastered it as a team.
Here are some things that kept us company each time we went out.
I got to be a boundary judge and learn the skills of how to read a sequence card and how to call the ins and outs and how to survive blistering heat and curious cows and carcas sightings. First my partner and I (another wrangled wife) had to drive 10 minutes to the location.
Here is an actual corner boundary that the pilots would see from the air.This is the other wife sitting in position ready to call outs/ins. The contraption is uber cool and thought up by an engineer/pilot who used a compass and his brains. AND there's math involved (what else).
There are 2 sets of 2 strings lined up perpendicular to the other set, and you line up the strings of one set with your eye and .... since 2 lines form a plane, you can determine when the aerobatic planes cross the boundary or not. We were at the "southeast" boundary, so our job was to call "out south", "in south", "out east", "in east".
Boy were we stressed about doing it right. We're not pilots, and we had to figure out what squiggly lines on the cards matched what things the pilots were doing in the air. Eventually, we mastered it as a team.
Here are some things that kept us company each time we went out.
Tuesday, August 05, 2008
Website Goals
Well, I am glad I started my homework website last year, and I'll continue it this year. I found many benefits:
* I made one of the 1st homework assignments be for parents to look at the site and send me an e-mail. This gave me their address for sending home grades, and it also made them aware.
* It gave me a place to post extra worksheets and solutions where they could download them (I didn't do this too much, but maybe will increase it this year)
* Students had an easy way to find homework assignments for whatever reasons.
* Parents now had a place to see/check whether their children had homework or tests coming up.
This year ... (with my 4 PREPS!) I'll continue it, and I want to enhance it:
* I want to somehow incorporate quick easy-to-make-&-upload videos showing various math techniques (I'll film them).
* I potentially want to link to videos from TeacherTube (since YouTube is blocked at our campus).
* I want to post notes for students that are absent (this one I'm iffy about for a variety of reasons: difficulty, space issues, student accountability, ...)
All in all, I'm happy with weebly.com. Hopefully, it will continue to be free or even cheap, and hopefully they'll resist putting ads on their/my page since that was a big draw for me.
* I made one of the 1st homework assignments be for parents to look at the site and send me an e-mail. This gave me their address for sending home grades, and it also made them aware.
* It gave me a place to post extra worksheets and solutions where they could download them (I didn't do this too much, but maybe will increase it this year)
* Students had an easy way to find homework assignments for whatever reasons.
* Parents now had a place to see/check whether their children had homework or tests coming up.
This year ... (with my 4 PREPS!) I'll continue it, and I want to enhance it:
* I want to somehow incorporate quick easy-to-make-&-upload videos showing various math techniques (I'll film them).
* I potentially want to link to videos from TeacherTube (since YouTube is blocked at our campus).
* I want to post notes for students that are absent (this one I'm iffy about for a variety of reasons: difficulty, space issues, student accountability, ...)
All in all, I'm happy with weebly.com. Hopefully, it will continue to be free or even cheap, and hopefully they'll resist putting ads on their/my page since that was a big draw for me.
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