In my geometry class, I'm trying to keep their algebra skills fresh (AND exciting!), so lately I've brought back lines: find the equation of a line parallel to ____ going through point ____; find 4 points on the line ______; etc. I reviewed point-slope form, slope-intercept form, standard form.
Well, many students came in for tutoring and were stuck on this problem:
Find 4 points on the line 3x + 2y = 12.
Them: "I don't know what to do."
Me: "How many points on a line?"
Them: "Infinity."
Me: "Yes, infinITE. What do you think is true about this equation and any point on this line."
Them: chirp chirp of crickets.
Me: explanation, showing, bla bla bla.
Them: "oh yea" .... work furiously.
Them: "I'm stuck. I can't find any more."
Me: looking and seeing that they have guessed and checked their capacity of integer valued (x,y) values.
Me: "Just pick an x and solve for y."
Them: "I tried, and NOTHING ELSE WORKS!"
Me: "Decimals and Fractions! They're not just for special occasions."
Them: "Oh, I didn't know you could have non-integer points."
.....
Monday, November 28, 2011
Tuesday, November 22, 2011
Eye Contact
For sad work-related issues of not being able to get out of work on time, I often miss my 1 favorite yoga class in the week. It's either that or be the jerk that walks into class late frequently ... so I settle for being the jerk every other week or so. What I love about the class is that the teacher always has a theme or some sort of life lesson she winds through the class. She also changes it up EVERY week. She's also very fit and warm and a good person and makes sure she learns everyone's names.
At the end of class, she stands outside the door, and people always clamor for her attention and want to talk to her as they are leaving, but she always says goodbye to everyone. What I notice the last few times is that the moment I'm leaving, she's engaged in conversation, and though I do get a, "bye," there's no eye contact since she's otherwise engaged. What I also notice is that it started to bug me. ... not in the sense of, "the nerve of the woman!" but in the sense of, "hey, notice I'm a human being amongst the other human beings here."
Then, of course, I noticed that I frequently do that to my students at various times. There are those students that by the very nature of their personalities just force you to pay attention to them. A LOT. Then there are the quiet polite ones that just go about their business, and maybe I may never make eye contact with them (much?). Maybe that may happen in most/all of their classes, and even if it doesn't, it's a shame it happens in mine. I get into the state of, I'm dealing with a class or a question you have or the math of it, and it's a "situation" not a person I'm dealing with.
So today, after each student was finished with their test, when I collected the paper, I made sure to smile and say a quiet thank you and actually make eye contact with each of my students.
Woot! One day of successful eye contact down. A bazillion more days to remember to do this.
At the end of class, she stands outside the door, and people always clamor for her attention and want to talk to her as they are leaving, but she always says goodbye to everyone. What I notice the last few times is that the moment I'm leaving, she's engaged in conversation, and though I do get a, "bye," there's no eye contact since she's otherwise engaged. What I also notice is that it started to bug me. ... not in the sense of, "the nerve of the woman!" but in the sense of, "hey, notice I'm a human being amongst the other human beings here."
Then, of course, I noticed that I frequently do that to my students at various times. There are those students that by the very nature of their personalities just force you to pay attention to them. A LOT. Then there are the quiet polite ones that just go about their business, and maybe I may never make eye contact with them (much?). Maybe that may happen in most/all of their classes, and even if it doesn't, it's a shame it happens in mine. I get into the state of, I'm dealing with a class or a question you have or the math of it, and it's a "situation" not a person I'm dealing with.
So today, after each student was finished with their test, when I collected the paper, I made sure to smile and say a quiet thank you and actually make eye contact with each of my students.
Woot! One day of successful eye contact down. A bazillion more days to remember to do this.
Thursday, November 17, 2011
Precalculus Trig Function Transformations
We've just finished a unit on transforming trig function graphs:
y = a sin b(x + c) + d.
We did various things and practice, but I think I found my new BFF towards the end of the unit once we were reviewing for the test.
A student was having a hard time looking at a graph of a transformed function and getting the equation. I had some old transparencies that had the coordinate plane on it with radians on the x axis. I also had half sheets of cut up transparencies and a ton of markers. I laid the 1/2 sheet over the graph and had the student draw the parent function of the sine graph (for example). Then she was able to slide the 1/2 transparency any place she wanted to see what the transformed graph would look like (barring amplitude and period changes ...... though I guess we could have used another 1/2 transparency overlayed on that one).
This seemed to help gel in her mind the steps she had to take. I think next year I may give all students such transparencies just to keep and play with for the duration of the unit. .... My 2nd thought was to have pipe cleaners they could manipulate into the shapes and then move those around on a graph.
Also, I loved this particular review question I gave. There was a picture of a (say a potential sine graph) that has been transformed in all sorts of ways. The question was: find 2 possible equations for this graph. I guess a variation question could be: find a sine and a cosine equation for this graph ... or find 2 sine equations and 2 cosine equations for this graph.
y = a sin b(x + c) + d.
We did various things and practice, but I think I found my new BFF towards the end of the unit once we were reviewing for the test.
A student was having a hard time looking at a graph of a transformed function and getting the equation. I had some old transparencies that had the coordinate plane on it with radians on the x axis. I also had half sheets of cut up transparencies and a ton of markers. I laid the 1/2 sheet over the graph and had the student draw the parent function of the sine graph (for example). Then she was able to slide the 1/2 transparency any place she wanted to see what the transformed graph would look like (barring amplitude and period changes ...... though I guess we could have used another 1/2 transparency overlayed on that one).
This seemed to help gel in her mind the steps she had to take. I think next year I may give all students such transparencies just to keep and play with for the duration of the unit. .... My 2nd thought was to have pipe cleaners they could manipulate into the shapes and then move those around on a graph.
Also, I loved this particular review question I gave. There was a picture of a (say a potential sine graph) that has been transformed in all sorts of ways. The question was: find 2 possible equations for this graph. I guess a variation question could be: find a sine and a cosine equation for this graph ... or find 2 sine equations and 2 cosine equations for this graph.
Saturday, November 12, 2011
End of the 6 Weeks...
Well, from 20+ failing students down to 3 for now and possibly only 1 or 2 after I grade some test corrections and put in more homework grades. What IS it with certain types of people that they have to hit rock bottom with their grades before they start putting out some effort? I guess it's probably a mix of human nature to get by with as little as possible plus teenage brains plus maybe a dose of "they don't REALLY mean it that I'll fail, do they?", plus an ounce of "math's hard, let's go shopping!".
On the positive side, one of my hardcore, "I hate math, and I probably hate you, and I'm going to be as obnoxious as possible to get some attention" students pulled it together in the last couple of weeks and started behaving semi-politely and actually put out an effort to understand the math and take her retests and learn some geometry. On the negative side, she's also the student that couldn't really with utmost certainty tell me what "8 over 4" really means in terms of life/math/reality. "one half? 2? I don't know! what are you asking?". Oy!
But on the "am I a glutton for punishment?" side, it always seems to be the most gratifying when THOSE kids get it together and pull through and actually learn something. Hah! Forget the nice kids that are always doing the right thing and being polite and being good students! Boring!
.... Just kidding.
On the positive side, one of my hardcore, "I hate math, and I probably hate you, and I'm going to be as obnoxious as possible to get some attention" students pulled it together in the last couple of weeks and started behaving semi-politely and actually put out an effort to understand the math and take her retests and learn some geometry. On the negative side, she's also the student that couldn't really with utmost certainty tell me what "8 over 4" really means in terms of life/math/reality. "one half? 2? I don't know! what are you asking?". Oy!
But on the "am I a glutton for punishment?" side, it always seems to be the most gratifying when THOSE kids get it together and pull through and actually learn something. Hah! Forget the nice kids that are always doing the right thing and being polite and being good students! Boring!
.... Just kidding.
Wednesday, November 09, 2011
Timed Trig Quizzes....
Well, it's towards the end of the 6 weeks (1 more day), and it's the last chance for my kidlets to do their "1 minute / 10 question / know your special radian sine/cosine/tangent angles" quiz. Whew! Most of them have passed, and I think they surprised themselves.
When I first gave it to them weeks ago, they couldn't even get 2 accurate (let alone complete the quiz). Now, they're just whipping them out. I kept saying that I wasn't worried and that they'd rise up to it and that they'd surprise themselves, but it would take work. .... Some of them even surprised me. You can't imagine the whining throughout the process (or maybe you can) .... Why is it timed? Why do we have to do this? I can't do this! This is impossible! Whaaaaaaaa! I'll never pass. Stopppppp! What if I don't pass????
Honestly, I don't remember how long I used to give them in the past ... and like a bad teacher, I didn't look it up. I assumed it was one minute, and now I'm wondering if it was 2 ... but I don't think so. Even my most snail-paced-think-through-everything-twice student was successful. Woot!
The repetition is the key, and it's even good if it takes them longer to pass because that's more time they have to spend memorizing all the angles.
When I first gave it to them weeks ago, they couldn't even get 2 accurate (let alone complete the quiz). Now, they're just whipping them out. I kept saying that I wasn't worried and that they'd rise up to it and that they'd surprise themselves, but it would take work. .... Some of them even surprised me. You can't imagine the whining throughout the process (or maybe you can) .... Why is it timed? Why do we have to do this? I can't do this! This is impossible! Whaaaaaaaa! I'll never pass. Stopppppp! What if I don't pass????
Honestly, I don't remember how long I used to give them in the past ... and like a bad teacher, I didn't look it up. I assumed it was one minute, and now I'm wondering if it was 2 ... but I don't think so. Even my most snail-paced-think-through-everything-twice student was successful. Woot!
The repetition is the key, and it's even good if it takes them longer to pass because that's more time they have to spend memorizing all the angles.
Saturday, November 05, 2011
Magic Hand and Transversals...
We started talking about 2 lines cut by a transversal this week in geometry. I had fun with the "magic hand" statement, and it seemed to work with my students. I held up my hand at the appropriate moment and asked them what it was ..... "a magic hand!", and then I placed it over the "4th line" that I had drawn.
I also mentioned that the two lines could be like sandwich slices and the transversal is the toothpick that goes through the sandwich. So when I had them identify types of angle pairs, I could keep saying, "who's the bread? who's the toothpick?". That seemed to help them be successful once the "magic hand" removed an extra line.
I also mentioned that the two lines could be like sandwich slices and the transversal is the toothpick that goes through the sandwich. So when I had them identify types of angle pairs, I could keep saying, "who's the bread? who's the toothpick?". That seemed to help them be successful once the "magic hand" removed an extra line.
