As I'm idling away the summer, I'm wondering what I can do to make my classroom more "homey" next year. I did a little better this year with being harsh with myself and tossing stuff I hadn't unpacked or use for a year. But then all the dreaded engineering boxes took up a bunch of room, and they never quite made it out of the cardboard boxes. My excuse was that I didn't want to buy an organization system on the fly without trying the year out and seeing what would make sense. That or I'm a lazy procrastinator. I'm picking the former.
Some of my ideas so far (don't know if they'll pan out) are:
* the teeny white Christmasy type lights strung around somehow.
* painting the ceiling tiles somehow.
* bringing in a metal porch swing (LOVE them and have 2 at home, one on the porch and one in my office)
* extra "calm" decorative lighting as opposed to the overhead stuff.
* painting the cinder block walls (I'm thinking I'm not motivated to make that happen, though)
* less tables (we don't have desks) and more students around the tables. This year I had 10 large tables in class, and there was hardly room to move around. I've also heard that I'll be most likely having a class of 30 or so, so I'd need at least 8 tables anyway if I had 4 2 a table. Ugh.
* I'd like a wall or board dedicated to articles I've found in my magazines or on the web. Stuff about cool jobs kids may not have heard about or things about inventors or students making a difference or inspiring stories.
* I loved having the mobiles from the last summer project hanging up all year, but those are coming down. Maybe I can have the students in class make other types of mobiles that are topic related.
* This craft gave me some ideas. Maybe I can make a BIG jigsaw puzzle template with 30 pieces (or more, one for each class .... eeeek), and then the students decorate the piece to reflect their personality, and then we hang the finished product all together. But if I have 120 students .... have to think about this one.
* I have a big wall of windows in my room, and we're on the 1st floor. I'm thinking of the students making things that would face out and the passers-by would have art work or math work to gaze at.
Okay, must think some more about this ...
Sunday, July 01, 2012
Monday, June 25, 2012
Great Opportunity
These past few days, a colleague and I were at MIT for EurekaFest. You can read about it here. Holy Cow was it an inspiring few days. There were many high school teams that spent all last year inventing something. They presented their inventions in a variety of ways (talks and booths and discussions). There were "adult" and "college" inventors that were also happy to discuss their experience. There were MIT professors that actually taught invention classes where the whole class invented something throughout the year (semester?). There was this inspiring gentleman. There was this mind-blowing invention.
I'm mentioning it here because we only learned about it from one of our students doing research and asking us if we could do this. To a student at this event, the one thing we kept hearing was that they were changed by their experience of going through the process. I know my colleague and I were inspired. So, if it sounds intriguing, I think you should think about applying for NEXT year. The initial process/application is due in April, so there's plenty of time to get organized.
I'm mentioning it here because we only learned about it from one of our students doing research and asking us if we could do this. To a student at this event, the one thing we kept hearing was that they were changed by their experience of going through the process. I know my colleague and I were inspired. So, if it sounds intriguing, I think you should think about applying for NEXT year. The initial process/application is due in April, so there's plenty of time to get organized.
Tuesday, June 19, 2012
Epiphany
I had a conversation with friends the other day about writing in general (no mention of blogs). They asked if I liked to write or if I found it challenging. I thought about it and said that I did not find it painful. I usually just blurted stuff out on the paper in a stream of consciousness type of way and then went back and adjusted later. My thought is that you basically have an idea of what you want to say, and if you start out by nitpicking every sentence, then that whole picture is lost in the effort of perfection. Anyway, it works for me ... for writing anyway.
For the last 5 days I've been gathering site links and ideas and such to start mapping out my computer programming curriculum. I found many helpful people and ideas and opinions including my own. Then apparently, I found all my baggage about teaching the class. And ..... I have not put down one sentence of how I want the year to proceed. What works for me in writing apparently got lost in translation when I had to carry it over to mapping out a whole new class. My idea of being (nearly) perfect is getting in the way of me actually doing anything to make progress. I keep having these "but ... but ... but ..." thoughts taking up residence in my head.
So my epiphany is just that. BLURT IT DOWN to at least have a starting place with which to work! If you don't start, you can't finish. How do you eat an elephant? One bite at a time! Rah, rah, rah. Okay, that's my goal for this afternoon: get a broad brush stroke down on paper.
For the last 5 days I've been gathering site links and ideas and such to start mapping out my computer programming curriculum. I found many helpful people and ideas and opinions including my own. Then apparently, I found all my baggage about teaching the class. And ..... I have not put down one sentence of how I want the year to proceed. What works for me in writing apparently got lost in translation when I had to carry it over to mapping out a whole new class. My idea of being (nearly) perfect is getting in the way of me actually doing anything to make progress. I keep having these "but ... but ... but ..." thoughts taking up residence in my head.
So my epiphany is just that. BLURT IT DOWN to at least have a starting place with which to work! If you don't start, you can't finish. How do you eat an elephant? One bite at a time! Rah, rah, rah. Okay, that's my goal for this afternoon: get a broad brush stroke down on paper.
Thursday, June 14, 2012
Summer Time...
Ahhhh, the joys of getting enough sleep. That's basically in the top 5 treats of summer vacation. That and the feeling that I have PLENTY of time to organize how I want to teach my 2 new preps next year. Hah! Knowing me, I'll put it off until the last minute and then scramble around wondering what happened to my carefree days.
I did pull out my old calculus bins, and I actually organized them chronologically. I recycled TONS of dated things from them. Now I'm pushing that topic to the back of my mind to gnaw on at odd moments. I'm still thinking of flipping that class daily, and am tossing around ideas to make it doable in the time frame I'll have. It makes me giddy to think I can actually assign problems for class practice (formerly known as homework) that involve "a" and "b" instead of actual numbers. You know, there's a piecewise function with, say, 3 pieces and instead of "3x + 7", one part has "3x + a", and the question is of the sort: find "a" so that the function is continuous. In the past, it's assigned, kids struggle, they come to class, then I walk through how to do it. Besides not being the best way for them, it also ate up class time. NOW I envision myself skipping through class with a goofy grin on my face and just feeding them little hints. POOF! More time in class and more challenging problems. We'll see what the reality really is like, but I'm willing to try it for one year.
This calculus class is also the class that will be through the ropes with me as a teacher for the 3rd time (geometry, precal, calc). To say we're like a dysfunctional family at this point basically sums it up.
My current project is the AP Computer Science class. I have 13 students that have signed up, and they have basically never programmed before. I've heard various theories about how I should use Alice or Scratch or something drag and droppy. I may be naive, and that will certainly come out as the school year happens, but I think that at the end of the day, the students still have to be able to write code and be careful with syntax and find their bugs and such. I think they're up to it. I'm forging ahead and introducing Java immediately. I feel that if I start with another type package then somewhere deep down I'm saying to the students: you can't handle Java. Here's a warm fuzzy puppy that bounces around the screen. Weeeeeee.
Saying that, I think I want to start immediately with the first class. In some form, I want them to write code that day (heavily scaffolded), possibly doing graphics. I have a long term first project in mind, but I have to work out the bugs.
Okay, that's me setting it down in stone. Let's see what happens as the year progresses.
I did pull out my old calculus bins, and I actually organized them chronologically. I recycled TONS of dated things from them. Now I'm pushing that topic to the back of my mind to gnaw on at odd moments. I'm still thinking of flipping that class daily, and am tossing around ideas to make it doable in the time frame I'll have. It makes me giddy to think I can actually assign problems for class practice (formerly known as homework) that involve "a" and "b" instead of actual numbers. You know, there's a piecewise function with, say, 3 pieces and instead of "3x + 7", one part has "3x + a", and the question is of the sort: find "a" so that the function is continuous. In the past, it's assigned, kids struggle, they come to class, then I walk through how to do it. Besides not being the best way for them, it also ate up class time. NOW I envision myself skipping through class with a goofy grin on my face and just feeding them little hints. POOF! More time in class and more challenging problems. We'll see what the reality really is like, but I'm willing to try it for one year.
This calculus class is also the class that will be through the ropes with me as a teacher for the 3rd time (geometry, precal, calc). To say we're like a dysfunctional family at this point basically sums it up.
My current project is the AP Computer Science class. I have 13 students that have signed up, and they have basically never programmed before. I've heard various theories about how I should use Alice or Scratch or something drag and droppy. I may be naive, and that will certainly come out as the school year happens, but I think that at the end of the day, the students still have to be able to write code and be careful with syntax and find their bugs and such. I think they're up to it. I'm forging ahead and introducing Java immediately. I feel that if I start with another type package then somewhere deep down I'm saying to the students: you can't handle Java. Here's a warm fuzzy puppy that bounces around the screen. Weeeeeee.
Saying that, I think I want to start immediately with the first class. In some form, I want them to write code that day (heavily scaffolded), possibly doing graphics. I have a long term first project in mind, but I have to work out the bugs.
Okay, that's me setting it down in stone. Let's see what happens as the year progresses.
Wednesday, June 06, 2012
Flipped AP Calculus Class
Curses on my principal! This year she's been on the "flipped classroom" train. She sends us e-mails. She "gently" suggests we just try it once. She sends more e-mails containing articles raving about flippin' flipping. I kept my head low. I had conversations with myself: What's she thinking! That's too much! I have other things that I'm juggling! I can't see how it would work with students that don't have computers. What if they don't watch at home? What if they come in and either didn't watch and say I didn't get it, or watch and say I didn't get it? Do I do it for every lesson? Every subject?
Then she sent a portion of an article by this teacher, who did this with AP Calculus, which I'm teaching next year. I've also been reflecting and brooding on all those students I had this year in precalculus who perfected the art of "playing school" by pretending to be taking notes and paying attention while they were just going through the motions. Passive "learning". I had no effective consequences for that, not in the "shame on you" way, but in the catch it and make them tune in way. By flipping, and some effective way I can give points or assess that they watched, then I can do the practice problems in class. I totally agreed with this teacher's statement that by the time the kids get home (and ours get home pretty late), their brains are fried, and they may not be giving their mental "all" to the math homework.
Anyway, I'm batting around the idea of doing this for next year for calculus. Teacher Tube? Screencast.com? Other? There seem to be a ton of resources in the above link. .... I'll THINK about it.
Then she sent a portion of an article by this teacher, who did this with AP Calculus, which I'm teaching next year. I've also been reflecting and brooding on all those students I had this year in precalculus who perfected the art of "playing school" by pretending to be taking notes and paying attention while they were just going through the motions. Passive "learning". I had no effective consequences for that, not in the "shame on you" way, but in the catch it and make them tune in way. By flipping, and some effective way I can give points or assess that they watched, then I can do the practice problems in class. I totally agreed with this teacher's statement that by the time the kids get home (and ours get home pretty late), their brains are fried, and they may not be giving their mental "all" to the math homework.
Anyway, I'm batting around the idea of doing this for next year for calculus. Teacher Tube? Screencast.com? Other? There seem to be a ton of resources in the above link. .... I'll THINK about it.
Friday, June 01, 2012
Nice To Meet You...
When I started this blog in January of 2005, I didn't know the what's/how's/why's of how this would transpire. I wanted to keep most (all?) of my privacy just in case there were repercussions. Within the last year or so, I've only JUST started mentioning to people I know that I blog, and THAT took me 6 years. Now it feels kind of stilted and phony to me to just keep signing e-mails or blog responses as "Ms. Cookie". I completely understand the reasoning for everyone doing it, but it started to feel "un-right" somehow for me. By the way, why that name? I like cookies. Really logical.
I've also been mentioning blogs as a great resource to other teachers, and again if feels phony when I fail to mention mine. So what if they come upon it and recognize my picture. Do they mention it to me? Do they not? Do I mention it? ARGH!
So, hello, nice to meet you. I'm Shireen D. I never started out wanting to be a teacher. Now I can't think of anything else I would rather spend my time doing. Blogging and reading blogs have been such great experiences that allow me to get advice and resources and camaraderie and hear other teachers' ideas, and I'm able to think out loud on what has worked and not worked for me. I'm less in a teaching vacuum because of the generosity and availability of other teachers that are processing their work for the rest of us to share.
Case in point today. We have a new teacher that will be teaching AP Statistics next year, and we quickly went online with various search phrases and were able to find blogs, activities, syllabi, outlines, etc. Now this teacher will be affecting 15 or more kids and will have great resources to do so. The inevitable question: WHAT DID WE DO BEFORE THE INTERNET?!
I've also been mentioning blogs as a great resource to other teachers, and again if feels phony when I fail to mention mine. So what if they come upon it and recognize my picture. Do they mention it to me? Do they not? Do I mention it? ARGH!
So, hello, nice to meet you. I'm Shireen D. I never started out wanting to be a teacher. Now I can't think of anything else I would rather spend my time doing. Blogging and reading blogs have been such great experiences that allow me to get advice and resources and camaraderie and hear other teachers' ideas, and I'm able to think out loud on what has worked and not worked for me. I'm less in a teaching vacuum because of the generosity and availability of other teachers that are processing their work for the rest of us to share.
Case in point today. We have a new teacher that will be teaching AP Statistics next year, and we quickly went online with various search phrases and were able to find blogs, activities, syllabi, outlines, etc. Now this teacher will be affecting 15 or more kids and will have great resources to do so. The inevitable question: WHAT DID WE DO BEFORE THE INTERNET?!
Wednesday, May 30, 2012
Last Day Reflections
Like something that still doesn't feel quite done, THE SCHOOL YEAR IS OVER! I gave my last 2 finals. I marveled that my Digital Electronics students actually learned something. I turned in my last grades with literally seconds to spare (over the ceiling intercom, "Ms. ____ are you done yet?"). I contemplated packing up my room and decided to do it later. I went to a last shindig with our juniors who were thanking industry partners for their week-long internship. I celebrated with a dinner out and a reading of a funny book. And now blogging. Woot!
Things I learned or was reminded of again this year:
* people before paper (if someone is vying for your time and you're trapped in your busy work, stop and talk with them; paper can usually wait).
* like all people, kids remember how you make them feel, not how stellar your knowledge was of a particular topic.
* being physically around a group of negative people too much is not healthy for anyone; it feeds on itself.
* change is inevitable.
* kids are still kids, and no matter how mature they act; there are still things they don't know and may appreciate hearing a different perspective on.
* people usually aren't doing the things they do to annoy you; everyone is mostly trying to get by the best way they currently know how; react accordingly.
* no school is perfect; warts happen; you have to know what your deal-breakers are and how to work healthily around things/situations if you can.
Things I learned or was reminded of again this year:
* people before paper (if someone is vying for your time and you're trapped in your busy work, stop and talk with them; paper can usually wait).
* like all people, kids remember how you make them feel, not how stellar your knowledge was of a particular topic.
* being physically around a group of negative people too much is not healthy for anyone; it feeds on itself.
* change is inevitable.
* kids are still kids, and no matter how mature they act; there are still things they don't know and may appreciate hearing a different perspective on.
* people usually aren't doing the things they do to annoy you; everyone is mostly trying to get by the best way they currently know how; react accordingly.
* no school is perfect; warts happen; you have to know what your deal-breakers are and how to work healthily around things/situations if you can.
Thursday, May 24, 2012
Final Exams......
This morning I happened to read some teacher suggestions (a union teacher journal) on writing in the classroom. One teacher mentioned that as she handed out tests to her class, she instructed the students to write an inspiring message on their test. She mentions that they would roll their eyes but do it anyway. Then if she forgot to mention the message on later, future tests, the students reminded her.
I gave some geometry finals today, and as they got ready, I told them to write inspiring messages on their scratch paper. I mentioned that they'd do great, and they have to free up their brain cells from stressing, so they can concentrate on doing math.
I read through their messages after the test:
* Don't overthink it! Relax and everything will be okay.
* Kick butt!
* You are the smartest person in the world!
* You know things .... just try your hardest.
* I'm proud of you.
I gave some geometry finals today, and as they got ready, I told them to write inspiring messages on their scratch paper. I mentioned that they'd do great, and they have to free up their brain cells from stressing, so they can concentrate on doing math.
I read through their messages after the test:
* Don't overthink it! Relax and everything will be okay.
* Kick butt!
* You are the smartest person in the world!
* You know things .... just try your hardest.
* I'm proud of you.
Feet Cubed....
As every high school student OBVIOUSLY knows, "3 feet cubed" is "3x12 inches cubed". Duh! You know, you just multiply by 12 because there are 12 inches in a foot.
Like everyone else, I've tried various ways to dispel this rumor: we've drawn models, we've used models, we've discussed. Seemingly to no avail. This year, I tried yet again with a different tactic.
We started out with a rectangular prism 3' x 2' x 4'. They found the volume in feet cubed. Then I asked them to find the volume in inches cubed, and to a person, they all wrote the wrong answer (24 x 12 = 288). Then without saying they were wrong I had them go back and redraw the prism into the inches equivalent and recalculate the volume, and OH NO, they were wrong with their first "288". Hmmmmm. So, this is stuff I've tried before. Now for the "new" attempt that MAYBE will work.
I had them write: 5 ft^3
Then change to: 5 * ft * ft * ft
Then EACH foot had to be converted to inches, so
= 5 *ft * ft * ft
= 5 * 12in * 12in * 12in
= 8640 in*in*in
= 8640 in^3
Let's see if this one sticks.
Like everyone else, I've tried various ways to dispel this rumor: we've drawn models, we've used models, we've discussed. Seemingly to no avail. This year, I tried yet again with a different tactic.
We started out with a rectangular prism 3' x 2' x 4'. They found the volume in feet cubed. Then I asked them to find the volume in inches cubed, and to a person, they all wrote the wrong answer (24 x 12 = 288). Then without saying they were wrong I had them go back and redraw the prism into the inches equivalent and recalculate the volume, and OH NO, they were wrong with their first "288". Hmmmmm. So, this is stuff I've tried before. Now for the "new" attempt that MAYBE will work.
I had them write: 5 ft^3
Then change to: 5 * ft * ft * ft
Then EACH foot had to be converted to inches, so
= 5 *
= 5 * 12in * 12in * 12in
= 8640 in*in*in
= 8640 in^3
Let's see if this one sticks.
Sunday, May 20, 2012
Solar Eclipse Video
Monday, May 14, 2012
Slow Learner
Today in discussing Surface Area and Volume of 3D figures, I found out why textbooks choose to flatten out a cylinder in this way:
as opposed to this way:
I was "not on the ball" when I was talking while simultaneously drawing it the "bad" way.
Oy!
Second, I think I've jumped on the "be bossy in how you accept homework" wagon. I strongly suggested in the past that students show work neatly when they do their homework or tests. I never went further than that. I've seen too many instances now where they or I can't follow their work and when there's a mistake, you have to do extra work to track it down.
Because we're doing SA and LA and V of 3D figures today, and because I've seen so many mistakes in the past (and made them!) just from sloppiness, I laid down the law today. I had a small discussion about how they're not just doing a problem, but they're communicating a process. If the reader has to question you about what you're doing, then you've failed as a communicator. If you have to track down your work later on, and it takes you longer because you're jumping around all the work and can't follow the thought process, then you've failed as a communicator.
I'm making them write things DOWN IN COLUMNS and drawing and labeling neat pictures and indicating what they're finding for each step. With lots of (good-natured) grumbling (see, I'm in denial), they got to work and the beginnings of things looked promising.
I think I want to start off next year as BOSSY PANTS in this manner.
Also, SO excited! I found out what I'm teaching next year (95% sure):
Precalculus preAP
AP Calculus AB
AP Computer Science
Digital Electronics
Woot! Who's going to be busy this summer? I'm going to miss the enthusiastic 8th and 9th graders, but I'll be excited to challenge my brain in a different way.
as opposed to this way:
I was "not on the ball" when I was talking while simultaneously drawing it the "bad" way.
Oy!
Second, I think I've jumped on the "be bossy in how you accept homework" wagon. I strongly suggested in the past that students show work neatly when they do their homework or tests. I never went further than that. I've seen too many instances now where they or I can't follow their work and when there's a mistake, you have to do extra work to track it down.
Because we're doing SA and LA and V of 3D figures today, and because I've seen so many mistakes in the past (and made them!) just from sloppiness, I laid down the law today. I had a small discussion about how they're not just doing a problem, but they're communicating a process. If the reader has to question you about what you're doing, then you've failed as a communicator. If you have to track down your work later on, and it takes you longer because you're jumping around all the work and can't follow the thought process, then you've failed as a communicator.
I'm making them write things DOWN IN COLUMNS and drawing and labeling neat pictures and indicating what they're finding for each step. With lots of (good-natured) grumbling (see, I'm in denial), they got to work and the beginnings of things looked promising.
I think I want to start off next year as BOSSY PANTS in this manner.
Also, SO excited! I found out what I'm teaching next year (95% sure):
Precalculus preAP
AP Calculus AB
AP Computer Science
Digital Electronics
Woot! Who's going to be busy this summer? I'm going to miss the enthusiastic 8th and 9th graders, but I'll be excited to challenge my brain in a different way.
Tuesday, May 08, 2012
Stacks & Queues
In Computer Programming we learned something about various data structures, two being "stacks" and "queues".
Stacks can be thought of like a pile of plates. You keep adding to your list (or plates that are stacked on a table), and when you want to remove one, you remove the top-most one (or the last thing you put on). You can liken it to "last on first out".
Queues are like movie lines - first one in is the first one out. So you can add to the end of a list, and then when things are removed, they peel off from the start of the list.
I thought about that today when I was teaching for two reasons. There are all these "extra" things we have to remember in addition to teaching our content:
* put kids on "mandatorials" if they fail for a grading period
* check in and make sure they're coming to tutorials
* don't forget to update your money log if you're a sponsor of a club
* check in with kids emotionally to see if anyone is acting "off" from their normal selves
* if you're a team leader, check in with other people teaching in your grade level
* do your 5? 6? observations of other teachers throughout the year
* have you planned for an interdisciplinary unit?
* what about a flipped class?
* check in before every test you give to make sure kids know how to study for tests or need extra help
* kids stressed? don't forget that extra activity you did that was short and sweet and was a temporary relief for them
* make sure you connect with the students
* there are no stupid questions, so get that look off your face and answer patiently (it's the FIRST time this kid is asking)
etc.
So this came to light today when I realized that I'd totally forgotten to do one of those things (more?) that should have been ingrained in my mind - the "check that they know how to set up a study schedule for learning" .... (because most of them have never learned how to study for math tests before). Then I thought, I'm like a "queue". I have so many more things popping onto my to-do list, that the old/first stuff falls off my radar while I'm concentrating on the "new fires".
Maybe I need a bunch of charts hanging around my room or somewhere I can see them and the kids can't. That way I can take a quick glance and see if anything needs to be addressed currently. ..... But then I'm thinking, the list would probably be SO long I wouldn't have space to hang it :).
Stacks can be thought of like a pile of plates. You keep adding to your list (or plates that are stacked on a table), and when you want to remove one, you remove the top-most one (or the last thing you put on). You can liken it to "last on first out".
Queues are like movie lines - first one in is the first one out. So you can add to the end of a list, and then when things are removed, they peel off from the start of the list.
I thought about that today when I was teaching for two reasons. There are all these "extra" things we have to remember in addition to teaching our content:
* put kids on "mandatorials" if they fail for a grading period
* check in and make sure they're coming to tutorials
* don't forget to update your money log if you're a sponsor of a club
* check in with kids emotionally to see if anyone is acting "off" from their normal selves
* if you're a team leader, check in with other people teaching in your grade level
* do your 5? 6? observations of other teachers throughout the year
* have you planned for an interdisciplinary unit?
* what about a flipped class?
* check in before every test you give to make sure kids know how to study for tests or need extra help
* kids stressed? don't forget that extra activity you did that was short and sweet and was a temporary relief for them
* make sure you connect with the students
* there are no stupid questions, so get that look off your face and answer patiently (it's the FIRST time this kid is asking)
etc.
So this came to light today when I realized that I'd totally forgotten to do one of those things (more?) that should have been ingrained in my mind - the "check that they know how to set up a study schedule for learning" .... (because most of them have never learned how to study for math tests before). Then I thought, I'm like a "queue". I have so many more things popping onto my to-do list, that the old/first stuff falls off my radar while I'm concentrating on the "new fires".
Maybe I need a bunch of charts hanging around my room or somewhere I can see them and the kids can't. That way I can take a quick glance and see if anything needs to be addressed currently. ..... But then I'm thinking, the list would probably be SO long I wouldn't have space to hang it :).
Sunday, May 06, 2012
EOY Wrap Up
Only 3 weeks and 2 extra days of teaching this year. Oy! As always when I come to this part of the year, I shake my head at how fast it went and what all I still have to do and how there's not enough time and too many testing interruptions to finish up strongly and and and ....Then I also start to get excited about next year. I think about the potential classes I'll teach (not 100% sure yet) and then I don't want to jinx anything, so I make myself THINK it'll be okay if I don't teach a particular course (you know, lie to myself). Then I get nervous because it seems 99.9% sure I will be teaching certain courses, then I wonder how it will all work out. Maybe all this mental gymnastics is just a smoke screen to bend my mind away from the fact that THERE'S HARDLY ENOUGH TIME LEFT THIS YEAR.
Anyway, I was out doing chores today and was at Barnes & Noble and picked up Ron Clark's new book. I did not know he started a new academy. I find his enthusiasm and energy and good thoughts and "can do" attitude and belief and vision so inspiring. Just the jolt I need to end the year. I think his school is 5th-8th, and I teach mostly high schoolers, but I still found many things I want to think on and mold and implement.
Next year, we'll have our 1st senior class. This will be the class that were freshmen when I started teaching at my "new" school. This is the class that in my first year caused me much grief and stress and joy and frustration and laughter. It will be sad and exciting to see them graduate, and it will feel like a different school without them in 2 years.
Fun things this past year:
1. Digital Electronics. At the start of the year, I had my students write on index cards what they were worried about for the coming year in DE. I clipped them together and put them away. Just recently, I found them and as a class we had a giggle reading them. We were all "I hope I don't get electrocuted!" ... "I hope it's not too hard!" ... "I won't know what to do!" And now for the most part, we're bread boarding geniuses, we can work with our BoeBot and circuits and K-Mapping and State Machines and such.
2. My online AP Computer Science class from Mizzou. I took it to "help" one of our students that wanted to take the course but didn't want to take it alone. I ended up learning a lot about the student's point of view in an AP class and trying to balance the work load all the while juggling the ton of other things that make up life. It was also interesting to take an AP class from a college course perspective.
3. Overloading of Duties/Happenings. Okay, not so fun in the stress department, but it's always fun to tackle new challenges. I: was NHS cosponsor, one of 3 HS team leaders, agreed to cosponsor an "inventing team" for next year (that started this year), sat in on TONS of interviews and learned TONS, taught a 1/2 hour weekly yoga class to our sometimes-unwilling students, tried a cross-country geometry project, had several guest speakers in DE (a mix of successful and not).
I'm eager for summer to start for the longer periods of R&R that I'll get and also for the workshops and such I'll get to attend and the planning for 2 new courses I'll be teaching (most likely) and the vow to myself not to sit so much and to get up and move.
Anyway, I was out doing chores today and was at Barnes & Noble and picked up Ron Clark's new book. I did not know he started a new academy. I find his enthusiasm and energy and good thoughts and "can do" attitude and belief and vision so inspiring. Just the jolt I need to end the year. I think his school is 5th-8th, and I teach mostly high schoolers, but I still found many things I want to think on and mold and implement.
Next year, we'll have our 1st senior class. This will be the class that were freshmen when I started teaching at my "new" school. This is the class that in my first year caused me much grief and stress and joy and frustration and laughter. It will be sad and exciting to see them graduate, and it will feel like a different school without them in 2 years.
Fun things this past year:
1. Digital Electronics. At the start of the year, I had my students write on index cards what they were worried about for the coming year in DE. I clipped them together and put them away. Just recently, I found them and as a class we had a giggle reading them. We were all "I hope I don't get electrocuted!" ... "I hope it's not too hard!" ... "I won't know what to do!" And now for the most part, we're bread boarding geniuses, we can work with our BoeBot and circuits and K-Mapping and State Machines and such.
2. My online AP Computer Science class from Mizzou. I took it to "help" one of our students that wanted to take the course but didn't want to take it alone. I ended up learning a lot about the student's point of view in an AP class and trying to balance the work load all the while juggling the ton of other things that make up life. It was also interesting to take an AP class from a college course perspective.
3. Overloading of Duties/Happenings. Okay, not so fun in the stress department, but it's always fun to tackle new challenges. I: was NHS cosponsor, one of 3 HS team leaders, agreed to cosponsor an "inventing team" for next year (that started this year), sat in on TONS of interviews and learned TONS, taught a 1/2 hour weekly yoga class to our sometimes-unwilling students, tried a cross-country geometry project, had several guest speakers in DE (a mix of successful and not).
I'm eager for summer to start for the longer periods of R&R that I'll get and also for the workshops and such I'll get to attend and the planning for 2 new courses I'll be teaching (most likely) and the vow to myself not to sit so much and to get up and move.
Monday, April 30, 2012
More Enlightening Conversations...
The more this year goes on, the more I wonder about what I don't know about students' misunderstandings. My geometry students were practicing today for our Geometry EOC test. I found some great resources online from Texas and North Carolina (whose problems I liked better). One problem gave the coordinates of the 3 vertices of a triangle and asked for the equation of the line that's the perpendicular bisector of one triangle side.
A student calls me over and asks me to refresh her memory on parallel and perpendicular lines. Okay. I asked her what was the same and what was different about 2 parallel lines. She got that the slopes were the same, but hesitated on whether the y-intercepts were the same. So I had her draw an xy-plane and draw me 2 parallel lines. I got this:
And with some prodding she said that the y-intercepts were not the same. Great. So I asked her what was true about perpendicular lines. She got that the slopes were opposite reciprocals. Great. I asked her if the y-intercepts were the same or different, expecting this to be a gimme. Now this is where it started to get enlightening. She couldn't tell me if the y-intercepts of 2 perpendicular lines were the same or different. So I thought, "great! the drawing helped before, so it'll help again." I asked her to use one of the lines before and draw a line that's perpendicular to it. I got this:
Slight alarm bells go off. I ask, "what's true about perpendicular lines?". She quickly states that they form 90 degree angles. So then I thought the x and y axes were throwing her off. So I made her draw a tilted line without the axes and put the perpendicular line on it somewhere. I got this:
Then I thought, well what if we start over and the 2nd line is her pencil that she can just move around to get perpendicular. I got this:
Then we had a LONG discussion (note that there are 23 other people in class practicing and thankfully none was too needy or off task) ... also note that the quiet girl next to this student was surreptitiously eavesdropping like she needed this information, too ... which made me nervous because I started thinking how many OTHER quiet strugglers are there out there? ... Anyway, I got it down to that IF the perpendicular lines form 90 degree angles (which she got), and the angles were supplementary (which she got), then the 2 angles should LOOK congruent. So next I got this:
And then this:
So what's the point of this story? I guess I always have in the back of my mind that if the student is not understanding something, they'll ask for help. But what if what they are not understanding is such a basic concept that it does not even come up in the scope of the course other than something that's used as a tool for the course (i.e. how do perpendicular lines look like when you draw them? what makes a shadow and how do shadows work) that the kid doesn't think or know to ask. And what if there's so much information and so many students to teach that you're going to miss these critical gaps. ... I won't always have the luxury of spending 5-8 minutes with one student and multiply that by the number of students.
Maybe I need some EXTRA problems on homework or class practice that can be a diagnosis of basics for each concept, and then I have to go over them very carefully to probe kids that may be missing elementary things that are holding them back and remediate further.
A student calls me over and asks me to refresh her memory on parallel and perpendicular lines. Okay. I asked her what was the same and what was different about 2 parallel lines. She got that the slopes were the same, but hesitated on whether the y-intercepts were the same. So I had her draw an xy-plane and draw me 2 parallel lines. I got this:
And with some prodding she said that the y-intercepts were not the same. Great. So I asked her what was true about perpendicular lines. She got that the slopes were opposite reciprocals. Great. I asked her if the y-intercepts were the same or different, expecting this to be a gimme. Now this is where it started to get enlightening. She couldn't tell me if the y-intercepts of 2 perpendicular lines were the same or different. So I thought, "great! the drawing helped before, so it'll help again." I asked her to use one of the lines before and draw a line that's perpendicular to it. I got this:
Slight alarm bells go off. I ask, "what's true about perpendicular lines?". She quickly states that they form 90 degree angles. So then I thought the x and y axes were throwing her off. So I made her draw a tilted line without the axes and put the perpendicular line on it somewhere. I got this:
Then I thought, well what if we start over and the 2nd line is her pencil that she can just move around to get perpendicular. I got this:
Then we had a LONG discussion (note that there are 23 other people in class practicing and thankfully none was too needy or off task) ... also note that the quiet girl next to this student was surreptitiously eavesdropping like she needed this information, too ... which made me nervous because I started thinking how many OTHER quiet strugglers are there out there? ... Anyway, I got it down to that IF the perpendicular lines form 90 degree angles (which she got), and the angles were supplementary (which she got), then the 2 angles should LOOK congruent. So next I got this:
And then this:
So what's the point of this story? I guess I always have in the back of my mind that if the student is not understanding something, they'll ask for help. But what if what they are not understanding is such a basic concept that it does not even come up in the scope of the course other than something that's used as a tool for the course (i.e. how do perpendicular lines look like when you draw them? what makes a shadow and how do shadows work) that the kid doesn't think or know to ask. And what if there's so much information and so many students to teach that you're going to miss these critical gaps. ... I won't always have the luxury of spending 5-8 minutes with one student and multiply that by the number of students.
Maybe I need some EXTRA problems on homework or class practice that can be a diagnosis of basics for each concept, and then I have to go over them very carefully to probe kids that may be missing elementary things that are holding them back and remediate further.
Thursday, April 26, 2012
Algebra Algebra Algebra
I don't know why I'm surprised. I knew that from teaching calculus a long time ago, that it always seemed to be the pesky algebra that mostly tripped kids up. I guess I thought it would be different with my current crop of precalculus kids. They're different, I told myself. They're more savvy, I said. They won't have the standard problems, I lied to me. No. They're not and not and they will. And I hesitate to say "algebra". More like "simplifying rational expressions".
We're going over algebraic manipulations of limits, and I gave them basic polynomials and basic "single numerator / single denominator" expressions. They did fine. They were all impressed with themselves that they could chat up limits like they owned the place. And then WHOA. We delved into fractions imbedded in fractions. Huh! What do you mean I have one over "w+4" minus 1/4 ALL over w? What would I do with that? What? Common denom whozits?
Oh! So to get the common denominator of "1 over 'w+4'" and "1/4", I can just add 4 to the top and bottom of 1/4! Who knew!
Or! Once I get that sorted out, when I then have to simplify dividing by w ...... oh! I can just bring it to the "top" and multiply by w, right?
Oy!
And in another problem, the numerator was "9 - v" and the denominator was "(v - 9)(.......)". The student didn't see the connection of how to easily and correctly manipulate the two. It seemed like cheating to her when I mentioned how.
I guess it's a never-ending refreshing of their memory and of practicing and going over concepts. They're so used to JUST dealing with fractions involving ONLY numbers that this may have been too much of a leap for them. Now I'm debating whether to delve into derivatives or to just sprinkle in more intensive algebra and unit circle refreshers in hopes that they'll have an easier time next year in calculus.
Thursday, April 19, 2012
The Limit Does Not Exist
I'm at that (one of many) fun part of precalculus where we talk about limits. We do a day on finding limits graphically. I have them choral chant and watch my bouncing finger run over the notation, "the limit of f of x as x approaches ____ is...". Then on the 2nd day we talk about finding limits algebraically. I usually have skeleton notes and am done with it. This year, I went a step further and made a final chart for them to paste in their notebooks.
It's also one of my favorite topics because I get to use my "spit in the ocean" phrase. When we talk about limits of f(x) as x approaches infinity, and I tell them to only look at the highest powered terms in each of the numerator and denominator, and we test examples on the graphing calculator ...... I describe the largest term like the ocean and everything else as spit. The spit does not change the volume of the ocean significantly.
And without fail, every year someone brings up "Mean Girls".
It's also one of my favorite topics because I get to use my "spit in the ocean" phrase. When we talk about limits of f(x) as x approaches infinity, and I tell them to only look at the highest powered terms in each of the numerator and denominator, and we test examples on the graphing calculator ...... I describe the largest term like the ocean and everything else as spit. The spit does not change the volume of the ocean significantly.
And without fail, every year someone brings up "Mean Girls".
Sunday, April 15, 2012
Perfecting Recipes...
Totally off topic, but one of my latest obsessions: the perfect chocolate chip cookie recipe.
I like to bake, and I like home-baked goodies (and I need to lose some pounds .... connection?). I'm a wee bit snobby about store-bought because when I see all those extra ingredients listed on the label, it does not sound appealing at all. And once you've tasted home-cooked, store bought just doesn't taste the same. Does that mean I'll turn my nose up at an Oreo? Heck no. I'm talking about those hard-plastic-encased "fresh made" stuff from the bakery section. I'll imbibe my extra calories the old-fashioned way, thank you very much.
Anyway, I thought I had a good thing going with my chocolate-chip cookie recipe. I like to add spices to it and increase the vanilla extract and put oatmeal flakes in the dough. I scooped them up with a tablespoon, and poof! we had delicious cookies.
Then a person had generously baked LARGE cookies and brought them to me twice. HUGE. I asked, and this person used a quarter cup measuring cup to put the dough on the cookie sheet. The texture was great, the size was great. Home-made cookies. Delicious.
Now this part is totally NOT sour grapes, but the flavor .... eh! It was a bit too bland and too sweet for me, but did I scarf them all down? Why, yes I did.
So a few weeks ago, I attempted to make these 1/4 cup sized cookies with one of my recipes, but I didn't know what temperature to bake them at or how long to cook them. The flavor came out great, but they were hard as rocks and the texture was too floury. I jokingly wrote a note to the above-mentioned person and nicely asked for her recipe. I figured I could tweak it with my flavorings and happily chomp away.
I was refused. Refused! What kind of person doesn't share a recipe? Maybe this is more common than I know. I'm always willing to share, and I'm happy to share and am flattered that someone wants a recipe. It's not like it's my own creation. It's not like my food will taste any less delicious if someone else is making them. Sheesh. The person was a bit apologetic and said, "I don't even share this recipe with my closest friends". Oy!
Game on girlie. I've since then been testing out recipes, and have finally found one that has the right sweetness level. I also like to add cinnamon and cardamom and cloves and nutmeg and oatmeal. I'm going to experiment with orange rind after a coworker mentioned she did that in a cookie that was delicious. I still don't like the texture of my latest batch, so I have to adjust that.
One interesting note. I'm wondering if everyone's vision of the "perfect" c.c. cookie is akin to everyone's idea of the perfect banana. You know how there's a tiny window when a banana's taste is JUST right? And how everyone has a different idea of when that window is? Well, after testing my cookies out on various people, I think this is the same with c.c. cookies. I've had conflicting suggestions on what would make the perfect texture/flavor/size from a variety of people. Everyone has installed their own window of "acceptability" of a c.c. cookie.
I do think that I have to not test these recipes but once a month or less. Unless I want to totally have to go buy new clothes. But I will create my cookie, and I will share.
I like to bake, and I like home-baked goodies (and I need to lose some pounds .... connection?). I'm a wee bit snobby about store-bought because when I see all those extra ingredients listed on the label, it does not sound appealing at all. And once you've tasted home-cooked, store bought just doesn't taste the same. Does that mean I'll turn my nose up at an Oreo? Heck no. I'm talking about those hard-plastic-encased "fresh made" stuff from the bakery section. I'll imbibe my extra calories the old-fashioned way, thank you very much.
Anyway, I thought I had a good thing going with my chocolate-chip cookie recipe. I like to add spices to it and increase the vanilla extract and put oatmeal flakes in the dough. I scooped them up with a tablespoon, and poof! we had delicious cookies.
Then a person had generously baked LARGE cookies and brought them to me twice. HUGE. I asked, and this person used a quarter cup measuring cup to put the dough on the cookie sheet. The texture was great, the size was great. Home-made cookies. Delicious.
Now this part is totally NOT sour grapes, but the flavor .... eh! It was a bit too bland and too sweet for me, but did I scarf them all down? Why, yes I did.
So a few weeks ago, I attempted to make these 1/4 cup sized cookies with one of my recipes, but I didn't know what temperature to bake them at or how long to cook them. The flavor came out great, but they were hard as rocks and the texture was too floury. I jokingly wrote a note to the above-mentioned person and nicely asked for her recipe. I figured I could tweak it with my flavorings and happily chomp away.
I was refused. Refused! What kind of person doesn't share a recipe? Maybe this is more common than I know. I'm always willing to share, and I'm happy to share and am flattered that someone wants a recipe. It's not like it's my own creation. It's not like my food will taste any less delicious if someone else is making them. Sheesh. The person was a bit apologetic and said, "I don't even share this recipe with my closest friends". Oy!
Game on girlie. I've since then been testing out recipes, and have finally found one that has the right sweetness level. I also like to add cinnamon and cardamom and cloves and nutmeg and oatmeal. I'm going to experiment with orange rind after a coworker mentioned she did that in a cookie that was delicious. I still don't like the texture of my latest batch, so I have to adjust that.
One interesting note. I'm wondering if everyone's vision of the "perfect" c.c. cookie is akin to everyone's idea of the perfect banana. You know how there's a tiny window when a banana's taste is JUST right? And how everyone has a different idea of when that window is? Well, after testing my cookies out on various people, I think this is the same with c.c. cookies. I've had conflicting suggestions on what would make the perfect texture/flavor/size from a variety of people. Everyone has installed their own window of "acceptability" of a c.c. cookie.
I do think that I have to not test these recipes but once a month or less. Unless I want to totally have to go buy new clothes. But I will create my cookie, and I will share.
Wednesday, April 11, 2012
Interviews...
This year provides another first for me. I'm on the "interviewer" side of conducting interviews for possible openings next year. I'm not the only one asking questions, thank goodness, because it's good to get varied feedback and reactions to candidates. But here are some surprising things that seem to be a running theme. And by surprising, I mean, "have you not gone to basic interview 101 school, people?"
When you are asked, "do you have any questions?", here possibly are not good responses:
* No, I really can't think of any.
* Um, what time is your school day over?
* No, but you know, people always seem to ask that.
* Do you have to tutor a lot?
When asked about your career goals, you may not want to mention that in a year or two you plan on doing something else.
When showing up, if you haven't brought any samples of your work, why not?
When asked why you want to work at this particular school, hopefully your answer shows that you've researched us and can say something beyond words that imply, "I want to work with an easy population". First off, there's what SEEMS to be true and then there's reality. And also you don't just say you want a change from where you are, and that's it.
Oh, and maybe you can show up on time.
And maybe you want to wear something other than your sloppy work clothes.
Just saying.
Anyway, very interesting.
When you are asked, "do you have any questions?", here possibly are not good responses:
* No, I really can't think of any.
* Um, what time is your school day over?
* No, but you know, people always seem to ask that.
* Do you have to tutor a lot?
When asked about your career goals, you may not want to mention that in a year or two you plan on doing something else.
When showing up, if you haven't brought any samples of your work, why not?
When asked why you want to work at this particular school, hopefully your answer shows that you've researched us and can say something beyond words that imply, "I want to work with an easy population". First off, there's what SEEMS to be true and then there's reality. And also you don't just say you want a change from where you are, and that's it.
Oh, and maybe you can show up on time.
And maybe you want to wear something other than your sloppy work clothes.
Just saying.
Anyway, very interesting.
Sunday, April 01, 2012
Triangle Inequalities
On Saturday we went to see a show by this company (amazing tap dancing) and here's some footage from a past show. And as I was sitting in my seat fidgeting with the ticket stub, I got what I think was a great idea. Then I thought, oh surely other people already do this, and I just missed the boat. And now, maybe I'll never sail on that boat again for a while because I may not be teaching geometry next year. And then I went back to fiddling and thinking with my ticket stub.
I was thinking about the lesson on the restrictions on the 3 side lengths that can potentially make a triangle - how any 2 sides of the triangle have to sum up to more than the length of the 3rd. I've taught it various ways. We always explore with a variety of things. BUT. I've never used anything I'm completely satisfied with:
- spaghetti: messy, hard to measure, the thickness may allow students to think it's still possible, hard to get the situation where 2 of the shapes EXACTLY add to the 3rd.
- linking cubes: too thick, and sometimes students would still think they could make a triangle when they couldn't.
- cut strips of paper: see above
- drawing the triangles using compasses set at various lengths: too cumbersome.
PAPER SHOW TICKET to the rescue! Here's my idea. Cut some long strips of thickish paper (cardboard/stock paper?), or have them cut them. Maybe give one or a few to each student. Then have the students experiment with laying it flat on the desk and folding in from the two ends. They can write down all the situations they tried and measure the three resulting sides in centimeters and see what sorts of situations allow them to make a triangle from the resulting 3 sections of the strip. You may even have guiding questions about: "what 3 lengths are not even in the running and why not?" .... "what 3 lengths ALMOST look like they'll make it, but don't?" ... something to that effect.
I think this will be much better than my old props: easy, able to try a variety of cases, cheap, effective.
I was thinking about the lesson on the restrictions on the 3 side lengths that can potentially make a triangle - how any 2 sides of the triangle have to sum up to more than the length of the 3rd. I've taught it various ways. We always explore with a variety of things. BUT. I've never used anything I'm completely satisfied with:
- spaghetti: messy, hard to measure, the thickness may allow students to think it's still possible, hard to get the situation where 2 of the shapes EXACTLY add to the 3rd.
- linking cubes: too thick, and sometimes students would still think they could make a triangle when they couldn't.
- cut strips of paper: see above
- drawing the triangles using compasses set at various lengths: too cumbersome.
PAPER SHOW TICKET to the rescue! Here's my idea. Cut some long strips of thickish paper (cardboard/stock paper?), or have them cut them. Maybe give one or a few to each student. Then have the students experiment with laying it flat on the desk and folding in from the two ends. They can write down all the situations they tried and measure the three resulting sides in centimeters and see what sorts of situations allow them to make a triangle from the resulting 3 sections of the strip. You may even have guiding questions about: "what 3 lengths are not even in the running and why not?" .... "what 3 lengths ALMOST look like they'll make it, but don't?" ... something to that effect.
I think this will be much better than my old props: easy, able to try a variety of cases, cheap, effective.
Friday, March 30, 2012
Whew! Almost the Weekend
This week had cr*ppy written all over it. So I'm just going to detox and purge the "bad" stuff:
* Tired from too little sleep.
* Drink too much coffee to make up for it.
* Can't sleep the following night because of the excess caffeine.
* Rinse. Repeat.
* Patience at an all time low due to sleep issues.
* Weird Schedules due to state testing.
* Don't read one of the bazillion e-mails about the schedule and get called out for it.
* Snap at children due to lack of patience.
* Feel bad and remember I don't have to say EVERYTHING I'm thinking.
* Have conversations in my head saying the sleep-deprived snotty things I shouldn't verbalize (also visualize snotty facial expressions I'd make with words).
* Skip yoga and tap and Lindy Hop due to sleepiness.
* Feel worse physically due to less exercise.
* Make up for "stuff" by mainlining huge chocolate chip cookies.
* Feel worse physically due to bad eating habits.
* Take on more work for next year in the form of an "inventing 'contest'".
* Hear about various ones of our/my students putting down our school.
* Take it personally.
* Wake up at 3am Friday to make a test I have to give today.
* Excited about the faculty meeting this morning taking up 1 hour of my planning time.
* Excited about being "tired stupid" today.
Off to go "running" at 4:30am before I get ready for work. Woot! At least I got my geometry test done. I envision caffeine and a cookie in my near future. Breakfast?
* Tired from too little sleep.
* Drink too much coffee to make up for it.
* Can't sleep the following night because of the excess caffeine.
* Rinse. Repeat.
* Patience at an all time low due to sleep issues.
* Weird Schedules due to state testing.
* Don't read one of the bazillion e-mails about the schedule and get called out for it.
* Snap at children due to lack of patience.
* Feel bad and remember I don't have to say EVERYTHING I'm thinking.
* Have conversations in my head saying the sleep-deprived snotty things I shouldn't verbalize (also visualize snotty facial expressions I'd make with words).
* Skip yoga and tap and Lindy Hop due to sleepiness.
* Feel worse physically due to less exercise.
* Make up for "stuff" by mainlining huge chocolate chip cookies.
* Feel worse physically due to bad eating habits.
* Take on more work for next year in the form of an "inventing 'contest'".
* Hear about various ones of our/my students putting down our school.
* Take it personally.
* Wake up at 3am Friday to make a test I have to give today.
* Excited about the faculty meeting this morning taking up 1 hour of my planning time.
* Excited about being "tired stupid" today.
Off to go "running" at 4:30am before I get ready for work. Woot! At least I got my geometry test done. I envision caffeine and a cookie in my near future. Breakfast?
Saturday, March 24, 2012
Logarithmic Graphing
In precalculus we finished our unit on logarithms by seeing what/why/how log graph paper is used. I showed them the crazy-uneven-looking paper and we got to it with:
this sheet.
Things that came up: name of our galaxy, how to do the work for the 2nd blank, giggling about Uranus, caution and care of units when you just see "58", number of feet in a mile, how much is a billion, how many millions in a billion, ...
I also love the type of examples that we used. Their homework that night was to find a sort of "show and tell" example about anything to do with astronomy. They came back with some cool facts, and we had fun sharing and being amazed at it all.
this sheet.
Things that came up: name of our galaxy, how to do the work for the 2nd blank, giggling about Uranus, caution and care of units when you just see "58", number of feet in a mile, how much is a billion, how many millions in a billion, ...
I also love the type of examples that we used. Their homework that night was to find a sort of "show and tell" example about anything to do with astronomy. They came back with some cool facts, and we had fun sharing and being amazed at it all.
Tuesday, March 20, 2012
Trigonometry Word Problems
We finally got to the cool section in geometry where the students FINALLY can figure out what those crazy "sin" "cos" and "tan" buttons are on the calculator. After practicing *basic* problems in class, I assigned this "word problem" homework.
A sample problem is:
1. For a 50 foot pole to be stable, engineers have decided that 3 equally-spaced guide wires (running from the top of the pole to the ground) have to create a 75deg angle with the ground.
a. How much total wire should they plan for?
b. How far from the pole should each wire be attached to the ground?
I tried to make "sensible" problems that weren't of the "shadow" or "kite" variety ... because at the end of the day, I guess I don't care how far out the kite is or why I would even want to know my shadow's length (and you know, students don't grasp this whole shadow thing anyway :) ).
Also, I found it was a good idea NOT TO ASSUME they knew what sonar was or what guide wires looked like, so we had a discussion before the end of class as to what the pictures might look like (with them doing most of the work, of course).
Also, spring break? why si, I did enjoy it, gracie.
A sample problem is:
1. For a 50 foot pole to be stable, engineers have decided that 3 equally-spaced guide wires (running from the top of the pole to the ground) have to create a 75deg angle with the ground.
a. How much total wire should they plan for?
b. How far from the pole should each wire be attached to the ground?
I tried to make "sensible" problems that weren't of the "shadow" or "kite" variety ... because at the end of the day, I guess I don't care how far out the kite is or why I would even want to know my shadow's length (and you know, students don't grasp this whole shadow thing anyway :) ).
Also, I found it was a good idea NOT TO ASSUME they knew what sonar was or what guide wires looked like, so we had a discussion before the end of class as to what the pictures might look like (with them doing most of the work, of course).
Also, spring break? why si, I did enjoy it, gracie.
Friday, March 09, 2012
Shadows on Planet Earth....
We just finished our unit on similar triangles, and as par for the course, there were the typical shadow problems. I know from past experience that students have problems with these: they draw shadows going in 2 different directions .... they don't know how to set things up .... etc. BUT. I thought it was a geometry misconception problem. No. From deeper questioning of various students today, I see that some students have no concept of shadows.
Various questions/answers:
* What makes a shadow ... or how is it made?
- shrug.
* How would you make your shadow longer if it's coming from a light post?
- move closer to the light?
* Draw the picture and point to the shadow.
- points to the hypotenuse.
How did I miss this scary fact in 12 years of teaching geometry? I guess I just made assumptions on why they were struggling, and didn't probe deeper.
Various questions/answers:
* What makes a shadow ... or how is it made?
- shrug.
* How would you make your shadow longer if it's coming from a light post?
- move closer to the light?
* Draw the picture and point to the shadow.
- points to the hypotenuse.
How did I miss this scary fact in 12 years of teaching geometry? I guess I just made assumptions on why they were struggling, and didn't probe deeper.
Thursday, March 08, 2012
Eavesdropping Assumptions
In geometry we are learning the special right triangles, and I wanted to give the students time to come up with memory tools for remembering which ratios went where on the 2 triangles. Having taught geometry for 12 years, most of the tools are repeats for me, but every so often I get some surprises that stick in my head.
I gave the students time to discuss, and it was a class late in the day, and I was observing who was doing what. I eavesdropped on 2 students and thought I overheard, "she was hung over, so that's why she didn't come to school". And then they both snickered and continued talking. "Great!" I thought. First of all someone is drinking, second of all these kids are off task. Third .... who's absent today ??? Fourth, do I make a big deal of it? Which part? The drinking or (more seriously :)) NOT talking geometry when they should be.
Then I asked for volunteers to share their memory tools. Here are some repeats (for me) and some refreshing new ones:
* The 30-60-90 has 3 different angles, so that's the one with 3 different numbers (1, 2, root 3).
* The 45-45-90 has twin angles, so the parents are the x's and the root 2 are the twins
* For each of them, the hy-pot-TWO-nuse has a 2 involved on the hypotenuse side.
* the root 3 is by the 30
Then one of the "drunk talker" students raised her hand:
* On the 30-60-90 triangle, the bottom one has one X boyfriend, one has 2 X boyfriends, and one has 3 X boyfriends, and she's still HUNG OVER HIM, so that's why there's a radical hanging over the 3.
I clarified that she really meant "hung up" on him, and I was the only lush thinking about alcohol, but then I had to laugh at myself for assuming the students weren't doing what I'd asked them to do when all along they were.
I gave the students time to discuss, and it was a class late in the day, and I was observing who was doing what. I eavesdropped on 2 students and thought I overheard, "she was hung over, so that's why she didn't come to school". And then they both snickered and continued talking. "Great!" I thought. First of all someone is drinking, second of all these kids are off task. Third .... who's absent today ??? Fourth, do I make a big deal of it? Which part? The drinking or (more seriously :)) NOT talking geometry when they should be.
Then I asked for volunteers to share their memory tools. Here are some repeats (for me) and some refreshing new ones:
* The 30-60-90 has 3 different angles, so that's the one with 3 different numbers (1, 2, root 3).
* The 45-45-90 has twin angles, so the parents are the x's and the root 2 are the twins
* For each of them, the hy-pot-TWO-nuse has a 2 involved on the hypotenuse side.
* the root 3 is by the 30
Then one of the "drunk talker" students raised her hand:
* On the 30-60-90 triangle, the bottom one has one X boyfriend, one has 2 X boyfriends, and one has 3 X boyfriends, and she's still HUNG OVER HIM, so that's why there's a radical hanging over the 3.
I clarified that she really meant "hung up" on him, and I was the only lush thinking about alcohol, but then I had to laugh at myself for assuming the students weren't doing what I'd asked them to do when all along they were.
Thursday, March 01, 2012
Logarithm Applications
I shuffled around my precalculus curriculum (was eager to get to intense trigonometry in the fall) and am JUST almost through logs and ln and e. My class spent a day on applications, and we had some fun conversations about the following scenarios. My last day will be spent showing them log graphing paper and log-log and semi-log and 1-cycle and "how do they get the partitions" and why would someone graph on log graph paper and all that. Sheesh! The year (as always) is whizzing by.
Here's what we did (heavily borrowed from a TON of math books:
Here's what we did (heavily borrowed from a TON of math books:
Tuesday, February 28, 2012
Class Time Stories
Who says children aren't ready for the more Grimm of the Grimm Fairy Tales? Today I introduced the special right triangles, but I wanted to quickly show my students where the crazy ratios came from. The story I'm about to repeat to you started with "they got divorced", and one student asked, "why does it always have to be about divorce? Why not an assassin?"... And so I give you the final story (picture all the geometry figures that go along with it).
Once upon a time there was this square. He was EVERY SQUARE, so his sides were of length "x" to stand for EVERY SQUARE. Life was grand. Suddenly! An assassin came along and PHSHWOOT sliced that square in half right through the diagonal and ran away with 1/2 the square laughing maniacally. The square was a broken man. He was half the man he used to be. (draw right triangle). What are his angles? (place a big question mark on the hypotenuse). The townspeople were not compassionate about the "square" after the tragic incident. They were more curious as to the length of his scar. (go through process of finding the hypotenuse in terms of x). The End. Or is it?
But wait, no one ever caught the assassin. Over in Equilateral Triangle Land, a hapless EVERY EQUILATERAL was innocently going about his days. His side lengths were 2x. Cue in the music. PHSHWOOT, the assassin strikes again ...... etc, etc. .... The end....
Once upon a time there was this square. He was EVERY SQUARE, so his sides were of length "x" to stand for EVERY SQUARE. Life was grand. Suddenly! An assassin came along and PHSHWOOT sliced that square in half right through the diagonal and ran away with 1/2 the square laughing maniacally. The square was a broken man. He was half the man he used to be. (draw right triangle). What are his angles? (place a big question mark on the hypotenuse). The townspeople were not compassionate about the "square" after the tragic incident. They were more curious as to the length of his scar. (go through process of finding the hypotenuse in terms of x). The End. Or is it?
But wait, no one ever caught the assassin. Over in Equilateral Triangle Land, a hapless EVERY EQUILATERAL was innocently going about his days. His side lengths were 2x. Cue in the music. PHSHWOOT, the assassin strikes again ...... etc, etc. .... The end....
Thursday, February 23, 2012
Drugs, Sex, & Rock-n-Roll
That was the title of today's notes in precalculus in which we were to delve into a revisiting of logarithms. I know, it's REALLY "s, d, & rnr" (as my wise 11th graders kept reminding me), but I thought about the drugs 1st (since my vitamins were sitting on the student desks, and I moved them to under my document camera and thought drugs), then I thought about the population growth model we'd be talking about, and DING, sex .... then it was only a short hop to how we'd also be briefly discussing decibel levels and BOOM, rock-n-roll.
I started class with a cool problem I got at NCTM a long time ago, something to the effect of:
An athlete ingests 16mg of drug at 8am, and has to take a drug test at 1pm. His body metabolizes the drug at a rate of 25% an hour, and to pass the drug test, he can have at most 1mg of drug in his body. Will he pass the drug test? If not then when (hour, minute, second) can he pass? How much could he have taken at 8am to actually pass at 1pm?
I broke it up into parts, and we had good discussions about various things:
* why not be 0mg to pass?
* how do you convert decimal numbers/answers to actual time?
* okay, this may not happen, but think about hospitals and drugs and surgery scenarios.
* what does metabolizing 25%/hour mean?
After this, then we got to sex. I'd looked up the US population as of mid 2011 (311,800,000), and separately found a model for US population, and asked if the model was accurate. That's all I gave them, and had them work things out and back up their reasoning. Good discussions:
* how do they get the models?
* how far off is it when we see the numbers? (% difference)
Then class was almost over, but I'd copied a brief example on how they calculate decibel levels of noise, and I mentioned cilia in the ear and how once it's damaged, it doesn't repair itself and such. Some kids talked about how their dad's or grandfathers were in rock bands or such and had huge hearing loss.
Of course we had a brief review of log rules and such and they did get basic review homework and practice, but it was fun to tease them along.
I started class with a cool problem I got at NCTM a long time ago, something to the effect of:
An athlete ingests 16mg of drug at 8am, and has to take a drug test at 1pm. His body metabolizes the drug at a rate of 25% an hour, and to pass the drug test, he can have at most 1mg of drug in his body. Will he pass the drug test? If not then when (hour, minute, second) can he pass? How much could he have taken at 8am to actually pass at 1pm?
I broke it up into parts, and we had good discussions about various things:
* why not be 0mg to pass?
* how do you convert decimal numbers/answers to actual time?
* okay, this may not happen, but think about hospitals and drugs and surgery scenarios.
* what does metabolizing 25%/hour mean?
After this, then we got to sex. I'd looked up the US population as of mid 2011 (311,800,000), and separately found a model for US population, and asked if the model was accurate. That's all I gave them, and had them work things out and back up their reasoning. Good discussions:
* how do they get the models?
* how far off is it when we see the numbers? (% difference)
Then class was almost over, but I'd copied a brief example on how they calculate decibel levels of noise, and I mentioned cilia in the ear and how once it's damaged, it doesn't repair itself and such. Some kids talked about how their dad's or grandfathers were in rock bands or such and had huge hearing loss.
Of course we had a brief review of log rules and such and they did get basic review homework and practice, but it was fun to tease them along.
Sunday, February 19, 2012
"Other" Life aka GettaLife
It seems I've come across the following sentiment a ton lately: balancing school life and nonschool life in order to not burn out and to not put all your "happiness" eggs in one basket.
I'm having a pretty good year this year, and I think part of it is that every week, I have things OTHER than school to look forward to. So just in case (and it'll always happen at some point) I have a super crappy day, then I can recharge with my nonschool existence.
Let's see ... Tuesdays I have my favorite (and only for now) yoga class at 6pm. I have to follow my new year's resolution and actually leave school by 5:40 in order to make it, but I've been pretty good so far. Thanks to my guardian angel across the hall that comes in and taps at her watch to make sure I don't backslide :).
Wednesdays I have tap dancing and Lindy Hop lessons at night. That's always fun. Either I feel like the galumphing dolt in tap class, or I rock it. Either way, fun. And in Lindy Hop. Social dancing. Fun.
Thursday mornings I treat myself to breakfast out at a popular local restaurant. I've been doing it for 3 years, and the waiters know me, and it feels like home. I read the paper and do the puzzles and ease into the day. Something to look forward to.
Fridays, well, there's most always nachos and liquids to look forward to after school.
Also, our whole math department has the same period off at the end of a day, so we hike it over to a local place for debriefing and caffeine.
And on my daily 1/2 hour commute to and from work, I look forward to either listening to a book on CD (thank you simplyaudiobooks) or learn "Italian Like Crazy". Which reminds me .... Italy! Spring Break! Lucky Dog!
These are many of the things that keep me sane during the crazy times.
I'm having a pretty good year this year, and I think part of it is that every week, I have things OTHER than school to look forward to. So just in case (and it'll always happen at some point) I have a super crappy day, then I can recharge with my nonschool existence.
Let's see ... Tuesdays I have my favorite (and only for now) yoga class at 6pm. I have to follow my new year's resolution and actually leave school by 5:40 in order to make it, but I've been pretty good so far. Thanks to my guardian angel across the hall that comes in and taps at her watch to make sure I don't backslide :).
Wednesdays I have tap dancing and Lindy Hop lessons at night. That's always fun. Either I feel like the galumphing dolt in tap class, or I rock it. Either way, fun. And in Lindy Hop. Social dancing. Fun.
Thursday mornings I treat myself to breakfast out at a popular local restaurant. I've been doing it for 3 years, and the waiters know me, and it feels like home. I read the paper and do the puzzles and ease into the day. Something to look forward to.
Fridays, well, there's most always nachos and liquids to look forward to after school.
Also, our whole math department has the same period off at the end of a day, so we hike it over to a local place for debriefing and caffeine.
And on my daily 1/2 hour commute to and from work, I look forward to either listening to a book on CD (thank you simplyaudiobooks) or learn "Italian Like Crazy". Which reminds me .... Italy! Spring Break! Lucky Dog!
These are many of the things that keep me sane during the crazy times.
Saturday, February 11, 2012
Figuring It Out On Your Own
As I was leaving school on Friday, a student wanted to use my phone and then hang out in the room while she waited for her ride. We chatted for a bit, and our talk turned to grades. I congratulated her on her recent high test score, and she mentioned that she's really proud of herself this year. Her lowest grade is an 82%. She's a sophomore. She's one of my more diligent students, and I wondered out loud why she wasn't in NHS, and she mentioned that she was a slacker her freshman year, and now her GPA reflects that.
I asked what would have helped her do better as a freshman. We batted around ideas. Here were basically all her responses:
* Would it have helped hearing from older students about the importance of grades?
-- No, I'd just tune them out and think they thought they were "all that"
* Would it have helped if adults talked about the importance of GPAs and college?
-- No, bla bla bla, just adult talk.
* Do you think anything would have helped?
-- No, I think I just had to figure it out on my own.
But that makes me wonder. Maybe it doesn't seem like we're getting through at the time, but maybe we're all planting seeds for future actions. Maybe collectively it's just a process everyone has to go through and who knows what will finally get through, so we have to keep trying and not get discouraged if there's not INSTANTANEOUS reversal of bad study habits.
I'm also thinking of a second student this year who's now a junior. This student was a bit flaky her first 2 years. Did the bare minimum and had the grades to prove it. All of a sudden this year, she's in the A and B range. She finally figured out that grades matter and that she IS smart and doesn't have to act the fluff head.
It's nice when you see things change for the better.
I asked what would have helped her do better as a freshman. We batted around ideas. Here were basically all her responses:
* Would it have helped hearing from older students about the importance of grades?
-- No, I'd just tune them out and think they thought they were "all that"
* Would it have helped if adults talked about the importance of GPAs and college?
-- No, bla bla bla, just adult talk.
* Do you think anything would have helped?
-- No, I think I just had to figure it out on my own.
But that makes me wonder. Maybe it doesn't seem like we're getting through at the time, but maybe we're all planting seeds for future actions. Maybe collectively it's just a process everyone has to go through and who knows what will finally get through, so we have to keep trying and not get discouraged if there's not INSTANTANEOUS reversal of bad study habits.
I'm also thinking of a second student this year who's now a junior. This student was a bit flaky her first 2 years. Did the bare minimum and had the grades to prove it. All of a sudden this year, she's in the A and B range. She finally figured out that grades matter and that she IS smart and doesn't have to act the fluff head.
It's nice when you see things change for the better.
Tuesday, January 31, 2012
Clock Update
I saw this idea somewhere a while ago, and due to the number of questions I keep getting, I thought I'd have this clock enhancement. I don't say anything, it's just there for them to process. Woot! Future time tellers of America.
Saturday, January 28, 2012
Special Quadrilaterals
We've just finished our unit on special quadrilaterals, and before our test, I thought I would try to drill home the value of marking up your figure with pertinent information to help you solve problems. I also made them cover up their previous attempts with jokes about their wandering eye that may do them harm. I decided to do it in a "race" type format.
I wanted the kids to compete against themselves and make progress between attempts, so I said that they would be timing themselves and grading themselves and being consistent with how they marked mistakes.
I put an online timer on my computer and the document camera (this one was nice). I just set the start time for 0 and end time for 2 minutes just in case.
At each attempt, in one color, the student was to mark up the figure with useful/correct markings that represented the figure. I reminded them to QUIETLY lay down their pencils at the end (by being goofy and demonstrating the jerky contestant who makes tons of noise at the end). Then when everyone was done (all eyes up), we graded in a different color. We did 3 attempts for each shape, and I kept asking for hand raised if they made improvement. I said they could do the 4th attempt on the night before the test.
Helpful? Don't know, but it was a chance to drive home the importance of marking and knowing the properties.
Here's the document:
I wanted the kids to compete against themselves and make progress between attempts, so I said that they would be timing themselves and grading themselves and being consistent with how they marked mistakes.
I put an online timer on my computer and the document camera (this one was nice). I just set the start time for 0 and end time for 2 minutes just in case.
At each attempt, in one color, the student was to mark up the figure with useful/correct markings that represented the figure. I reminded them to QUIETLY lay down their pencils at the end (by being goofy and demonstrating the jerky contestant who makes tons of noise at the end). Then when everyone was done (all eyes up), we graded in a different color. We did 3 attempts for each shape, and I kept asking for hand raised if they made improvement. I said they could do the 4th attempt on the night before the test.
Helpful? Don't know, but it was a chance to drive home the importance of marking and knowing the properties.
Here's the document:
Thursday, January 26, 2012
Thinking, Contributing, and Confidence...
It finally hit me the other day, the students in my "regular" geometry class were so gun shy of answering questions. You know. I'd say something like, "and what kind of quadrilateral is this forced to be if it has ____ properties?".
Chirp.
Then someone bravely says, "rhombus." Then downcast eyes. Then, "oh I don't know, forget it." More downcast eyes with the body language of, "move on lady, nothing to see here." Even though it turns out the answer was right.
So after it happened again in my next "regular" class. I stopped the lesson and said the following:
You know if I could grade you all on your participation in your learning, it would go something like this.
* 3 points if you answer my question, and it's right. Because you're thinking and active in your learning.
* 2 points if you answer my question, and it's wrong. Because you're still in the game and willing to process your information and try.
* 1 point if you are paying attention and answering in your head but for whatever reason, you don't speak.
* 0 points if you just sit passively and think, oh, someone else will figure it out.
* -1 point if you sit there and think, hmmmm what's for lunch.
Then I mentioned the, "you can't just passively sit there and learn math" spiel. Then I went back to the lesson.
Hmmmm. Then there was lots of participation. And I would interject with, "3 points" .... "2 points" ... etc. ... hopefully it lasts.
Chirp.
Then someone bravely says, "rhombus." Then downcast eyes. Then, "oh I don't know, forget it." More downcast eyes with the body language of, "move on lady, nothing to see here." Even though it turns out the answer was right.
So after it happened again in my next "regular" class. I stopped the lesson and said the following:
You know if I could grade you all on your participation in your learning, it would go something like this.
* 3 points if you answer my question, and it's right. Because you're thinking and active in your learning.
* 2 points if you answer my question, and it's wrong. Because you're still in the game and willing to process your information and try.
* 1 point if you are paying attention and answering in your head but for whatever reason, you don't speak.
* 0 points if you just sit passively and think, oh, someone else will figure it out.
* -1 point if you sit there and think, hmmmm what's for lunch.
Then I mentioned the, "you can't just passively sit there and learn math" spiel. Then I went back to the lesson.
Hmmmm. Then there was lots of participation. And I would interject with, "3 points" .... "2 points" ... etc. ... hopefully it lasts.
Wednesday, January 25, 2012
Statistics vs Calculus
It's choice sheet time, and our current crop of precalculus students (and algebra 2 students for that matter) are asking questions:
* What IS calculus?
* What IS statistics?
* Which one should I take?
* Can I take both eventually?
We've been having conversations on the fly, but I thought it would be good to get it all down on paper and send out a mass school e-mail. This way the students have a more informed way of making a decision as opposed to, "so and so said THIS one was easier .... or THIS one was the one to take .... or my friends are taking this one...".
Here's the document:
* What IS calculus?
* What IS statistics?
* Which one should I take?
* Can I take both eventually?
We've been having conversations on the fly, but I thought it would be good to get it all down on paper and send out a mass school e-mail. This way the students have a more informed way of making a decision as opposed to, "so and so said THIS one was easier .... or THIS one was the one to take .... or my friends are taking this one...".
Here's the document:
Sunday, January 22, 2012
Collaboration
I just got back from the Houston Regional T3 workshop and learned yet more things I can do with the TI-nspire.
* I now know how to use the student software to be useful to me
* I know how to link between calculator and computer/calculator to transfer things
* I know how to upload pictures onto the calculator and then use it for math, say on a graph page or a geometry page
* I know how to easily do piecewise function graphing
I'm very excited to use these activities for upcoming lessons.
AND. Something someone said sparked another idea. I'm wondering if there are any precalculus teachers out there with about 22 students that are willing to collaborate with my 22 students. I don't have a firm idea of the final product, but my thinking is along the lines of: we would somehow match up our "remote" pairs of students, and then they would have to work together to create something - blog, song, newsletter, podcast, other .... that has to do with precalculus - either teaching something as a review, finding a new thing that is associated with precalculus, coming up with a memory tool for a concept we've learned .... I want to leave it open enough, so that they can be creative and most likely think of something we don't envision. I do want to have more firm rules and periodic due dates along the way. I'm thinking of a project/activity that we give them about 3 or so weeks for. In this way, our students can find a new "math buddy" in another state, and they can learn skills of working with a total stranger to complete a task (good future working-life skill).
Any takers? If so, leave a comment, or send me e-mail (math_mambo@yahoo.com), and we can take it from there.
For that matter I have roughly 4 classes of geometry that we can do the same thing with. But in that case, I'd ultimately need about 86 or so total students.
* I now know how to use the student software to be useful to me
* I know how to link between calculator and computer/calculator to transfer things
* I know how to upload pictures onto the calculator and then use it for math, say on a graph page or a geometry page
* I know how to easily do piecewise function graphing
I'm very excited to use these activities for upcoming lessons.
AND. Something someone said sparked another idea. I'm wondering if there are any precalculus teachers out there with about 22 students that are willing to collaborate with my 22 students. I don't have a firm idea of the final product, but my thinking is along the lines of: we would somehow match up our "remote" pairs of students, and then they would have to work together to create something - blog, song, newsletter, podcast, other .... that has to do with precalculus - either teaching something as a review, finding a new thing that is associated with precalculus, coming up with a memory tool for a concept we've learned .... I want to leave it open enough, so that they can be creative and most likely think of something we don't envision. I do want to have more firm rules and periodic due dates along the way. I'm thinking of a project/activity that we give them about 3 or so weeks for. In this way, our students can find a new "math buddy" in another state, and they can learn skills of working with a total stranger to complete a task (good future working-life skill).
Any takers? If so, leave a comment, or send me e-mail (math_mambo@yahoo.com), and we can take it from there.
For that matter I have roughly 4 classes of geometry that we can do the same thing with. But in that case, I'd ultimately need about 86 or so total students.
Sunday, January 15, 2012
Pa-ra-lel-o-grams
I've been obsessively using the TI-nspire as a discovery tool in my classes these last 2 weeks. In geometry, we just started parallelograms, and I wanted them to explore the 5 properties of parallelograms, and it worked great.
One extra thing that I'm excited about is that I had them hold up their closed fists, and I asked them to put up a finger for every syllable of "parallelogram". Five! Ohhh! Five properties. So. Every time they discovered a new property on the calculator, I had them run through the list so far and tick off a new finger for the newly discovered property. We did this until we got through all 5 properties. Woot! Memory tool. Hopefully, they'll remember that there are 5 and parallelogram has 5 syllables, and they can recite all the properties:
1. parallel opposite sides
2. congruent opposite sides
3. congruent opposite angles
4. supplementary adjacent angles
5. diagonals bisect each other
One extra thing that I'm excited about is that I had them hold up their closed fists, and I asked them to put up a finger for every syllable of "parallelogram". Five! Ohhh! Five properties. So. Every time they discovered a new property on the calculator, I had them run through the list so far and tick off a new finger for the newly discovered property. We did this until we got through all 5 properties. Woot! Memory tool. Hopefully, they'll remember that there are 5 and parallelogram has 5 syllables, and they can recite all the properties:
1. parallel opposite sides
2. congruent opposite sides
3. congruent opposite angles
4. supplementary adjacent angles
5. diagonals bisect each other
Monday, January 09, 2012
Six Word Memoirs
Recently, I was reminded of the "six word memoirs", and I decided to have that as my first day back homework for my precalculus students.
I had them create a small poster with 2 such memoirs, one for their "math life" and one for their "other/real life". Here's the assignment:
Here are some samples. Some were creative, some were eh, some were funny. I told them I'd do it to, so I'm tossing mine in the mix. Each poster has 2 memoirs on it.
I had them create a small poster with 2 such memoirs, one for their "math life" and one for their "other/real life". Here's the assignment:
Here are some samples. Some were creative, some were eh, some were funny. I told them I'd do it to, so I'm tossing mine in the mix. Each poster has 2 memoirs on it.
Sunday, January 08, 2012
Challenging Precal Problems
A while ago, I gave my precalculus class a "clock faced" problem that was not something they were used to seeing. Some of them rose to the challenge and figured it out. Most started the problem and then petered out. Too many didn't know what to do.
I struggle with how to effectively teach problem solving skills, so here is my latest attempt that will be their homework tomorrow.
I struggle with how to effectively teach problem solving skills, so here is my latest attempt that will be their homework tomorrow.
Friday, January 06, 2012
Polygon Angles
I've tried various ways over the years of presenting the following 2 facts:
* (n-2)*180 is the sum of the interior angles of a polygon.
* 360 is the sum of the exterior angles of any polygon.
Yes, the students remember ultimately, but as I was looking over my old files this year to do it again, things just didn't sit right ... or I was in the mood for a change ... or I'm a different person now, and I want to approach it differently.
I hit upon the following method, and I think I like it the best (ask me what I think next time). Here are things I like about it: it's not talk, talk, talk. It's not, "let's do it all theoretically and then POOF here's the formula." It's not, "let's all explore a different polygon by drawing and measuring and seeing what happens and there'll be human error, but we'll hand wave that away." It's pretty efficient. It's different from what I usually do, so it'll stick in MY students' minds (hopefully).
I had everyone get a piece of colored paper and fold it in 4ths and cut the 4 separate rectangles. Then on one rectangle, I had them draw a heptagon (we drew a light circle, put 7 dots on it, and connected the dots). We took a colored marker to the border of the heptagon and made sure that some color was on the interior. We drew diagonals from one vertex. We cut out the heptagon. Then we cut the triangles out.
Then I said, so what we want to explore is if I had asked you to measure all the interior angles and add them up what would you get. So now look at what we have done, and see if you can figure out the answer and then ALSO figure out why I asked you to do these particular tasks.
Then I waited and eavesdropped. Then I asked a kid to explain. Then I had them tape this into their composition books to look something like this:
Then (after some other polygon stuff), on another piece of the colored paper, I had them draw an octagon but extend the sides to show the exterior angles. Before I had them do the following thing, I had them take thumb votes on the scenario, "as the number of sides increases, what do you think happens to the sum of the exterior angles as shown: thumbs up for increases, down for decreases, sideways for stays the same, or open palm for it depends on other factors." They thought and voted. Then we did....
Then I had them cut out the interior octagon and leave the border. We reviewed what the sum of the interior angles was (6 * 180). Then we built up what the sum of all the "lines" angles were (8 * 180). Then we thought and discovered and here's what they taped in their notebooks:
Then as always I ran out of time and was rushed and couldn't do any practice problems, so my resolution of stopping class 1 minute before the bell so they could pack up was not put into place today!
* (n-2)*180 is the sum of the interior angles of a polygon.
* 360 is the sum of the exterior angles of any polygon.
Yes, the students remember ultimately, but as I was looking over my old files this year to do it again, things just didn't sit right ... or I was in the mood for a change ... or I'm a different person now, and I want to approach it differently.
I hit upon the following method, and I think I like it the best (ask me what I think next time). Here are things I like about it: it's not talk, talk, talk. It's not, "let's do it all theoretically and then POOF here's the formula." It's not, "let's all explore a different polygon by drawing and measuring and seeing what happens and there'll be human error, but we'll hand wave that away." It's pretty efficient. It's different from what I usually do, so it'll stick in MY students' minds (hopefully).
I had everyone get a piece of colored paper and fold it in 4ths and cut the 4 separate rectangles. Then on one rectangle, I had them draw a heptagon (we drew a light circle, put 7 dots on it, and connected the dots). We took a colored marker to the border of the heptagon and made sure that some color was on the interior. We drew diagonals from one vertex. We cut out the heptagon. Then we cut the triangles out.
Then I said, so what we want to explore is if I had asked you to measure all the interior angles and add them up what would you get. So now look at what we have done, and see if you can figure out the answer and then ALSO figure out why I asked you to do these particular tasks.
Then I waited and eavesdropped. Then I asked a kid to explain. Then I had them tape this into their composition books to look something like this:
Then (after some other polygon stuff), on another piece of the colored paper, I had them draw an octagon but extend the sides to show the exterior angles. Before I had them do the following thing, I had them take thumb votes on the scenario, "as the number of sides increases, what do you think happens to the sum of the exterior angles as shown: thumbs up for increases, down for decreases, sideways for stays the same, or open palm for it depends on other factors." They thought and voted. Then we did....
Then I had them cut out the interior octagon and leave the border. We reviewed what the sum of the interior angles was (6 * 180). Then we built up what the sum of all the "lines" angles were (8 * 180). Then we thought and discovered and here's what they taped in their notebooks:
Then as always I ran out of time and was rushed and couldn't do any practice problems, so my resolution of stopping class 1 minute before the bell so they could pack up was not put into place today!
Monday, January 02, 2012
What I Did on Vacation...
What's a vacation without lots of surfing on old and new favorites:
(I thought I'd share so that I'm not the only one losing many hours of my day)
(sorry, or you're welcome, whatever the case may be)
AwkwardFamilyPhotos
FoodGawker
MovieTrailers
HomeExercise
FunnySite
InterestingVideos
(I thought I'd share so that I'm not the only one losing many hours of my day)
(sorry, or you're welcome, whatever the case may be)
AwkwardFamilyPhotos
FoodGawker
MovieTrailers
HomeExercise
FunnySite
InterestingVideos
Friday, December 30, 2011
Almost Over...
These days of enough sleep will soon come to an end. I'll miss the sleeping part, but I won't miss the sitting around on my heiny part. I'm wondering if it almost wouldn't be better to have a week shorter break, and then take those 5 days and sprinkle them around for FIVE FOUR-DAY weeks at various times during the year. Then it would be like mini vacations all the time.
I went to a wedding of an old friend yesterday, a retired math teacher getting married for the first time, WOOT, and not surprisingly, he invited a bunch of other math teacher friends he'd taught with throughout his career. I was chatting with a few, and we happened upon the discussion of administration. A retired woman was commenting on the fact that as the years went on in her teaching, she'd see various administrators come and go, and they got younger and younger and greener and greener and she just had to ride out the tide.
Some other retired middle school teacher's husband commented on the fact that at the various school parties he noticed a hefty amount of alcohol. Ahem.
Another teacher was reminiscing about the days when there would be a "homework hotline" where they were paid $10/hour to sit and wait in the evening for possible student calls for math/english help.
Another retired teacher was mentioning the fact that she now gets paid $26/hour to tutor 10 students at a particular school. I know of another retired math teacher that tutors students in a wealthy district for about $40-$50/hour and for most of the year (half the year?) has about 20 students on his roster once a week. Yeesh. I guess there won't be any shortage of things to do when that time comes. ...
I went to a wedding of an old friend yesterday, a retired math teacher getting married for the first time, WOOT, and not surprisingly, he invited a bunch of other math teacher friends he'd taught with throughout his career. I was chatting with a few, and we happened upon the discussion of administration. A retired woman was commenting on the fact that as the years went on in her teaching, she'd see various administrators come and go, and they got younger and younger and greener and greener and she just had to ride out the tide.
Some other retired middle school teacher's husband commented on the fact that at the various school parties he noticed a hefty amount of alcohol. Ahem.
Another teacher was reminiscing about the days when there would be a "homework hotline" where they were paid $10/hour to sit and wait in the evening for possible student calls for math/english help.
Another retired teacher was mentioning the fact that she now gets paid $26/hour to tutor 10 students at a particular school. I know of another retired math teacher that tutors students in a wealthy district for about $40-$50/hour and for most of the year (half the year?) has about 20 students on his roster once a week. Yeesh. I guess there won't be any shortage of things to do when that time comes. ...
Wednesday, December 21, 2011
Success!
That's what I deem this first day of vacation.
It started out with a much needed 8 hours of sleep. Continued on later with a brisk exercise walk in our "freezing" 46 degree weather. Followed by a yummy lunch and 2.5 hour nap. Enhanced by starting a book ("Odd Thomas" by Dean Koontz) recommended by a work friend. To be concluded with having friends over with delicious take out from a neighborhood Italian restaurant.
This year has aged me ... or maybe I'm just aging. I don't wear glasses (except for driving), but I've been noticing a fuzzier appearance to the world. I guess that's what 46+ years will do to you. I'm also not getting enough sleep during the school week/year, so I feel haggard. I'm also skipping yoga too much because I feel trapped at work too late (maybe that will be my New Year's resolution: leave on time on Tuesdays). This causes me to feel stiff and achy and stressed. I think I may piggy back that resolution onto another resolution a friend told me about: try at least one new type of drink a month (to get out of her same old same old rut).
I did enjoy two new endeavors this semester. The first was teaching Digital Electronics. Loved it! It's a nice mix of logic and math and breadboards and LEDs and such that you control with your skill.
The second was an online Java course I took (and will continue taking in the spring). It's the AP Computer Science curriculum taught through the University of Missouri. The teacher is great, the curriculum is well laid out. The topic is fun. I get to program again. I even made a version of "green globs" for my final project, and it worked! I love the push I have to actually go through the subject because of the deadlines and grades and tests I have to submit. I know if I just said I'd do it on my own it would be so easy to put it off all the time because I am busy.
All in all, it was a good semester, and MOST of all, I'm going to enjoy my free time by napping and reading and movie-ing and puzzling and such.
It started out with a much needed 8 hours of sleep. Continued on later with a brisk exercise walk in our "freezing" 46 degree weather. Followed by a yummy lunch and 2.5 hour nap. Enhanced by starting a book ("Odd Thomas" by Dean Koontz) recommended by a work friend. To be concluded with having friends over with delicious take out from a neighborhood Italian restaurant.
This year has aged me ... or maybe I'm just aging. I don't wear glasses (except for driving), but I've been noticing a fuzzier appearance to the world. I guess that's what 46+ years will do to you. I'm also not getting enough sleep during the school week/year, so I feel haggard. I'm also skipping yoga too much because I feel trapped at work too late (maybe that will be my New Year's resolution: leave on time on Tuesdays). This causes me to feel stiff and achy and stressed. I think I may piggy back that resolution onto another resolution a friend told me about: try at least one new type of drink a month (to get out of her same old same old rut).
I did enjoy two new endeavors this semester. The first was teaching Digital Electronics. Loved it! It's a nice mix of logic and math and breadboards and LEDs and such that you control with your skill.
The second was an online Java course I took (and will continue taking in the spring). It's the AP Computer Science curriculum taught through the University of Missouri. The teacher is great, the curriculum is well laid out. The topic is fun. I get to program again. I even made a version of "green globs" for my final project, and it worked! I love the push I have to actually go through the subject because of the deadlines and grades and tests I have to submit. I know if I just said I'd do it on my own it would be so easy to put it off all the time because I am busy.
All in all, it was a good semester, and MOST of all, I'm going to enjoy my free time by napping and reading and movie-ing and puzzling and such.
Friday, December 16, 2011
Challenge
This problem makes me happy in its difficulty and challenge. I threw down the gauntlet to my precalculus students. We'll see if they run with it to the finish line or not. Either way, I wanted the smartie smarts to at least know there are some problems out there that require more than just rote brain power.
Friday, December 09, 2011
End-O-Semester...
As always it's just slam-banged and gotten here already. Now it's a scramble to get all things graded and finals written and reviews made and failers cheered on to get their act together and mouths kept shut due to lack of sleep and knowledge that if something comes out of my tired brain/mouth it will be a regrettable snarky comment that won't do anyone any good.
On a positive note, I have this extremely clever 8th grader this year. She's quiet and polite, but every time the timing is right, she comes up with these zingers. For example, today I quickly made up a review sheet for geometry, and it had an answer bank on the bottom. Being the last-minute person that I am, it was all hand-written. Well, as a shock to no one, there were 2 mistakes in the answer bank due to my non-checking of my work. So as their class started, and I handed out the hand-written sheet, I mentioned that there were some "pen-o's" on the sheet (you know, typos, but penos). This class also knows since I've mentioned it several times that I have a pen buying problem, and I'm trying to go through my current bazillion stash before I succumb again to purchasing more.
Anyway, after I said, "pen-o", she said, "is that like wino but with pens?" Then we chuckled and mentioned that I should join PA, "hello, my name is ____ and I have a pen problem."
On a positive note, I have this extremely clever 8th grader this year. She's quiet and polite, but every time the timing is right, she comes up with these zingers. For example, today I quickly made up a review sheet for geometry, and it had an answer bank on the bottom. Being the last-minute person that I am, it was all hand-written. Well, as a shock to no one, there were 2 mistakes in the answer bank due to my non-checking of my work. So as their class started, and I handed out the hand-written sheet, I mentioned that there were some "pen-o's" on the sheet (you know, typos, but penos). This class also knows since I've mentioned it several times that I have a pen buying problem, and I'm trying to go through my current bazillion stash before I succumb again to purchasing more.
Anyway, after I said, "pen-o", she said, "is that like wino but with pens?" Then we chuckled and mentioned that I should join PA, "hello, my name is ____ and I have a pen problem."
Monday, November 28, 2011
Not Just For Special Occasions...
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."
.....
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."
.....
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.
Tuesday, November 01, 2011
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