My students are still working on their Line Project, and I'm glad I assigned it because various things have come up that I think are good learning experiences for them and for me. I had separated their completion of the project into 3 successive class periods, and for the 1st one they had to turn in a set of data points and a computer-generated scatter plot to show the linear correlation. Well!
Most kids were fine, but others had a variety of issues:
* "The spreadsheet won't make a scatter plot of my data!" (the student was entering data of height vs. weight, and the heights were typed in as 4ft 5in, 4ft 6in, ...)
* "Here's my data ... SEE! Linear" (the set of points was EXACTLY linear since the student found a site that said that every 1 second ___ kids drop out of school, and the student had used that to create 5 coordinate points)
The 2nd class period, they had to turn in their own hand-created scatter plot and best fit line and equation and idea for a prediction using their line equation. Issues:
* Some kids used rise/run to calculate their slope, but the scale of their graph wasn't in "1's".
* Some prediction ideas were: I predict the cost of a loaf of bread will rise 31 cents every 7 years (they used their slope instead of their equation)
* Some just connected the data points, forgetting the example we worked on in class for best-fit line.
And so on. This seems to have taken them out of their comfort zone of how our math class has been going, so I'm glad they're being "mathematicians in action" and learning extra skills. I'm also glad I broke it up into 3 days of checkpoints since I'm guessing I saved myself (and them) the agony of incorrect or NO final products. While I was walking around critiquing their graphs this past class, I gave them THIS to work on.
On a side note, after my hectic week of various extra tasks added on to the already busy schedule, I went out for drinks with my friend, and we had an interesting discussion about the difference between "unethical" and "immoral". What types of things would fall into each separate category? Would some things be both? What's the distinguishing characteristics of something that is one or the other?
Saturday, January 30, 2010
Sunday, January 24, 2010
Lines Project
In algebra 1 we've covered most line topics I think are important:
* calculating slope from a graph and from 2 points without a graph
* looking at a graph and finding the line equation in all 3 ways (standard, pt-slope,slope-int)
* being given either 2 points or a point and a slope and calculating any of the 3 equations.
* looking at any of the 3 line equations and graphing
* looking at any of the 3 line equations and finding 5 points on the line (and the intercepts)
* seeing that if you have a graph and it's line equation in any form, that you can plug in any point on the line and it will "work" and plug in any equation not on the line, and it won't work in the equation.
(I've probably missed some, but this is what I remember)
We still have to talk about parallel and perpendicular lines, but soon we'll move on to systems of equations. Before we do that, I thought that this would be the perfect time to assign a line project to my students. In all their later topics and math courses, lines will just be an aside where it's already assumed they have learned about them.
We had a discussion about positive and negative linear correlation and no correlation and correlation that is not linear. We went through the process of creating best fit lines and using that line to make a prediction for another point that is not represented by your data. Then I discussed that in real life, people collect data, and if they all fell on a straight line, the mathematicians/scientists would faint from the rareness of this occurrence, and that usually, if the data seems to be linear, it'll look like our scatter plots that have a linear correlation, and THAT'S how this is used in real life. People make a model and then use that model to make predictions.
Then I assigned this project that I will collect in a succession of 3 class periods. I already have had one student send me her data that was interesting. She found information about teacher pay from the 40's to the 2000's, and you can see that it looks linear until about 1980, and then there's a BIG leap of the points and then it looks linear again. After a back and forth e-mail discussion, she found that some site stated that there was a 400% increase in pay in 1980 .... hmmm, haven't verified that, but I remember some of my older teacher friends mentioning their super low pay in the 70's.
* calculating slope from a graph and from 2 points without a graph
* looking at a graph and finding the line equation in all 3 ways (standard, pt-slope,slope-int)
* being given either 2 points or a point and a slope and calculating any of the 3 equations.
* looking at any of the 3 line equations and graphing
* looking at any of the 3 line equations and finding 5 points on the line (and the intercepts)
* seeing that if you have a graph and it's line equation in any form, that you can plug in any point on the line and it will "work" and plug in any equation not on the line, and it won't work in the equation.
(I've probably missed some, but this is what I remember)
We still have to talk about parallel and perpendicular lines, but soon we'll move on to systems of equations. Before we do that, I thought that this would be the perfect time to assign a line project to my students. In all their later topics and math courses, lines will just be an aside where it's already assumed they have learned about them.
We had a discussion about positive and negative linear correlation and no correlation and correlation that is not linear. We went through the process of creating best fit lines and using that line to make a prediction for another point that is not represented by your data. Then I discussed that in real life, people collect data, and if they all fell on a straight line, the mathematicians/scientists would faint from the rareness of this occurrence, and that usually, if the data seems to be linear, it'll look like our scatter plots that have a linear correlation, and THAT'S how this is used in real life. People make a model and then use that model to make predictions.
Then I assigned this project that I will collect in a succession of 3 class periods. I already have had one student send me her data that was interesting. She found information about teacher pay from the 40's to the 2000's, and you can see that it looks linear until about 1980, and then there's a BIG leap of the points and then it looks linear again. After a back and forth e-mail discussion, she found that some site stated that there was a 400% increase in pay in 1980 .... hmmm, haven't verified that, but I remember some of my older teacher friends mentioning their super low pay in the 70's.
Wednesday, January 20, 2010
Tuesday, January 19, 2010
Three Day Weekend
I went to Chicago for the nice 3-day weekend, and had a fun time walking around and people watching and freezing and sight-seeing. Here's the cool Water Tower Building:
This is "The Bean" in Millennium Park.
This is a river cutting through town and gives a nice idea of how cold it was:
I loved the ease of the subway (CTA) system and my old-styled hotel (thank you, Expedia.com and yelp.com reviewers). I loved trying out their many vegetarian restaurants and knit shops and independent bookstores (thanks again yelp.com reviewers). This will tide me over until my next adventure.
This is "The Bean" in Millennium Park.
This is a river cutting through town and gives a nice idea of how cold it was:
I loved the ease of the subway (CTA) system and my old-styled hotel (thank you, Expedia.com and yelp.com reviewers). I loved trying out their many vegetarian restaurants and knit shops and independent bookstores (thanks again yelp.com reviewers). This will tide me over until my next adventure.
Thursday, January 14, 2010
Near Miss
Yesterday at the start of geometry class I had the homework answers projected from the document camera, and was silently reviewing in my mind what we would be doing that day while my students checked their answers. I was ready to perfunctorily ask if they had any questions before we moved on to "the real learning". Okay, I'm not that robotic, but on hindsight, that's what it feels like because I almost missed a great learning moment.
On one particular question a bunch of students raised their hands. The question was something to the effect of: In a pentagon, the angles are consecutive multiples of 4. Find the measure of each angle. Instead of simply putting up the answer, I put my work down also since I thought there would be several confused students that would want it broken down: 4x + 4(x+1) + 4(x+2) + 4(x+3)+ 4(x+4) = 540 and then went from there.
The students with their raised hands weren't confused, they were chomping at the bit to show how they did the problem. Oh my goodness were there some clever kiddies there. They love to come up to the overhead and present (note to self: stop being a projector hog), and one by one they showed us what they did.
1st student: well, I divided 540 by 5 and got 108. That's a multiple of 4. The angles couldn't all be 108, but I thought they'd hover around it, so 108 was an angle, then for 2 other angles, I added and subtracted 4 and had 3 angles: 104, 108, 112. Then I added 4 to 112 and subtracted 4 from 104 to get my angles: 100,104,108,112,116.
2nd student: well, I started with 100 degrees for each angle (a multiple of 4), and with 5 angles that adds up to 500, so I had 40 degrees left to play with. Then I tried to break down 40 into 5 consecutive multiples of 4. 4, 8, 12, 16, 20. I added these up, and they were more than 40, so I just used 4,8,12,16 and it worked.
3rd student: well, I divided 540 by 5 and got 108. I divided 108 by 4 and saw that 108=27 * 4. So I then I found the consecutive numbers around 27: 25,26,27,28,29, and those were the consecutive multiples of 4, so I multiplied by those and got the answer.
4th student: well, I knew they were consecutive multiples of 4, so I set up an equation:
x + (x+4) + (x+8) + (x+12) + (x+16) = 540 and solved that.
I was very impressed and humbly reminded that there are teaching moments quite available to me even when I'm not "teaching".
On one particular question a bunch of students raised their hands. The question was something to the effect of: In a pentagon, the angles are consecutive multiples of 4. Find the measure of each angle. Instead of simply putting up the answer, I put my work down also since I thought there would be several confused students that would want it broken down: 4x + 4(x+1) + 4(x+2) + 4(x+3)+ 4(x+4) = 540 and then went from there.
The students with their raised hands weren't confused, they were chomping at the bit to show how they did the problem. Oh my goodness were there some clever kiddies there. They love to come up to the overhead and present (note to self: stop being a projector hog), and one by one they showed us what they did.
1st student: well, I divided 540 by 5 and got 108. That's a multiple of 4. The angles couldn't all be 108, but I thought they'd hover around it, so 108 was an angle, then for 2 other angles, I added and subtracted 4 and had 3 angles: 104, 108, 112. Then I added 4 to 112 and subtracted 4 from 104 to get my angles: 100,104,108,112,116.
2nd student: well, I started with 100 degrees for each angle (a multiple of 4), and with 5 angles that adds up to 500, so I had 40 degrees left to play with. Then I tried to break down 40 into 5 consecutive multiples of 4. 4, 8, 12, 16, 20. I added these up, and they were more than 40, so I just used 4,8,12,16 and it worked.
3rd student: well, I divided 540 by 5 and got 108. I divided 108 by 4 and saw that 108=27 * 4. So I then I found the consecutive numbers around 27: 25,26,27,28,29, and those were the consecutive multiples of 4, so I multiplied by those and got the answer.
4th student: well, I knew they were consecutive multiples of 4, so I set up an equation:
x + (x+4) + (x+8) + (x+12) + (x+16) = 540 and solved that.
I was very impressed and humbly reminded that there are teaching moments quite available to me even when I'm not "teaching".
Saturday, January 09, 2010
Rates of Change & Slope
As school started back up again, in algebra 1 we started our unit on equations of lines by talking about rates of change. Last year I just jumped right into slope first, and verbally mentioned some applications (if I remember correctly), but this year I thought I'd give them a context first. I started with a worksheet on rates of change and had them work through the first 2 problems with not much prompting. Then we discussed their answers. I made sure they used units. I made sure we saw ALL ways of writing the numbers. My classes (everyone's?) seem unsure that 9/4 and 2.25 and 2 1/4 can all be correct answers. They still look at me like they don't QUITE believe I'm not pulling a fast one on them.
Then they did the next two, and we discussed, and so on. I made sure to mix up the units, I have some with negative rates of change on the back. After a few, if it didn't come up, I discussed and made them write their calculations on the side as (y2-y1)/(x2-x1) using the appropriate numbers. If it didn't come up, I made sure to investigate what would happen if you used different points or a different order.
In my block class, we had just enough time to do this and then to have a discussion about rates of change and slope and how they're the same (barring units).
I'm thinking this went well because on the second day, when we discussed rise/run and started graphs to y=mx+b equations, they were pretty good and quick on calculating slope. Also, when I stepped back and asked them to identify positive and negative slopes, they had a picture of water levels increasing or decreasing and were pretty accurate.
Oh, one funny thing. I like to give them memory tools to keep things straight, and on "rise over run", I said, well what goes on top? the y's, and y's rhymes with rise. Then I told them I couldn't think of a memory tool that links run with x's, so I put it to them. Maybe these have already been done before, but I forgot, so I really liked some of the ones my kids came up with:
you run from your ex
you run from T-rex
you run cross country (x)
you run on a flat surface, and x is on the horizontal axis.
Then they did the next two, and we discussed, and so on. I made sure to mix up the units, I have some with negative rates of change on the back. After a few, if it didn't come up, I discussed and made them write their calculations on the side as (y2-y1)/(x2-x1) using the appropriate numbers. If it didn't come up, I made sure to investigate what would happen if you used different points or a different order.
In my block class, we had just enough time to do this and then to have a discussion about rates of change and slope and how they're the same (barring units).
I'm thinking this went well because on the second day, when we discussed rise/run and started graphs to y=mx+b equations, they were pretty good and quick on calculating slope. Also, when I stepped back and asked them to identify positive and negative slopes, they had a picture of water levels increasing or decreasing and were pretty accurate.
Oh, one funny thing. I like to give them memory tools to keep things straight, and on "rise over run", I said, well what goes on top? the y's, and y's rhymes with rise. Then I told them I couldn't think of a memory tool that links run with x's, so I put it to them. Maybe these have already been done before, but I forgot, so I really liked some of the ones my kids came up with:
you run from your ex
you run from T-rex
you run cross country (x)
you run on a flat surface, and x is on the horizontal axis.
Thursday, January 07, 2010
Silliness
I got a much-needed laugh today from a student. In my quest to drink more water and to stay caffeinated, I bring two 1-liter bottles of water to school every day. One (the BLUE one) I use with my electric water boiler to make tea (for normal days where you got enough sleep) or with my single-serving coffee maker to make hazelnut coffee (for the oh my god wake me up days). This water allows me 2 large (20 oz) cups of hot beverage (and I might add that it's very hard to find good, 20 oz reusable hot beverage cups. Thank you Starbucks). Add a little non-sugared soy milk and I'm in heaven. The other bottle (the YELLOW one) is to just drink straight. Of course there's the bathroom vs. class time issue, so usually I drink 1/2 of it during lunch time, and then the other half at the end of the work day.
Today, I had a mixture of chalk or dust in the throat and/or an on-coming cold and/or allergies, and I desperately needed a sip of water while I was teaching, so that I could continue without turning into a sputtering mess. I did something I'd apparently never done in class before. I got the yellow water bottle and took a few sips.
A girl looks at me for a bit and then says, "why would anyone drink water out of a yellow water bottle?"
After I finished laughing, I came back with, "I'm recycling". Ew.
Today, I had a mixture of chalk or dust in the throat and/or an on-coming cold and/or allergies, and I desperately needed a sip of water while I was teaching, so that I could continue without turning into a sputtering mess. I did something I'd apparently never done in class before. I got the yellow water bottle and took a few sips.
A girl looks at me for a bit and then says, "why would anyone drink water out of a yellow water bottle?"
After I finished laughing, I came back with, "I'm recycling". Ew.
Thursday, December 31, 2009
New Year's Teaching Resolutions
Okay, so New Year for teachers is really August/September, but it's never bad to reflect on how the year has gone so far and what things I could work on for the 2nd half of the school year. Also, by now I have some sort of groove going with the kids (good or bad), and that gives me more to work with.
1. I'm still not happy with my homework I assign. Ideally I would like it to be 80% or so new material, and 20% mixed review. That's always in the back of my mind, and it seems to have taken up permanent residence there. My issue is that I'm scrambling to create or assign homework at my favorite minute - the last one, so ... Now I'm old enough to know that this is the way I work, so I need to think of something I can do within my limitations.
Idea: While I'm creating the current homework or while I'm entering it in GradeSpeed, jot down 2 similar problems to that night's homework along with topic covered while it's fresh in my mind. If I do this for a while, then I'll build up a store of problems ready-made, and then in my future last minute, I can hunt and peck around this list and just add them to the homework. Better yet, type in or scan in the problems onto my school website, and then just point the students in that direction and tell them which additional problems to do each night.
2. At the end of each class, I really only have a good sense of how a portion of my students understand the current material. There are still too many ways in class to pretend like you're listening and comprehending, but really tuning out in the myriad of teenage ways. I'd like to have a quick easy take on everyone, and have them understand if they get it or not. Problem: I'm usually bell-to-bell, and feel 5 minutes of something else won't happen without squeezing out important content.
Idea:
Hmmm, no immediate ideas. My original idea was to have them do a problem by themselves similar to what they just learned (with? without notes?), but then I'm sitting here thinking about how I learn best, and maybe like everyone else, part of the process is to go back over what you just learned and try to rephrase it or think about it a piece at a time: what were the important points, what did this or that mean, what would happen in such a situation, etc. Maybe a starting idea to see how it works would be to force myself to stop class 5 minutes early, and have a standard set of prompts related to my thoughts above, and the kids have to silently go over their notes and work and brains and answer the questions/prompts about the topic, not solving a problem, but thinking about what was learned. No talking to others, because then I wouldn't know what they know (even though you learn by discussing, but I see this short 5 minutes as not amenable to this).
3. There are still some students who I basically never talk to. You know how it is. A handful of students in each class seem to dominate the time or attention or are the boisterous ones that always engage you in conversation. Then there are the quiet ones who sit there and behave and, well, are quiet. Sure I'll call on them, and they'll answer the question, but that's the extent of our interaction.
Idea: List such kids, and make it a point to engage in conversation with them before class starts at least____ times a 6 weeks. I don't know, I'd have to make a list of all such kids and cross them off or "check" them when I converse with them, then I could probably engage, say 2 per class, so 4-6 per week (block schedule), and then see how many such cycles I could go through. Hmmm, seems calculated. Well I guess it is, but that's what I've got.
Okay, those are not my only concerns, but let's not get carried away and have too much on our plates and end up doing nothing. Happy last day of the year to all of us. Hope 2010 holds all sorts of joy and hope and an enjoyment of at least parts of every day.
1. I'm still not happy with my homework I assign. Ideally I would like it to be 80% or so new material, and 20% mixed review. That's always in the back of my mind, and it seems to have taken up permanent residence there. My issue is that I'm scrambling to create or assign homework at my favorite minute - the last one, so ... Now I'm old enough to know that this is the way I work, so I need to think of something I can do within my limitations.
Idea: While I'm creating the current homework or while I'm entering it in GradeSpeed, jot down 2 similar problems to that night's homework along with topic covered while it's fresh in my mind. If I do this for a while, then I'll build up a store of problems ready-made, and then in my future last minute, I can hunt and peck around this list and just add them to the homework. Better yet, type in or scan in the problems onto my school website, and then just point the students in that direction and tell them which additional problems to do each night.
2. At the end of each class, I really only have a good sense of how a portion of my students understand the current material. There are still too many ways in class to pretend like you're listening and comprehending, but really tuning out in the myriad of teenage ways. I'd like to have a quick easy take on everyone, and have them understand if they get it or not. Problem: I'm usually bell-to-bell, and feel 5 minutes of something else won't happen without squeezing out important content.
Idea:
Hmmm, no immediate ideas. My original idea was to have them do a problem by themselves similar to what they just learned (with? without notes?), but then I'm sitting here thinking about how I learn best, and maybe like everyone else, part of the process is to go back over what you just learned and try to rephrase it or think about it a piece at a time: what were the important points, what did this or that mean, what would happen in such a situation, etc. Maybe a starting idea to see how it works would be to force myself to stop class 5 minutes early, and have a standard set of prompts related to my thoughts above, and the kids have to silently go over their notes and work and brains and answer the questions/prompts about the topic, not solving a problem, but thinking about what was learned. No talking to others, because then I wouldn't know what they know (even though you learn by discussing, but I see this short 5 minutes as not amenable to this).
3. There are still some students who I basically never talk to. You know how it is. A handful of students in each class seem to dominate the time or attention or are the boisterous ones that always engage you in conversation. Then there are the quiet ones who sit there and behave and, well, are quiet. Sure I'll call on them, and they'll answer the question, but that's the extent of our interaction.
Idea: List such kids, and make it a point to engage in conversation with them before class starts at least____ times a 6 weeks. I don't know, I'd have to make a list of all such kids and cross them off or "check" them when I converse with them, then I could probably engage, say 2 per class, so 4-6 per week (block schedule), and then see how many such cycles I could go through. Hmmm, seems calculated. Well I guess it is, but that's what I've got.
Okay, those are not my only concerns, but let's not get carried away and have too much on our plates and end up doing nothing. Happy last day of the year to all of us. Hope 2010 holds all sorts of joy and hope and an enjoyment of at least parts of every day.
Tuesday, December 29, 2009
Winter Trip
Just this past weekend we went to Santa Fe and stayed at a nice B&B just south of town. We also went snowshoeing for the 1st time, and now I'm a convert. It was easy to rent equipment from REI and fun to trudge through the snow for a couple of days. We lasted about 2-3 hours each day, with much resting on the way up, and a quick scurrying downhill with the promise of lunch to spur us on. I liked the partial packed snow better than the much-trampled on road/paths that were available. I also liked hanging out at the Santa Fe Baking Co. & Cafe and people watching and checking my e-mail and blogs. Here are some pictures of our outing and of our B&B place and of a funny bird that was snuffling around in the snow on one of our breaks.
Thursday, December 24, 2009
Discussions About High School
Ahhhh vacation. Time of 9-10 hours of sleep a night, of eating too much, of drinking more than needed, of talking with various people about high school.
Today I had lunch with another math teacher that I used to work with. We were discussing kids who didn't persevere and didn't have a good work ethic .... you know, "kids these days". Then we started talking about when we were in high school, and she mentioned that she wasn't such a hot student back then. Then I mentioned that as a student I wasn't that "student-y". I did what I needed to do to get good grades, but I don't remember really being engaged about topics or thinking hard or being any of the things I want for my students these days. Then I look at how we turned out as adults. My friend is a conscientious teacher who really thinks about what and how she teaches, and I want to believe I'm the same way, and I didn't really learn how to be a good student until I was in grad school and saw how other students worked. So, really, in the end, even though our high school performance wouldn't have predicted it, we turned out okay.
Then that leads me to think that even though some of the kids we teach these days don't do what we want them to do, they still are absorbing the lessons we teach them either formally (math math math) or informally (be a good person, do the right thing, think about what you're learning). And that ultimately, in the end, most likely they'll turn out to be productive adults that end up having a good work ethic or end up having a strong moral compass. Just because they're one way now, when they're 14, that doesn't mean that's how they're destined to be forever. And even though they don't seem to be absorbing what we're telling them, maybe they are at some level, and if not now, then maybe later.
Then this evening we were at an open house for Christmas Eve at our neighbors' home. They have 3 children that have graduated from high school and are now out in the world. I talked with one of the girls (20's) about high school, and she mentioned how she HATED it. "The kids were so mean." We also talked about whether or not we remembered teachers' names. Now even though she's been out for only a few years, she doesn't remember many. I've been out for more than 20, and I don't either. But I do remember 2 teacher's names. What made them different? One was a "public speaking" teacher. That was the most useful class I took. I guess I remember his name because the class had such an impact on me. Another was my freshman English teacher's name. He was all "cool" and wore jeans (in the late 70's), and had a shag rug (ooh aah), and our desks were in a circle, and I still remember his lessons on: effect/affect ... it's/its ... their/they're and so on.
I guess all this is to give myself a little pep talk to remind myself that how my students are today may not be the perfect indication of how they'll ultimately turn out.
Today I had lunch with another math teacher that I used to work with. We were discussing kids who didn't persevere and didn't have a good work ethic .... you know, "kids these days". Then we started talking about when we were in high school, and she mentioned that she wasn't such a hot student back then. Then I mentioned that as a student I wasn't that "student-y". I did what I needed to do to get good grades, but I don't remember really being engaged about topics or thinking hard or being any of the things I want for my students these days. Then I look at how we turned out as adults. My friend is a conscientious teacher who really thinks about what and how she teaches, and I want to believe I'm the same way, and I didn't really learn how to be a good student until I was in grad school and saw how other students worked. So, really, in the end, even though our high school performance wouldn't have predicted it, we turned out okay.
Then that leads me to think that even though some of the kids we teach these days don't do what we want them to do, they still are absorbing the lessons we teach them either formally (math math math) or informally (be a good person, do the right thing, think about what you're learning). And that ultimately, in the end, most likely they'll turn out to be productive adults that end up having a good work ethic or end up having a strong moral compass. Just because they're one way now, when they're 14, that doesn't mean that's how they're destined to be forever. And even though they don't seem to be absorbing what we're telling them, maybe they are at some level, and if not now, then maybe later.
Then this evening we were at an open house for Christmas Eve at our neighbors' home. They have 3 children that have graduated from high school and are now out in the world. I talked with one of the girls (20's) about high school, and she mentioned how she HATED it. "The kids were so mean." We also talked about whether or not we remembered teachers' names. Now even though she's been out for only a few years, she doesn't remember many. I've been out for more than 20, and I don't either. But I do remember 2 teacher's names. What made them different? One was a "public speaking" teacher. That was the most useful class I took. I guess I remember his name because the class had such an impact on me. Another was my freshman English teacher's name. He was all "cool" and wore jeans (in the late 70's), and had a shag rug (ooh aah), and our desks were in a circle, and I still remember his lessons on: effect/affect ... it's/its ... their/they're and so on.
I guess all this is to give myself a little pep talk to remind myself that how my students are today may not be the perfect indication of how they'll ultimately turn out.
Friday, December 18, 2009
Hellooooo Holidays
After the longest week ever and the most emotional, it's finally break time. And by break I mean that now I have time to catch up on my engineering curriculum, so that I have something to teach when I return in 2 weeks. But by break I also mean sleeping past 5am and not being stressed out and in a hurry all day long to make sure I do everything and do it well.
I made 3 finals up from (mostly) scratch, and I like some of the questions I came up with or adjusted from other sources. They also spawned ideas for future lessons.
algebra:
Let s=the amount of suger you ingest (in mg)
Let c=the number of cavities you have
the independent variable is ___________
the dependent variable is ____________
_____ is a function of _______
The correct function notation is s(c) or c(s) (circle one).
This got me to thinking that the next time I am at the first day of teaching functions, after we go through some like this, I'm going to have the students each come up with a scenario and work it through and then we'll share out. That way they'll spend more time processing the concept and figure out what it takes to be dependent and independent and how things relate to each other and what functions are.
In engineering, part of the test was on statistics, so one question I adjusted from something I found on line was:
In a certain neighborhood, the following are household incomes:
$40000, $46000,$54000, ... (and 4 more like this), then $250000000
Find the mean______
Find the median_____
Your engineering firm wants a good sense of the income level for marketing purposes. Which number better represents the neighborhood income and why?
The median came out as something like $51000, and the mean came out roughly $230000000. It was interesting to me that not everyone got it right. More discussion in class next time.
I made 3 finals up from (mostly) scratch, and I like some of the questions I came up with or adjusted from other sources. They also spawned ideas for future lessons.
algebra:
Let s=the amount of suger you ingest (in mg)
Let c=the number of cavities you have
the independent variable is ___________
the dependent variable is ____________
_____ is a function of _______
The correct function notation is s(c) or c(s) (circle one).
This got me to thinking that the next time I am at the first day of teaching functions, after we go through some like this, I'm going to have the students each come up with a scenario and work it through and then we'll share out. That way they'll spend more time processing the concept and figure out what it takes to be dependent and independent and how things relate to each other and what functions are.
In engineering, part of the test was on statistics, so one question I adjusted from something I found on line was:
In a certain neighborhood, the following are household incomes:
$40000, $46000,$54000, ... (and 4 more like this), then $250000000
Find the mean______
Find the median_____
Your engineering firm wants a good sense of the income level for marketing purposes. Which number better represents the neighborhood income and why?
The median came out as something like $51000, and the mean came out roughly $230000000. It was interesting to me that not everyone got it right. More discussion in class next time.
Friday, December 11, 2009
Stressed Out 9th Graders
Phew what a week. It was the last week before finals. Highlights included getting cussed out by a student in a "joking" manner who then subsequently skipped another of the classes she had with me. Being treated to tales of my extremely stressed out students who said they went to their rooms the previous night and started laughing and crying simultaneously without being able to stop. Watching a hugfest take place in my room comprised of various students who were trying to pacify each other. Oh my.
I guess part of it is that my freshman are the oldest kids in this school. We're "growing" a full high school and will have 12th graders at the start of the 2012 school year. At the start of one class, after I'd heard the laughing/crying story, I had a spontaneous idea. I had colored paper in my room, so I had them each take a sheet; I took one, too. I then told them that we all were going to get our stress out on the paper for 5 minutes, and I wouldn't collect their papers. It was for their eyes only, and they could write whatever they wanted to. I told them that at the end they could crumple it up or tear it to bits or take it home and burn it or whatever. I set the timer, and we all wrote away. At the end, we "put our stress away" and moved on with our review. It seemed to calm them down (temporarily?), and we were able to get some work done.
On a positive note, my cussing student was suspended for the remainder of the week, and the class she was in (my most challenging class personality-wise) went better on Friday. On another positive note, all this work stress and other related stress has brought a few of us together, and I've actually talked more with other teachers than I have in the previous two 6 weeks. Here's to finally feeling like I belong to this new school.
I guess part of it is that my freshman are the oldest kids in this school. We're "growing" a full high school and will have 12th graders at the start of the 2012 school year. At the start of one class, after I'd heard the laughing/crying story, I had a spontaneous idea. I had colored paper in my room, so I had them each take a sheet; I took one, too. I then told them that we all were going to get our stress out on the paper for 5 minutes, and I wouldn't collect their papers. It was for their eyes only, and they could write whatever they wanted to. I told them that at the end they could crumple it up or tear it to bits or take it home and burn it or whatever. I set the timer, and we all wrote away. At the end, we "put our stress away" and moved on with our review. It seemed to calm them down (temporarily?), and we were able to get some work done.
On a positive note, my cussing student was suspended for the remainder of the week, and the class she was in (my most challenging class personality-wise) went better on Friday. On another positive note, all this work stress and other related stress has brought a few of us together, and I've actually talked more with other teachers than I have in the previous two 6 weeks. Here's to finally feeling like I belong to this new school.
Wednesday, December 09, 2009
Checking Your Work
It recently came to my attention that there are students who don't FULLY understand how to check their work. During this past semester in algebra 1, we solved equations and inequalities and such. To force them to check their work, periodically I would assign it point value on their homework, so they could get at most 80% if they didn't check their work.
Here are various things I noticed. Sometimes students would start checking their work at the 2nd step or the simplified step of the original problem. We discussed why that was a bad idea (potential mistake at the 1st step, and even though your answer looks correct, it's not for the original problem).
Sometimes students would "check" their work, plugging in their answer, and at the end get some number that had nothing to do with the original equation, and then place a check mark at the end. CHECK. I've checked my work. Done. Not correct, but I don't get it, I think just going through the process and the ever-important check mark at the end is good.
And finally, sometimes students would check their work. It wouldn't pan out. But then they wouldn't take it from there. Oh well, it didn't work. I'm stopping. I don't think to go back and follow my work process to see where my mistake was.
Ideas for next time (or later this year?): write out various problems all worked out, and then have students analyze the situation: is the problem correct? how do you know. If the checking didn't work out, where is the mistake? Find it (and have some mistakes in the problem and some in the checking). Have some problems where everything seems to work out, and the problem has the checking occur from the 2nd step on of the problem and "look" correct but in reality not solve the original problem.
Here are various things I noticed. Sometimes students would start checking their work at the 2nd step or the simplified step of the original problem. We discussed why that was a bad idea (potential mistake at the 1st step, and even though your answer looks correct, it's not for the original problem).
Sometimes students would "check" their work, plugging in their answer, and at the end get some number that had nothing to do with the original equation, and then place a check mark at the end. CHECK. I've checked my work. Done. Not correct, but I don't get it, I think just going through the process and the ever-important check mark at the end is good.
And finally, sometimes students would check their work. It wouldn't pan out. But then they wouldn't take it from there. Oh well, it didn't work. I'm stopping. I don't think to go back and follow my work process to see where my mistake was.
Ideas for next time (or later this year?): write out various problems all worked out, and then have students analyze the situation: is the problem correct? how do you know. If the checking didn't work out, where is the mistake? Find it (and have some mistakes in the problem and some in the checking). Have some problems where everything seems to work out, and the problem has the checking occur from the 2nd step on of the problem and "look" correct but in reality not solve the original problem.
Saturday, December 05, 2009
Interpreting Functions
I think the kids get functions this year. After we looked at graphs and tables and mappings and saw what functions looked like for these situations (one day) and got a formal definition of functions, the next block day, I started by giving them pairs of objects like: rainfall and tulips. I asked which one depends on the other one? Which one is the input? Which one would be "x" and which one would be "y"? And, the new one for them: which one is a function of the other one? (we discussed what that means). We did that for 3 pairs of things.
Then I noted that THAT was a ton of writing, and we assigned variables to things like r and t, and I showed them t(r) and noted that the input, r, was INSIDE the parentheses, and the output, t, was OUTSIDE the parentheses, and if you were talking to your math boyfriend over the phone, you'd say, "t of r" or "t is a function of r".
Then we got to things like B(h) where B is your tutoring bill and h is the hours of tutoring. I asked them to interpret: B(3) = 120. We did this for 4 problems or so. I liked those types of questions, and we took them to graphs and tables the next day where I made them interpret v(5) or m(10) where there was context around the problems.
Next up, studying for finals and finals and a LONG BREAK to get more than 6.something hours of sleep each weeknight.
Then I noted that THAT was a ton of writing, and we assigned variables to things like r and t, and I showed them t(r) and noted that the input, r, was INSIDE the parentheses, and the output, t, was OUTSIDE the parentheses, and if you were talking to your math boyfriend over the phone, you'd say, "t of r" or "t is a function of r".
Then we got to things like B(h) where B is your tutoring bill and h is the hours of tutoring. I asked them to interpret: B(3) = 120. We did this for 4 problems or so. I liked those types of questions, and we took them to graphs and tables the next day where I made them interpret v(5) or m(10) where there was context around the problems.
Next up, studying for finals and finals and a LONG BREAK to get more than 6.something hours of sleep each weeknight.
Friday, November 27, 2009
Music & Computer Work
Frequently my IED (engineering) class is on the computer all period working on the CAD program (Inventor). Several of the students daily ask me if they can listen to music while they work. I always say no. BUT it's "Pandora", they say, there's no talking, they say, it helps me concentrate, they say. Ms./Mr. So-And-So let's me in THEIR class, they say. No, I say.
I had a bunch of reasons all jumbled up in my brain, and I didn't sort it out as to the real reason I was such a grinch until the other day. Here's my main reason. More and more I see people in society all plugged in and earbudded into isolation and in their own little worlds not interacting with the people in the present and around them. I guess I want my students to see and be with the students around them at the current time and learn to interact with them - whether it's talking with them about what they're doing, chatting about various things, or learning to focus with the outside noise potentially disturbing them. You know, being part of our community.
And also because I'm a grinch.
I had a bunch of reasons all jumbled up in my brain, and I didn't sort it out as to the real reason I was such a grinch until the other day. Here's my main reason. More and more I see people in society all plugged in and earbudded into isolation and in their own little worlds not interacting with the people in the present and around them. I guess I want my students to see and be with the students around them at the current time and learn to interact with them - whether it's talking with them about what they're doing, chatting about various things, or learning to focus with the outside noise potentially disturbing them. You know, being part of our community.
And also because I'm a grinch.
Tuesday, November 24, 2009
Reviews
It's almost time for finals, and I scurried around last minute as is my nature to make a review for algebra and geometry. While I was doing so, I remembered various conversations I'd had with my algebra students this semester whenever test time rolled around.
I want them to be active learners and to take the initiative to think of what's going to be tested, go over problems of a type, come in for help if needed, etc, etc. Yea, I know, maybe it's all pipe dreams and wishful thinking, but how do you get them there. I tried with a study guide (not a review sheet), and after some tweaking, used it the few remaining times I had tests. I never went back and surveyed the students on paper to see if it changed their study habits. Maybe they just found it one more chore to do, but maybe it put a seed in their heads about how to study.
Or maybe not. Right after another test, we were discussing it in class, and some students raised their hands:
"other teachers give us a review sheet with questions to practice"
"other teachers give us points when we turn in the review sheet"
Yeesh. They think there's something magic about the extra review problems I could come up with. And THEN they want someone else to give them motivation to actually review. I said as much (in nice teacher talk words) to them in response to these questions. I don't know who I sold, or who still thinks, "meanie. give us the review!"
I want them to be active learners and to take the initiative to think of what's going to be tested, go over problems of a type, come in for help if needed, etc, etc. Yea, I know, maybe it's all pipe dreams and wishful thinking, but how do you get them there. I tried with a study guide (not a review sheet), and after some tweaking, used it the few remaining times I had tests. I never went back and surveyed the students on paper to see if it changed their study habits. Maybe they just found it one more chore to do, but maybe it put a seed in their heads about how to study.
Or maybe not. Right after another test, we were discussing it in class, and some students raised their hands:
"other teachers give us a review sheet with questions to practice"
"other teachers give us points when we turn in the review sheet"
Yeesh. They think there's something magic about the extra review problems I could come up with. And THEN they want someone else to give them motivation to actually review. I said as much (in nice teacher talk words) to them in response to these questions. I don't know who I sold, or who still thinks, "meanie. give us the review!"
Monday, November 16, 2009
Treadmill Year
I teach 4 different preps this year, and always feel rushed to get done what I need to get done. I want to do a good job (obviously), and always go over and over in my mind what I'm teaching, how I'm teaching it, how it could be better, etc. Three of my preps are single classes, and one prep I teach 3 times per lesson. That's the lucky prep (algebra 1) because I can refine it by the 3rd time. Or maybe I should say that my 3rd class of algebra 1 is my lucky class, and the other 2 are my guinea pigs (squea squea).
Why am I mentioning this? Because like maybe all teachers I'm a world-class self-beater-upper in that I'm always thinking I could have taught it better or given better problems or better something. I finally have started saying to myself, "you're doing the best you can. do it and move on." Who knows how long I'll listen to myself.
What I am loving is my GoogleDocs account. I'm doing my lesson plans on there this year, and I like that the documents are available no matter what computer I use and where I am (home or school).
What's going on so far:
geometry - we just learned CPCTC. I'm following the curriculum I taught in New Jersey, and we're doing flow proofs. I think those are more logical than 2 column proofs, and it shows me and the students what statements are needed and how for what conclusions.
algebra 1 - we have just covered patterns and linking them to tables, graphs, rules, and descriptions using tiles. I moved away from tiles the 2nd day, and wanted them to find rules and use the rules without drawing pictures, and I like the problems I gave them. Sample:
Suppose 13 15 17 19 21 ... is a sequence of "tiles.
a. Let "13" be the 1st figure in the sequence, write the rule.
b. Let "13" be the 5th figure in the sequence, write the rule.
c. Let "13" be the 20th figure in the sequence, without counting backwards, write the rule.
d. Let "13" be the 100th figure in the sequence, write the rule.
e. For "a.", suppose you have used 51 tiles, what figure number are you at?
f. For "a.", suppose you have 200 tiles to use, what's the maximum figure number you can create?
And for each of these (a-d), I made them write what each variable and each # represented.
Then we moved on to other "tile" like problems:
A cell phone company charges $29.95 per month with a 3cent per minute fee, (after a bunch of leading questions to link to tiles): write the rule. This one was interesting because of the units issue. Many kids started with
b = 29.95 + 3m .... we had a discussion about units and got it to
b = 29.95 + 0.03m
etc.
engineering - we've talked about dial calipers and statistics and geometry. Lots of good discussion about how statistics is used in engineering.
TAKS math class - we've taken a LOT of deep breaths because of behavior issues and just plowed on. Today we learned how to count. After some snarky comments, they kind of got into it. I gave them 4 different colored snap cubes and we learned how to count "choosing 2 for a team" then "choosing a president and a vp" then choosing 3 for a team, etc.
Monday, November 09, 2009
Hall Conversations
Last week was not a good week. I was crabby and in a funk to begin with (perimenopause anyone? ... or maybe I just want to place a reason to this cloud that goes by periodically lately). Then in my TAKS help class, on Thursday, I had to deal with outrageous rudeness. The kids are usually pretty good, save for the "I'd rather talk to my friends than do math" behavior. Two particular students were in the chatty mood. One had already come into class with an attitude. About 20 minutes into class, I said, "when we start our next activity, one of you needs to move tables", and I walked away to let them process that. The next activity started, and neither had moved, I asked again, and here came the craziness. One girl gets a big attitude on her face, crosses her arms and says, "I'm not moving".
Excuse me? Step out into the hall, I need to talk to you. I got the other students started on their work, and so began the conversation in the hall. She would not let up. Finally, she's all in a snit and states she's ready to come back in and work. I don't think so. I brought out a chair, and she remained in the hall doing her work for the next hour. Oh my.
Then on Friday in my last class of the day on student mentioned she left her work in another teacher's class, and could she go get it. No, not right now. She was not happy, but she continued to work. Then about 20 minutes later, she asked to go to the bathroom. I was thinking she wanted to go roam the halls and find her homework in the meantime, but she was jiggling in her seat, and she's generally a good kid, so I said, "go quickly and come back".
Twenty minutes later she shows up. Oh my was I angry. Again I started the kids on an activity, and talked to her in the hall. I mentioned why I was upset, and asked where she'd gone (to a counselor), and why she hadn't asked (you asked me in front of the class, and I didn't want to say it out loud), and how she could possibly handle it in the future (come up and whisper your request in my ear or call me over).
Anyway, she was near tears, and I was angry and yuk, not a good way to end the day/week (wooHOO for margaritas with friends after work to decompress). Today I asked the counselor if she'd been in to see her, and she said yes, she'd been having family issues and all sorts of sad things and we should be on the lookout to support her. Great! Big Ogre Teacher with the angry face berating a poor child.
Deep Breaths and Fresh Starts this week.
Excuse me? Step out into the hall, I need to talk to you. I got the other students started on their work, and so began the conversation in the hall. She would not let up. Finally, she's all in a snit and states she's ready to come back in and work. I don't think so. I brought out a chair, and she remained in the hall doing her work for the next hour. Oh my.
Then on Friday in my last class of the day on student mentioned she left her work in another teacher's class, and could she go get it. No, not right now. She was not happy, but she continued to work. Then about 20 minutes later, she asked to go to the bathroom. I was thinking she wanted to go roam the halls and find her homework in the meantime, but she was jiggling in her seat, and she's generally a good kid, so I said, "go quickly and come back".
Twenty minutes later she shows up. Oh my was I angry. Again I started the kids on an activity, and talked to her in the hall. I mentioned why I was upset, and asked where she'd gone (to a counselor), and why she hadn't asked (you asked me in front of the class, and I didn't want to say it out loud), and how she could possibly handle it in the future (come up and whisper your request in my ear or call me over).
Anyway, she was near tears, and I was angry and yuk, not a good way to end the day/week (wooHOO for margaritas with friends after work to decompress). Today I asked the counselor if she'd been in to see her, and she said yes, she'd been having family issues and all sorts of sad things and we should be on the lookout to support her. Great! Big Ogre Teacher with the angry face berating a poor child.
Deep Breaths and Fresh Starts this week.
Thursday, November 05, 2009
Algebra Algebra Algebra
Phew! That's what seems to be consuming my thoughts these days. I like teaching it for the 2nd year, and also I like that I know what's coming up on the horizon in the higher level math classes for the kids, so I can know what skills to focus on. For example, we just covered solving proportions, and I had some problems with the variable in the denominator. Well. The kids learned from 8th grade that you can just change the equation by taking the reciprocal of both sides and then solve.
So 12/5 = 7/x becomes 5/12 = x/7.
This is all well and good, and sometimes that's the simplest way to solve, but what if in algebra 2 or above you come across:
3x/(x+1) = (3x-2)/x.
Then "flipping" does not get you any closer to the answer.
Oh. Then someone mentioned "cross multiplying". Well, I didn't even want to go there because of all the misuse of that I've seen later on: OH! magically any time I see 2 fractions together involving variables whether or not there's an equal sign, I'm going to cross multiply without knowing why it works or even IF it works. Voila!
Anyway .... tons of algebra fun. I did have a discussion with my coworker, and she had this brilliant idea that I tried with solving absolute value equations ... but it can work with solving any equation. Write down the equation. On top of it, write numbers in circles in the order of operation of what would be done to x if you were to plug in a number. Then on the side I listed PEMDAS and the circled numbers in order and wrote in words what that was:
1. multiply by 3
2. subtract 4
3. take absolute value
4. add 10
Then under that sidebar, I wrote "to solve: undo in backwards order SADMEP"
4. subtract 10
3. 2 cases
2. add 4
1. divide by 3
Then the kids had a road map of what to do, and they didn't do weird things like get rid of stuff inside the absolute value symbols before taking care of them.
So 12/5 = 7/x becomes 5/12 = x/7.
This is all well and good, and sometimes that's the simplest way to solve, but what if in algebra 2 or above you come across:
3x/(x+1) = (3x-2)/x.
Then "flipping" does not get you any closer to the answer.
Oh. Then someone mentioned "cross multiplying". Well, I didn't even want to go there because of all the misuse of that I've seen later on: OH! magically any time I see 2 fractions together involving variables whether or not there's an equal sign, I'm going to cross multiply without knowing why it works or even IF it works. Voila!
Anyway .... tons of algebra fun. I did have a discussion with my coworker, and she had this brilliant idea that I tried with solving absolute value equations ... but it can work with solving any equation. Write down the equation. On top of it, write numbers in circles in the order of operation of what would be done to x if you were to plug in a number. Then on the side I listed PEMDAS and the circled numbers in order and wrote in words what that was:
1. multiply by 3
2. subtract 4
3. take absolute value
4. add 10
Then under that sidebar, I wrote "to solve: undo in backwards order SADMEP"
4. subtract 10
3. 2 cases
2. add 4
1. divide by 3
Then the kids had a road map of what to do, and they didn't do weird things like get rid of stuff inside the absolute value symbols before taking care of them.
Wednesday, October 28, 2009
Literal Equations
We've moved on to solving literal equations for a variable. I like this transition because it reinforces the same skills they've been working on forEVER. One thing came up in my first of 3 classes to teach it this year that made me change tactics for the next 2 classes.
We were all about "isolating the variable" and "undoing what's done to the variable you're solving for" and such. Then as I'm walking around, lo and behold, a student was actually moving the variable. She wanted to get it to the other side. What was she doing?! Don't touch that variable!
That led to the following in my next 2 classes. Suppose the problem is
Solve 3A = 2w + 4p for w.
I first made them get out another colored pen/pencil, and then identify the variable they were solving for. Then they had to write that variable in a DIFFERENT color:
3A = 2w + 4p
Then I made them draw an arrow to the w and write in their notes, "DON'T TOUCH THIS" while humming the M.C. Hammer song of the same name. We continued on, and most everyone successfully colored the "solve for" variables and left them alone in the remaining problems.
We were all about "isolating the variable" and "undoing what's done to the variable you're solving for" and such. Then as I'm walking around, lo and behold, a student was actually moving the variable. She wanted to get it to the other side. What was she doing?! Don't touch that variable!
That led to the following in my next 2 classes. Suppose the problem is
Solve 3A = 2w + 4p for w.
I first made them get out another colored pen/pencil, and then identify the variable they were solving for. Then they had to write that variable in a DIFFERENT color:
3A = 2w + 4p
Then I made them draw an arrow to the w and write in their notes, "DON'T TOUCH THIS" while humming the M.C. Hammer song of the same name. We continued on, and most everyone successfully colored the "solve for" variables and left them alone in the remaining problems.
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