I sure love her stuff!
(She's also done some joint videos with Sal Khan recently. Not sure what I think of those...)
Friday, August 26, 2011
Thursday, August 18, 2011
Days 2 and 3
I think it's going to be a good semester.
On Monday, all 3 classes had homework that included the bit I mentioned for Calc II: First, find 5 problems you can do, and do them. Then find 5 problems you can't do and write them up to share with your group. So on Tuesday, in both Pre-Calc and Calc II, they worked for part of the time on the problems they had brought in. I gave them a sheet titled homework sharing that told them to put any problems no one in the group could do onto the board. And then "If you see a problem on the board you can do (or offer ideas on), go on up and do it."
After about 30 minutes, there were about 7 problems on the board, 2 or 3 of them solved. We discussed 2 or 3 of the unsolved ones, and still need to discuss the last few.
Then we worked on the problem Kate brought up a few days ago, Follow that Diagonal, except that I called it Crossing Tiles. They have not finished solving it yet; I plan to come back to it.
At the end of class, I asked them to let me know what they think of the way we're working together. As students were leaving, W and D asked me if I had worked with CPM. I replied, "That's a high school program, so I haven't worked with it, but I have heard of it. I'm guessing you didn't like it. Can you email me to tell me what you didn't like? That will help me improve what I'm doing."
Shortly after class, another student came to my office, and with a shaky voice asked if I was planning to lecture. She said she needs lecture. I felt for her! She seemed so scared about telling me she wanted me to do something different. I thanked her and said I would sometimes lecture. I know that in the business world it's accepted that each complaint you hear about represents possibly hundreds of complaints you didn't hear. So I figured lots of the students were probably nervous and wanted some lecture.
Having them work in groups got them to know each other more, but they still didn't have much sense of who I am. So I planned a lecture (sort of) for Wednesday. As I came in, I asked them to sit in the same group areas, but to push the desks into pairs facing forward. I started with a request on the board: Write your definition of a circle. I talked about the fact that I want them to feel safe. Even though I know that group work is what will get them the most engaged in mathematical thinking, I want to give them what will help them see that they're safe with me. (It was a good moment to point out the retest policy on the syllabus for those who hadn't noticed.)
Definitions of Circles
I love performing, so Wednesday was my favorite day so far. I gave them one minute to finish up their definition, and two minutes to share with their partner and revise. I got volunteers to offer their definitions, which I wrote on the board. There were 4.
Then I asked for votes on whether a definition was a good one or not. If not, did a circle not fit the definition, or could things that are not circles slip in? I asked those who voted no to volunteer to come up and show us a counter-example. From those we fixed the definitions. We ended up with 4 very different definitions of a circle, all pretty much working. Except that I thought there might be a counter-example to one of them.
Here they are:
I had students google (on their smart phones, of course) "rolls smoothly, not a circle". We didn't find anything. I said I'd get back to them. Later in the day, I was able to google a better phrase: 'constant diameter', and Cut the Knot came through. I'll show this to them today.
I had lots more planned, but I loved where we went with this inquiry into definitions. Maybe today, when I talk about distance and the Pythagorean Theorem (leading into equations of circles), I can help them get a better feel for the difference between definitions and theorems. It doesn't sound like there was much lecture, but I did talk way more than the first two days.
Calc II
My Calc II students were happier about working in groups, because that Calc I review sheet* was full of problems they wanted to get more solid on. We also worked on a problem I found at the Exeter site, Turning Two Squares Into One. I had forgotten scissors and rulers, and had to run up to the office to get them. We used this as a springboard to discuss the Pythagorean Theorem. Last semester I found out my Calc II students were terribly weak in trig, so today we review that.
On Tuesday and Wednesday, I work from 9:30 to 3, plus what I do at home. On Monday and Thursday, I work from 9:30am to 8pm, a very long day. I ought to get out and do something physical in the late afternoon, so I don't get exhausted in my evening class. Hmm...
OK, I've made a simple, boring handout for my Pre-Calc class, so they won't need the textbook to work on problems (first week of class, expensive,...).
I'm writing these rambling here's-what-I-did posts more for myself than for my readers, but I'd definitely like to know whether the handouts I'm posting are of any use to you. And I'd love your thoughts about what I'm doing.
_____
*What I uploaded yesterday left out the equations. :^( I just uploaded a pdf of this handout. Or email me if you want it editable.
On Monday, all 3 classes had homework that included the bit I mentioned for Calc II: First, find 5 problems you can do, and do them. Then find 5 problems you can't do and write them up to share with your group. So on Tuesday, in both Pre-Calc and Calc II, they worked for part of the time on the problems they had brought in. I gave them a sheet titled homework sharing that told them to put any problems no one in the group could do onto the board. And then "If you see a problem on the board you can do (or offer ideas on), go on up and do it."
After about 30 minutes, there were about 7 problems on the board, 2 or 3 of them solved. We discussed 2 or 3 of the unsolved ones, and still need to discuss the last few.
Then we worked on the problem Kate brought up a few days ago, Follow that Diagonal, except that I called it Crossing Tiles. They have not finished solving it yet; I plan to come back to it.
At the end of class, I asked them to let me know what they think of the way we're working together. As students were leaving, W and D asked me if I had worked with CPM. I replied, "That's a high school program, so I haven't worked with it, but I have heard of it. I'm guessing you didn't like it. Can you email me to tell me what you didn't like? That will help me improve what I'm doing."
Shortly after class, another student came to my office, and with a shaky voice asked if I was planning to lecture. She said she needs lecture. I felt for her! She seemed so scared about telling me she wanted me to do something different. I thanked her and said I would sometimes lecture. I know that in the business world it's accepted that each complaint you hear about represents possibly hundreds of complaints you didn't hear. So I figured lots of the students were probably nervous and wanted some lecture.
Having them work in groups got them to know each other more, but they still didn't have much sense of who I am. So I planned a lecture (sort of) for Wednesday. As I came in, I asked them to sit in the same group areas, but to push the desks into pairs facing forward. I started with a request on the board: Write your definition of a circle. I talked about the fact that I want them to feel safe. Even though I know that group work is what will get them the most engaged in mathematical thinking, I want to give them what will help them see that they're safe with me. (It was a good moment to point out the retest policy on the syllabus for those who hadn't noticed.)
Definitions of Circles
I love performing, so Wednesday was my favorite day so far. I gave them one minute to finish up their definition, and two minutes to share with their partner and revise. I got volunteers to offer their definitions, which I wrote on the board. There were 4.
Then I asked for votes on whether a definition was a good one or not. If not, did a circle not fit the definition, or could things that are not circles slip in? I asked those who voted no to volunteer to come up and show us a counter-example. From those we fixed the definitions. We ended up with 4 very different definitions of a circle, all pretty much working. Except that I thought there might be a counter-example to one of them.
Here they are:
- N's definition: A moving point travels around a fixed point, always at the same distance.
- A's definition: A shape with no beginning and no end, that's symmetrical.
- X's definition: The diameter stays the same in every direction.
- Y's definition: A shape with all points equidistant from the center.
I had students google (on their smart phones, of course) "rolls smoothly, not a circle". We didn't find anything. I said I'd get back to them. Later in the day, I was able to google a better phrase: 'constant diameter', and Cut the Knot came through. I'll show this to them today.
I had lots more planned, but I loved where we went with this inquiry into definitions. Maybe today, when I talk about distance and the Pythagorean Theorem (leading into equations of circles), I can help them get a better feel for the difference between definitions and theorems. It doesn't sound like there was much lecture, but I did talk way more than the first two days.
Calc II
My Calc II students were happier about working in groups, because that Calc I review sheet* was full of problems they wanted to get more solid on. We also worked on a problem I found at the Exeter site, Turning Two Squares Into One. I had forgotten scissors and rulers, and had to run up to the office to get them. We used this as a springboard to discuss the Pythagorean Theorem. Last semester I found out my Calc II students were terribly weak in trig, so today we review that.
On Tuesday and Wednesday, I work from 9:30 to 3, plus what I do at home. On Monday and Thursday, I work from 9:30am to 8pm, a very long day. I ought to get out and do something physical in the late afternoon, so I don't get exhausted in my evening class. Hmm...
OK, I've made a simple, boring handout for my Pre-Calc class, so they won't need the textbook to work on problems (first week of class, expensive,...).
I'm writing these rambling here's-what-I-did posts more for myself than for my readers, but I'd definitely like to know whether the handouts I'm posting are of any use to you. And I'd love your thoughts about what I'm doing.
_____
*What I uploaded yesterday left out the equations. :^( I just uploaded a pdf of this handout. Or email me if you want it editable.
Tuesday, August 16, 2011
First Day of Class
Mostly fabulous. Definitely exhausting. Must write it down so I won't forget the details.
My first class was Pre-Calc at 10, but I had to get to campus before 9 so I could stop by another teacher's 8am calc II class, which had too many students, and recruit for my 1pm calc II class, which had too few students. (Many of the science students are in labs at that time.)
Pre-Calc
I finally got a chance to look at my Pre-Calc classroom and was disappointed to find out it's not a 'smart' classroom - no internet to screen capacity. I showed it to a colleague who prefers chalkboards. He said he'd think about switching rooms with me.
Here are my notes for Pre-Calc:
I wasn't able to get into the room before the students did, so my seat cards were useless. But the students helped me move the desks, and the grouping gave us more space between the groups - very nice in our crowded classrooms.
It was so different from my usual first day. I talked way less, and they got to play with math more. The axes exercise went well, and I used it in all 3 classes. I wonder if any problems will arise from not going over my policies. I handed out a 'syllabus search' as part of their homework in 2 of the 3 classes, so they'll be nudged to read the syllabus. The times I used on my plan were no use at all.
[Please let me know whether the links in this post work. They're to documents I've shared in google documents. It's my first time doing this. I am so slow to pick up each new techie bit - that's why I had to go to Maria's workshop.]
Axes Exercise
This came from the Complex Instruction workshop. I loved how much mathematical thinking they had to do while being prompted to get to know each other. For next year, I think I'll change the instructions on the bottom. (People thought the dots had to represent them in the same order they were sitting. Question for CI (Complex Instruction) experts: Is it better to have less instruction on a sheet like this, so they have to figure it out?)
If I were good at CI, I would have been writing myself notes about good things students were doing, so I could let them know how their actions helped their group. Mostly I had no time for that. When I did have a moment, I had trouble hearing enough to know what was going on.
In the Pre-Calc class, I got one volunteer for the share out, and rolled dice for a second 'volunteer'. I had 10 groups but no 10-sided die. I rolled 2 dice, and thought about how the odds were stacked against group 7. I didn't bring that up, but I might another time. We clapped for the brave souls who came up and explained their group's work.
We discussed conventional ideas about what qualities someone who's good at math would have, versus what's really true. That's about all we got to.
I want to remember to use the side board for instructions. I want to keep trying to respond to their questions with questions, instead of answering them. I'm not good at that.
Calc II
I had two hours between class, but I still had to print out my syllabi. I had purposely not prepped much for this class, since I wasn't sure it would go. We got 16 students, so it's good to go. And I know from last semester that more people may join us over the coming week.
This group was slower to get started with the axes exercise than my lower level classes. Once they got into it, they did it well, and enjoyed talking to each other, but they seemed less comfortable with jumping into something that was strange to them.
As they finished, they picked up a Calc I review sheet.
I had no homework sheet for them, so I told them their homework was to find 5 Calc I problems they could do and do them, and to find 5 they couldn't do and write them down to share with their group tomorrow.
Intermediate Algebra
Terrible classroom. One whiteboard covered in information I thought might need to stay, one chalkboard on wheels. But we worked with what we had. I'll try to change rooms, but it might be impossible.
This class is part of a program funded by First Five money, and has a smaller enrollment cap than our usual 40. Unfortunately our computer system can't handle the quirks of this class, so there were lots of people who came, hoping to get in, even though it was full. And everyone who is in still has to register online for this one, but I couldn't get their add codes, because WebAdvisor was down.
It took a while to get all the registration details taken care of, but this is a 2 1/2 hour class (5:40-8pm), so we had plenty of time to do some math. Their homework included putting some fractions in order, and the suggestion to play Flower Power at Manga High if they had any trouble with that.
After our break, I use Energizing Brain Breaks, a little book I bought online; I find a silly physical exercise in it for us to do together, to wake us up. I also talk about how cross-lateral motion is supposed to help brain development.
At 8:30pm, after 12 hours at work, I dragged myself home, mostly content. And now I'd better get to work prepping for today!
My first class was Pre-Calc at 10, but I had to get to campus before 9 so I could stop by another teacher's 8am calc II class, which had too many students, and recruit for my 1pm calc II class, which had too few students. (Many of the science students are in labs at that time.)
Pre-Calc
I finally got a chance to look at my Pre-Calc classroom and was disappointed to find out it's not a 'smart' classroom - no internet to screen capacity. I showed it to a colleague who prefers chalkboards. He said he'd think about switching rooms with me.
Here are my notes for Pre-Calc:
Before class: Push desks into pods of 4, number the groups
Stand at door with handouts for exercise, and seat cards.On side board:· “Look here every day,· make a name tent (diagram)· make sure to sign the attendance sheet neatly (groups diagram)· adds at end of week
Axes exercise: (10:10-10:25)· Groups do it· Share out
Do ‘good at math?’ exercise (10:25-10:35)
Talk about brain function and learning: neurons, synapses, myelin sheath, confusion (10:35-10:45)http://vv.carleton.ca/~neil/neural/neuron-a.html
Crossing Tiles problem: (10:45-10:58)Do in groups
Announce: (10:58-11:00)· Must have a textbook, can use older edition, see me to learn how to one for under $10, you will be dropped if you don’t get one (I want to give my effort to those who will care enough about succeeding to take care of their end.)· Photos on TuesdayHand out syllabus pack at door at end
I wasn't able to get into the room before the students did, so my seat cards were useless. But the students helped me move the desks, and the grouping gave us more space between the groups - very nice in our crowded classrooms.
It was so different from my usual first day. I talked way less, and they got to play with math more. The axes exercise went well, and I used it in all 3 classes. I wonder if any problems will arise from not going over my policies. I handed out a 'syllabus search' as part of their homework in 2 of the 3 classes, so they'll be nudged to read the syllabus. The times I used on my plan were no use at all.
[Please let me know whether the links in this post work. They're to documents I've shared in google documents. It's my first time doing this. I am so slow to pick up each new techie bit - that's why I had to go to Maria's workshop.]
Axes Exercise
 |
| Work in the middle of the table with your team. Label the x and y axis each with an attribute (no physical attributes please) such that each dot represents one person in the team. |
This came from the Complex Instruction workshop. I loved how much mathematical thinking they had to do while being prompted to get to know each other. For next year, I think I'll change the instructions on the bottom. (People thought the dots had to represent them in the same order they were sitting. Question for CI (Complex Instruction) experts: Is it better to have less instruction on a sheet like this, so they have to figure it out?)
If I were good at CI, I would have been writing myself notes about good things students were doing, so I could let them know how their actions helped their group. Mostly I had no time for that. When I did have a moment, I had trouble hearing enough to know what was going on.
In the Pre-Calc class, I got one volunteer for the share out, and rolled dice for a second 'volunteer'. I had 10 groups but no 10-sided die. I rolled 2 dice, and thought about how the odds were stacked against group 7. I didn't bring that up, but I might another time. We clapped for the brave souls who came up and explained their group's work.
We discussed conventional ideas about what qualities someone who's good at math would have, versus what's really true. That's about all we got to.
I want to remember to use the side board for instructions. I want to keep trying to respond to their questions with questions, instead of answering them. I'm not good at that.
Calc II
I had two hours between class, but I still had to print out my syllabi. I had purposely not prepped much for this class, since I wasn't sure it would go. We got 16 students, so it's good to go. And I know from last semester that more people may join us over the coming week.
This group was slower to get started with the axes exercise than my lower level classes. Once they got into it, they did it well, and enjoyed talking to each other, but they seemed less comfortable with jumping into something that was strange to them.
As they finished, they picked up a Calc I review sheet.
I had no homework sheet for them, so I told them their homework was to find 5 Calc I problems they could do and do them, and to find 5 they couldn't do and write them down to share with their group tomorrow.
Intermediate Algebra
Terrible classroom. One whiteboard covered in information I thought might need to stay, one chalkboard on wheels. But we worked with what we had. I'll try to change rooms, but it might be impossible.
This class is part of a program funded by First Five money, and has a smaller enrollment cap than our usual 40. Unfortunately our computer system can't handle the quirks of this class, so there were lots of people who came, hoping to get in, even though it was full. And everyone who is in still has to register online for this one, but I couldn't get their add codes, because WebAdvisor was down.
It took a while to get all the registration details taken care of, but this is a 2 1/2 hour class (5:40-8pm), so we had plenty of time to do some math. Their homework included putting some fractions in order, and the suggestion to play Flower Power at Manga High if they had any trouble with that.
After our break, I use Energizing Brain Breaks, a little book I bought online; I find a silly physical exercise in it for us to do together, to wake us up. I also talk about how cross-lateral motion is supposed to help brain development.
At 8:30pm, after 12 hours at work, I dragged myself home, mostly content. And now I'd better get to work prepping for today!
Thursday, August 11, 2011
MCC Math Technology Bootcamp
What an amazing week!
I know I won't have time to write this up after I go home (I'm teaching in 4 days, yikes!), so I'm going to throw some thoughts out now.
Here's our schedule from the week. Ask me about anything on this that I forget to write about.
I've been collecting links and notes in an email to myself (it seems like the easiest way to take notes while online). Here are a bunch of them.
Monday
http://practiceboard.com/
http://www-history.mcs.st-and.
http://dabbleboard.com/draw
http://www.ted.com/index.php/
http://www.mindomo.com/view?m=
http://www.thencat.org/
Tuesday
Images are really enticing to us, and to students. Use lots of images in your course shell so you can see which resource is which.
The slideshow we were looking at was done online at slideshare.net.
Her students use cell phone cameras to take pics of hw, they can jing from anywhere it's on a computer.
To grade hw, she uses jing to record her talking about what they turned in.
"Build me a rational function that has the following properties, jing it to me."
At the end of the first week of classes, she calls the non-participators. (and then the best...)
googleform: give me your phone number, ...
Get a netbook instead of a graphing calculator, go to mcdonalds, starbucks, panera, etc...
At MCC they have a fall read. (All faculty read the same book.)
twitter conversation (in the right order): http://twonvo.com/
penattention is a free pgm so the cursor shows up better while you're using a tablet.
Wednesday
youtube lectures available on smartphones
my first screencast link: http://www.screencast.com/t/
My project of the day was to make a video in Camtasia. I made it on Math Myths. It's a quick and dirty first project of a rank beginner.
Thursday
use control for right-click for contextual menus
http://www.mathsisfun.com/
buy personal whiteboards on amazon (I did it! I got 60. They arrive on Monday.)
Her cool classroom has kidney bean shaped tables, to get the students working together. Maria said: "In a classroom with desks in rows, you're pushed to lecture more, that's what the room tells you to do. People have taught the same class in this room and in a traditional room, and it makes the 2 classes completely different. They hated the traditional room."
Maria again (on finding money for smartboards), "We gave up our maple license to get the smartboard." (It's about a thousand dollars.)
She has the whole class go to the board in pairs to work on the problem she poses. Some students liked it so much they put whiteboards up at home. (!)
Maria: "Clickers are expensive and I don't see any point in using them." She uses polleverywhere.com. It's free.
Friday
We'll be doing Ignite presentations: 20 slides, 15 seconds each, 5 minutes total. It's Thursday now. I'm working on mine while I listen to today's presentations (not ideal...). I'm almost done...
I'll leave early on Friday to go back to GR and be with my son. On Saturday we fly home to CA. On Sunday I prep all my classes. On Monday I teach. Wish me the best!
If I've made you envious and you'd like to come next year, watch Maria Andersen's blog, Teaching College Math, for announcements about next summer's workshop.
I know I won't have time to write this up after I go home (I'm teaching in 4 days, yikes!), so I'm going to throw some thoughts out now.
Here's our schedule from the week. Ask me about anything on this that I forget to write about.
I've been collecting links and notes in an email to myself (it seems like the easiest way to take notes while online). Here are a bunch of them.
Monday
http://practiceboard.com/
http://www-history.mcs.st-and.
http://dabbleboard.com/draw
http://www.ted.com/index.php/
http://www.mindomo.com/view?m=
http://www.thencat.org/
Tuesday
Images are really enticing to us, and to students. Use lots of images in your course shell so you can see which resource is which.
The slideshow we were looking at was done online at slideshare.net.
Her students use cell phone cameras to take pics of hw, they can jing from anywhere it's on a computer.
To grade hw, she uses jing to record her talking about what they turned in.
"Build me a rational function that has the following properties, jing it to me."
At the end of the first week of classes, she calls the non-participators. (and then the best...)
googleform: give me your phone number, ...
Get a netbook instead of a graphing calculator, go to mcdonalds, starbucks, panera, etc...
At MCC they have a fall read. (All faculty read the same book.)
twitter conversation (in the right order): http://twonvo.com/
penattention is a free pgm so the cursor shows up better while you're using a tablet.
Wednesday
youtube lectures available on smartphones
my first screencast link: http://www.screencast.com/t/
My project of the day was to make a video in Camtasia. I made it on Math Myths. It's a quick and dirty first project of a rank beginner.
Thursday
use control for right-click for contextual menus
http://www.mathsisfun.com/
buy personal whiteboards on amazon (I did it! I got 60. They arrive on Monday.)
Her cool classroom has kidney bean shaped tables, to get the students working together. Maria said: "In a classroom with desks in rows, you're pushed to lecture more, that's what the room tells you to do. People have taught the same class in this room and in a traditional room, and it makes the 2 classes completely different. They hated the traditional room."
Maria again (on finding money for smartboards), "We gave up our maple license to get the smartboard." (It's about a thousand dollars.)
She has the whole class go to the board in pairs to work on the problem she poses. Some students liked it so much they put whiteboards up at home. (!)
Maria: "Clickers are expensive and I don't see any point in using them." She uses polleverywhere.com. It's free.
Friday
We'll be doing Ignite presentations: 20 slides, 15 seconds each, 5 minutes total. It's Thursday now. I'm working on mine while I listen to today's presentations (not ideal...). I'm almost done...
I'll leave early on Friday to go back to GR and be with my son. On Saturday we fly home to CA. On Sunday I prep all my classes. On Monday I teach. Wish me the best!
If I've made you envious and you'd like to come next year, watch Maria Andersen's blog, Teaching College Math, for announcements about next summer's workshop.
Monday, August 1, 2011
What's at the Center of my Classroom? Community, if I'm Lucky...
[This post is part of the July-long Virtual Conference on Core Values, posted a few days late. I highly recommend clicking on over to check out the other posts from the conference, whose thematic question this year was 'What's at the Center of Your Classroom?'.]
I teach math at a community college. My goal is to help the students in each of my classes form a learning community, but I don't reach that goal most of the time. It's embarrassing and discouraging to still be struggling so much after 25 years of teaching. Maybe writing this post will help me clarify what that community means to me, and how I hope to help my students get there.
What is a community? How many of us really have any experience of what a community is? For most of my life, I have not been a church-goer. (My spiritual values don't mesh well with most churches.) When I lived in Muskegon, Michigan, I got pulled into the Unitarian fellowship there, and I found out what a community was. Sometimes it was just as dysfunctional as many of our families. But like being wrapped in the arms of a super-big family, the folks from the fellowship were there for me when I really needed them. I think many progressives, like me, don’t have much of that sort of experience. I don’t have a church that fits me, but perhaps someday I’ll find that. In the meantime, I want to create a bit of community with my students.
The less concrete communities of math bloggers and math circlers have also made a difference in my life; they've helped me to become more of a mathematician. I love working on math with other people. It's fun to put our heads together to solve a problem, and it's enlightening to see how differently other people will approach it. It has made a huge difference in my life. I want that for my students.
I also know how successful Uri Treisman's work [pdf] was, when he got groups of students to work together on challenging problems, as a way of helping students of color become more successful at UC Berkeley. I've known about his work for many years, and tried to use his model - challenging problems, students working in groups. Something's missing, though, because my results aren't as predictable as his were.
They Made the Class Their Own
I want to tell the story of one of my classes last fall. By a bit of a fluke, I was teaching 3 sections of one course, Beginning Algebra, and nothing else. In 2 of the 3 sections, there were students who interfered with the class running smoothly.* But in one section, the students really pulled together. There were times when they were frustrated, and sometimes even the most motivated students wanted to blame their failures on me. But mostly, they figured out what they wanted to learn, asked more and more questions, and made the class their own.
Many of them also came in 1 to 2 hours early and worked together, almost daily. The fact that our classroom was empty before class really helped get that rolling. Robert, one of the students, took on the role of teacher, and they were much more comfortable questioning him than they were questioning me in front of the whole class. (I wasn't in the room much, so I had fears that they would trust his statements too much, just like they usually trust mine too much. I'm not sure whether or not that happened.) Robert's life may have been changed by that experience - he may become a teacher himself some day. I hope so. I believe these chosen hours of study helped all the students who participated, but the evidence doesn't show it. I think this class started out with shakier foundations than either of the others.**
The last semester before my sabbatical year, I had another class that really bonded. In that class, Nailah organized regular study sessions but did not lead them. It was much more free-form, with everyone writing problems on the board, asking questions, and offering explanations. That model seems more effective to me, but each class may need to find its own way. (I invented a Community Organizer award to honor Nailah's good work.)
In the Spring I taught Intermediate Algebra, so quite a few of my students came along to the next class (10 from the 1st group, 3 from the 2nd, and 3 from the 3rd). Although that class didn't ever gel as a community as well as my best fall class, it probably had the best pass rate I've ever managed. Our cap is 40 students, but I went over to let in returning students. Overall 38 passed, 11 failed. None of the returning students failed. Although over 20% failed, 38 people passing is a record for me. I'd rather not have the class so big - I never felt like I could really address the whole class at once. But it worked better than I expected it to.
So how do I encourage community, and how do they take it on?
I blogged about the Complex Instruction workshop I participated in earlier this summer. At the workshop we worked some challenging problems and discussed what makes a problem 'group-worthy'. As I plan for the fall, I'm looking for 'group-worthy' problems. I hope that working in groups of 4, and changing groups at least for each unit (about monthly), will help my students become more of a community.
One of the biggest problems is that students resist all this. They want the teacher to 'explain clearly', so they can take good notes, and follow the teacher's steps to do their homework. All this groupwork and figuring things out themselves feels strange to them. In some classes they don't trust me enough to take the risk of working at learning math in a new way. The Complex Instruction paradigm has the teacher give very clear instructions on how to work together - the students get their fix from that, instead of from being told how to 'do the math'. I hope it helps.
I don’t have a satisfying ending for this post, because I’m still trying to find a consistent approach that will help me co-create community with each of my classes.
_________
* Students at our community college have to take one 'college level' math course to move on to a 4-year college. Beginning Algebra is two levels below the 'college level' courses. Most students in this course are not happy about math.
** Pass rates: this group, 18 passed, 20 failed with D or F (yikes!); 2nd group, 25 passed, 11 failed; 3rd group, 21 passed, 16 failed. In the past I've had more students drop, instead of failing. They are not allowed, by the state of California, to drop in the last three weeks of class. With my retesting policy, lots of students on the edge hoped to pull themselves up, and stuck it out to the end. In Nailah's class (mentioned in the next paragraph), before I did as much retesting, I ended up with only 20 students; 13 passed, 7 failed.
I teach math at a community college. My goal is to help the students in each of my classes form a learning community, but I don't reach that goal most of the time. It's embarrassing and discouraging to still be struggling so much after 25 years of teaching. Maybe writing this post will help me clarify what that community means to me, and how I hope to help my students get there.
What is a community? How many of us really have any experience of what a community is? For most of my life, I have not been a church-goer. (My spiritual values don't mesh well with most churches.) When I lived in Muskegon, Michigan, I got pulled into the Unitarian fellowship there, and I found out what a community was. Sometimes it was just as dysfunctional as many of our families. But like being wrapped in the arms of a super-big family, the folks from the fellowship were there for me when I really needed them. I think many progressives, like me, don’t have much of that sort of experience. I don’t have a church that fits me, but perhaps someday I’ll find that. In the meantime, I want to create a bit of community with my students.
The less concrete communities of math bloggers and math circlers have also made a difference in my life; they've helped me to become more of a mathematician. I love working on math with other people. It's fun to put our heads together to solve a problem, and it's enlightening to see how differently other people will approach it. It has made a huge difference in my life. I want that for my students.
I also know how successful Uri Treisman's work [pdf] was, when he got groups of students to work together on challenging problems, as a way of helping students of color become more successful at UC Berkeley. I've known about his work for many years, and tried to use his model - challenging problems, students working in groups. Something's missing, though, because my results aren't as predictable as his were.
They Made the Class Their Own
I want to tell the story of one of my classes last fall. By a bit of a fluke, I was teaching 3 sections of one course, Beginning Algebra, and nothing else. In 2 of the 3 sections, there were students who interfered with the class running smoothly.* But in one section, the students really pulled together. There were times when they were frustrated, and sometimes even the most motivated students wanted to blame their failures on me. But mostly, they figured out what they wanted to learn, asked more and more questions, and made the class their own.
Many of them also came in 1 to 2 hours early and worked together, almost daily. The fact that our classroom was empty before class really helped get that rolling. Robert, one of the students, took on the role of teacher, and they were much more comfortable questioning him than they were questioning me in front of the whole class. (I wasn't in the room much, so I had fears that they would trust his statements too much, just like they usually trust mine too much. I'm not sure whether or not that happened.) Robert's life may have been changed by that experience - he may become a teacher himself some day. I hope so. I believe these chosen hours of study helped all the students who participated, but the evidence doesn't show it. I think this class started out with shakier foundations than either of the others.**
The last semester before my sabbatical year, I had another class that really bonded. In that class, Nailah organized regular study sessions but did not lead them. It was much more free-form, with everyone writing problems on the board, asking questions, and offering explanations. That model seems more effective to me, but each class may need to find its own way. (I invented a Community Organizer award to honor Nailah's good work.)
In the Spring I taught Intermediate Algebra, so quite a few of my students came along to the next class (10 from the 1st group, 3 from the 2nd, and 3 from the 3rd). Although that class didn't ever gel as a community as well as my best fall class, it probably had the best pass rate I've ever managed. Our cap is 40 students, but I went over to let in returning students. Overall 38 passed, 11 failed. None of the returning students failed. Although over 20% failed, 38 people passing is a record for me. I'd rather not have the class so big - I never felt like I could really address the whole class at once. But it worked better than I expected it to.
So how do I encourage community, and how do they take it on?
- I try to provide a safe atmosphere in which to make mistakes. My syllabus has this: "Some people like to joke around with their friends by putting each other down. Math is too intimidating for that. No put-downs in this class, please." And when I'm correcting someone's mistake, I try to point out the 'part of what they're thinking' that is right.
- Every day I have people check with a neighbor on a problem they're working on (most days that happens often), and most weeks they work in groups of 4 a few times.
- They work together to catch me in mistakes - that gets them donut points. I bring donuts once the class has caught me in 30 mistakes.
- I talk about the research that shows that working together helps students succeed, and encourage them to study with a partner.
- My students often sit together in the math lab, studying to retake mastery tests.
I blogged about the Complex Instruction workshop I participated in earlier this summer. At the workshop we worked some challenging problems and discussed what makes a problem 'group-worthy'. As I plan for the fall, I'm looking for 'group-worthy' problems. I hope that working in groups of 4, and changing groups at least for each unit (about monthly), will help my students become more of a community.
One of the biggest problems is that students resist all this. They want the teacher to 'explain clearly', so they can take good notes, and follow the teacher's steps to do their homework. All this groupwork and figuring things out themselves feels strange to them. In some classes they don't trust me enough to take the risk of working at learning math in a new way. The Complex Instruction paradigm has the teacher give very clear instructions on how to work together - the students get their fix from that, instead of from being told how to 'do the math'. I hope it helps.
I don’t have a satisfying ending for this post, because I’m still trying to find a consistent approach that will help me co-create community with each of my classes.
_________
* Students at our community college have to take one 'college level' math course to move on to a 4-year college. Beginning Algebra is two levels below the 'college level' courses. Most students in this course are not happy about math.
** Pass rates: this group, 18 passed, 20 failed with D or F (yikes!); 2nd group, 25 passed, 11 failed; 3rd group, 21 passed, 16 failed. In the past I've had more students drop, instead of failing. They are not allowed, by the state of California, to drop in the last three weeks of class. With my retesting policy, lots of students on the edge hoped to pull themselves up, and stuck it out to the end. In Nailah's class (mentioned in the next paragraph), before I did as much retesting, I ended up with only 20 students; 13 passed, 7 failed.
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