https://www.youtube.com/watch?v=c7456hm-KMQ
Mike drop. 'Nuff said.
Friday, July 22, 2016
AP Calculus Final Projects
After the AP calculus test we learn some new material (L'Hopital's rule and integration by parts) and then the students complete a final project. They run the gamut from real-life related rates problems (including data) to illustrations of scenarios to 3-D printing of solids produced by revolutions. I love this time of year and the students produced excellent work. This year two groups produced raps related to calculus, this is the more polished of the two:
https://www.youtube.com/watch?v=c7456hm-KMQ
Mike drop. 'Nuff said.
https://www.youtube.com/watch?v=c7456hm-KMQ
Mike drop. 'Nuff said.
Friday, May 6, 2016
Times they are a changin'!
Change is in the wind! For some time I've been thinking about some of the techniques I employ in my teaching (such as reflective writing activities) and wondering if I'm implementing them to the best of my ability.
A little bit of background: over the years I've used reflective writing in many forms. The impetus to use writing activities is from research I've encountered and also from my own experience- I found that articulating my experiences in words helped me understand them better and also helped me make connections between different topics.
While at Paul Smith's College I began using Paul Hickman's Interactive Collaborative Electronic Learning Logs (ICE Learning Logs for short) on a daily basis. I continued this when I moved to the secondary level albeit on a weekly basis to save time. I continue to be pressed for time, and sadly admit that I have done away with regular writing activities in my Regents Physics classes entirely in order to cover material more rapidly. I still use reflective activities with my advanced classes.
My AP Physics students reflect quarterly on their performance in class. My AP Calculus students reflect on a weekly basis in an alternating format: one week is a private discussion between the student and I in a shared google doc, and the following week is a group discussion board where students post anonymously (though I know who each author is).
I feel as though these activities are quite valuable, both for learning content and for helping students come to see themselves as part of the science/math community. However, I do not have concrete evidence to back this up- just my observations and anecdotal statements from students.
Cut back to the present: I've decided to take the plunge to start work on a doctorate so I can find out for myself what helps my students learn best. I've found a home at the Science and Mathematics Education Research Group in the Department of Integrated Studies at McGill University. I'm thrilled to be opening a new chapter in my career and am also lucky to have been granted a leave of absence from my current teaching position to take advantage of this incredible opportunity.
I'll do my best to keep up with this blog and share new ideas as I come across them- maybe I'll even do a better job than I have as of late!
A little bit of background: over the years I've used reflective writing in many forms. The impetus to use writing activities is from research I've encountered and also from my own experience- I found that articulating my experiences in words helped me understand them better and also helped me make connections between different topics.
While at Paul Smith's College I began using Paul Hickman's Interactive Collaborative Electronic Learning Logs (ICE Learning Logs for short) on a daily basis. I continued this when I moved to the secondary level albeit on a weekly basis to save time. I continue to be pressed for time, and sadly admit that I have done away with regular writing activities in my Regents Physics classes entirely in order to cover material more rapidly. I still use reflective activities with my advanced classes.
My AP Physics students reflect quarterly on their performance in class. My AP Calculus students reflect on a weekly basis in an alternating format: one week is a private discussion between the student and I in a shared google doc, and the following week is a group discussion board where students post anonymously (though I know who each author is).
I feel as though these activities are quite valuable, both for learning content and for helping students come to see themselves as part of the science/math community. However, I do not have concrete evidence to back this up- just my observations and anecdotal statements from students.
Cut back to the present: I've decided to take the plunge to start work on a doctorate so I can find out for myself what helps my students learn best. I've found a home at the Science and Mathematics Education Research Group in the Department of Integrated Studies at McGill University. I'm thrilled to be opening a new chapter in my career and am also lucky to have been granted a leave of absence from my current teaching position to take advantage of this incredible opportunity.
I'll do my best to keep up with this blog and share new ideas as I come across them- maybe I'll even do a better job than I have as of late!
Thursday, March 17, 2016
Friday, January 29, 2016
Grouping Activity
A long while back I read a post from Frank Noschese called subversive lab grouping. In a nutshell, you give students cards which tell them what groups they're in. But it's not as easy as it sounds- there is overlap between the words on the cards. For example, I've given students cards with letters on them. They start by trying to put all the vowels together, or maybe all the capital letters. But it doesn't form the right number of groups (4 groups with three students each), so they have to discard their model and start over. The key turns out to be the number of straight lines used to form each letter. X is two, as are T and L. So that's one group. W, M, and E are similarly grouped. Frank and his followers have thrown down a bunch of other ideas for groups, some of which I've adopted, but I've also made up my own.
My students love this activity and wanted me to write about it. Since this is the first request I've ever received for a blog entry, I figured I ought to honor it! I usually use it in calculus- I'm not sure why, but I haven't implemented it with my other classes yet. Maybe I will... one limitation is that you have to specify the number of groups and their sizes. If students are unexpectedly absent, it can throw a wrench in the works.
If anyone is interested in the groups I use, just say the word and I'll be happy to put them up.
My students love this activity and wanted me to write about it. Since this is the first request I've ever received for a blog entry, I figured I ought to honor it! I usually use it in calculus- I'm not sure why, but I haven't implemented it with my other classes yet. Maybe I will... one limitation is that you have to specify the number of groups and their sizes. If students are unexpectedly absent, it can throw a wrench in the works.
If anyone is interested in the groups I use, just say the word and I'll be happy to put them up.
Hands-on calculus
I started this post back in December, but never finished it. Here's the final product.
We've been working on related rates in calculus. One of the "classic" calculus problems involves a ladder in motion. Its typically moves away from a wall at a constant rate, and the students are asked to determine how fast the top of the ladder is falling.
At least the problem has context, even if the constant rate bit is a stretch. Last year I tried to turn this problem into reality, and it didn't quite work out. This year we did much better. Key things:
-put wheels on the top of the ladder so it rolls smoothly down the wall
-rest the bottom of the ladder on a constant velocity buggy (borrow one from the physics teacher)
-use a good tripod
Here's a snapshot of our setup (screenshot from LoggerPro):
I scaled the video, set up a coordinate system, and tracked the bottom of the meterstick (using the rearmost wheel on the vehicle). This produced the graph of the horizontal position of the bottom of the meterstick below.
I added a trendline so we could get velocity, and then I asked the students to use the length of the meterstick/wheel contraption along with this velocity to predict how rapidly the top of the meterstick would be falling when the base was 32 cm away from the wall (hence the cluster of points near that position).
This is where related rates came in, and the students ended up with an answer. We confirmed it by analyzing the same video and tracking the top of the meterstick.
We got a really nice parabolic shape, and the instantaneous velocity of the top of the meterstick matched their prediction. It was pretty successful- as one student put it, "it's so nice to use math to analyze something complicated that happens in the real world!"
We've been working on related rates in calculus. One of the "classic" calculus problems involves a ladder in motion. Its typically moves away from a wall at a constant rate, and the students are asked to determine how fast the top of the ladder is falling.
At least the problem has context, even if the constant rate bit is a stretch. Last year I tried to turn this problem into reality, and it didn't quite work out. This year we did much better. Key things:
-put wheels on the top of the ladder so it rolls smoothly down the wall
-rest the bottom of the ladder on a constant velocity buggy (borrow one from the physics teacher)
-use a good tripod
Here's a snapshot of our setup (screenshot from LoggerPro):
I scaled the video, set up a coordinate system, and tracked the bottom of the meterstick (using the rearmost wheel on the vehicle). This produced the graph of the horizontal position of the bottom of the meterstick below.
I added a trendline so we could get velocity, and then I asked the students to use the length of the meterstick/wheel contraption along with this velocity to predict how rapidly the top of the meterstick would be falling when the base was 32 cm away from the wall (hence the cluster of points near that position).
This is where related rates came in, and the students ended up with an answer. We confirmed it by analyzing the same video and tracking the top of the meterstick.
We got a really nice parabolic shape, and the instantaneous velocity of the top of the meterstick matched their prediction. It was pretty successful- as one student put it, "it's so nice to use math to analyze something complicated that happens in the real world!"
Monday, December 14, 2015
Whiteboards
I haven't written much lately. Hopefully that will change soon- we did an awesome related rates activity in class today and I want to write it up after we debrief it tomorrow.
However, I wanted to share this picture:
This is work a student did for her weekly reflection. She did it on a whiteboard and then pasted an image of this into the Google Doc we share together. This is her very own whiteboard- I got a new set last summer and relegated my old ones to the backup squad (because I couldn't bring myself to junk them completely). When some of my students commented on the new boards, I told them the story. They clamored to be allowed to take the old boards home- they love doing work on them! Heart warming, I tell you what!
By the way, if you're wondering about the optimization problem I made up, it's pasted below...
A person’s productivity, P, can be modeled as the product of their mental acuity (MA) and the time that he or she spends working. A graduate student in advanced mathematics is busy 16 hours of the day, so she has 8 hours that can be devoted to either sleep or work. The problem is that the amount of sleep she gets drastically affects her mental acuity. She has monitored her daily output and believes that her mental acuity is best modeled as MA=100-12*(8-t)^2 where t is the amount of sleep she gets every night. She has been working so hard that her mental acuity is at an all-time low, so she needs your help to determine how much time she should spend working to optimize her output.
If you’re stuck, she feels like she would probably start by writing down an expression for the amount of time she spends working in terms of her free time and the amount of time she spends sleeping.
And yes, for those intrepid readers, I do realize, courtesy of one of my students, that my MA function implies that mental acuity will peak at 0 hours of sleep. Quite the oversight- I'll do better next year. Speaking of mental acuity as a function of time spent sleeping...
However, I wanted to share this picture:
This is work a student did for her weekly reflection. She did it on a whiteboard and then pasted an image of this into the Google Doc we share together. This is her very own whiteboard- I got a new set last summer and relegated my old ones to the backup squad (because I couldn't bring myself to junk them completely). When some of my students commented on the new boards, I told them the story. They clamored to be allowed to take the old boards home- they love doing work on them! Heart warming, I tell you what!
By the way, if you're wondering about the optimization problem I made up, it's pasted below...
A person’s productivity, P, can be modeled as the product of their mental acuity (MA) and the time that he or she spends working. A graduate student in advanced mathematics is busy 16 hours of the day, so she has 8 hours that can be devoted to either sleep or work. The problem is that the amount of sleep she gets drastically affects her mental acuity. She has monitored her daily output and believes that her mental acuity is best modeled as MA=100-12*(8-t)^2 where t is the amount of sleep she gets every night. She has been working so hard that her mental acuity is at an all-time low, so she needs your help to determine how much time she should spend working to optimize her output.
If you’re stuck, she feels like she would probably start by writing down an expression for the amount of time she spends working in terms of her free time and the amount of time she spends sleeping.
And yes, for those intrepid readers, I do realize, courtesy of one of my students, that my MA function implies that mental acuity will peak at 0 hours of sleep. Quite the oversight- I'll do better next year. Speaking of mental acuity as a function of time spent sleeping...
Monday, September 28, 2015
Saving time and sharing
Morning! This is going to be a quick post just to share something new I recently learned. I've been using OneNote for more than a year now in lieu of Smart Notebook. OneNote has some quirks, but it does a much better job of keeping me organized. And the newest reason I love it is because I realized I can give my students viewing privileges for the class notes/discussion. No more exporting pdf's and emailing them to absentees or posting them to the website- it's all there in a single link. So excited, especially because so many students have been traveling lately to do awesome things.
Also, check out Genius Scan. It can insert images directly into OneNote (with a purchase). I really like it for getting student work up in front of the class in an anonymous way, especially when we run out of time and have to pick up the following day (darn those short periods!).
Secondly (and finally), I gave a presentation at the Fall Institute for the Global Teacher Fellowship about my journey to Australia. If you're interested, you can find it here.
Cheers!
Also, check out Genius Scan. It can insert images directly into OneNote (with a purchase). I really like it for getting student work up in front of the class in an anonymous way, especially when we run out of time and have to pick up the following day (darn those short periods!).
Secondly (and finally), I gave a presentation at the Fall Institute for the Global Teacher Fellowship about my journey to Australia. If you're interested, you can find it here.
Cheers!
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