Happy pi day!

My students went hard! 

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.

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!"

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...

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!

Day 9: Melbourne High School and Albert Park College

Yesterday I visited Steve Draper at Melbourne High School and Jane Coyle at Albert Park College.

The daily schedule at Melbourne High School is more similar to what my own school runs: seven 43 minute periods every day. The school is an all-boys school and is selective entry, so students take an exam to get in. Most enter in year 9, but the occasional student enters in the latter years. There seems to be a strong emphasis on marks and scores from the get-go, and Steve told me that sometimes it can be frustrating when the students are more focused on the grade they get than learning the material. I actually think that the Victorian scheme of assessing students puts a stronger emphasis on underdstanding that the NYS Regents- the year 11 course is basically a dry run for year 12 and it's relatively low stress. 

I observed a physics 12 class on electric power and transformers. Steve did some awesome demos including melting nails and solder. The students were really engaged by this. Then I observed a year 11 prac (lab), during which the students were looking at the I vs. V curve for a globe (light bulb). They were using a different experimental setup than I employ for this sort of activity: breadboards, variable resistors, and a single 9V battery. I usually do it via the Modeling-esque version of batteries and bulbs, which has the students build a simple circuit and then add additional batteries. I can't get the same fine scale for really small voltages, but in terms of setup and data collection it goes faster. It was really interesting to see the same activity I do executed a different way. Finally, I observed a year 12 maths methods course (by the way, NEVER call it math here). It was about binomial distributions, and their teacher was pushing them well past the content that they're likely to see on the state test and into confidence intervals. Neat stuff.

After my visit Steve and I went for coffee with Dan O'Keefe. We had an interesting discussion about the nature of education and how schools can best prepare students. Steve made an interesting point about how the current educational system is basically a remnant of a different time and we're headed for a vastly different future. He recently attended an edutech conference (http://www.edutech.net.au/) and mentioned that the skills employers most want out of graduates are adaptability and creative problem solving abilities. I agree wholeheartedly and think that it's high time that traditional education be re-imagined.

Speaking of which, this leads me to my visit with Jane Coyle at Albert Park College. Albert Park is a state-run school and is not selective entry. It is a very new school- the current year 11 class is the first cohort to go through. The school has such a strong reputastion that people have begun moving to the area just so that their children can attend it. This is actually a bit of a problem, as the space is not quite big enough for the extra classes that have been added. It puts a strain on the staff and the building.

The facilities are really nice: large open spaces and small tables for group work. All the students bring their own device to class every day, so there is no need to have permanent desktops around the room. The school has an excellent set of Vernier equipment which it puts to good use with lots of student-centered activities. Jane also uses a flipped style, but it's not just straight videos. Her students are also expected to do reading assignments outside of class, but Jane stressed that the reading quizzes she administerers via Google Forms are just for comprehension/completion, not to check to see if they fully understand everything. That role is saved for clas time. Periods are 60 minutes and students generally meet 4 periods a week: two singles and a double.

The Year 11 double period I observed on a Friday afternoon was remarkably focused and the students had a lot of energy. They worked Newton's second law problems in small groups and then worked on an Atwood prac. It was nice that they all had electronic access to the writeup sheet and instructions so they could start their reports right then and there (Google Sites).

There are 7 girls taking year 11 physics out of a total of 31. There were 4 in the class I observed, and I asked them if they were going to continue on next year. Two of them said they will definitely take year 12 physics. The third said maybe- she seems to struggle a bit with the content. The fourth is trying to decide between physics or a pre-university course that she can earn university credit for taking.

Jane and I had a great discussion about why so few females take physics in Australia. This was actually the focus of her Masters work, so she was very well informed! Her research, which involved surveying female students in maths methods courses, found that:

• The female students analyze prerequisites for university and know what they need to take. Then they focus on those courses. Since physics isn't a prerequisite for any university courses of stud, they generally dont take it [though this limits their options if they don't end up pursuing medicine]
• A strong indicator of whether or not female students will study physics is a connection with someone who knows science- usually a family member
• Seeing another female who has studied science or teaches science also increases the liklihood that they will study physics
• Finally, exposure to a career that employs physics- especially an altruistic career or one that involves helping people or society such as Engineers Without Borders- increases the liklihood that girls will study physics

Jane works very hard to be visible and get to know the younger students in an effort to grow the school's physics enrollment. It is already the highest of the co-educational schools I visited, but she sees a lot of room for improvement. Our research interests are very similar and we had a terrific discussion.

The day ended with an interesting lecture at Melbourne University and then a farewell dinner with Dan, Colin, Jane, Barbara, Neil, and Paul Cuthbert. It has been a fantastic trip and my mind is reeling from everything I've seen- can't wait to implement some of these great ideas next fall! I'd like to formally thank all of the teachers who invited me into their schools, answered my endless questions, and made me feel right at home. I'd also like to recognize that none of this would have been possible without the support of the Rural School and Community Trust- thank you for making this journey happen! 

Day 8: Ivanhoe Girls' Grammar School and Billanook College

Today I visited two Pauls: Paul Fitz-Gerald at Ivanhoe Girls' Grammar School (IGSS) and Paul Fielding at Billanook College. A common thread between the two, aside from a mild geographical proximity, was the Space Camp they run in the summer. Students from both schools spend an entire week during their holiday break learning about aerodynamics and flight first hand. They go for a flight in a glider and also in a plane, launch model rockets, and design their own gliders. The camp looks fascinating- wish I could get all of my students together for a week in the summer to do something like this!

Before I forget, Paul Fielding showed me a really neat camera called a Key Cam that uses a micro SD card and is affordable enough to be attached to a rocket. The footage is remarkably good and the unit is affordable enough that it's not the end of the world if it doesn't survive the landing.

I observed a year 10 class at IGSS that was studying inertia. Well, actually a pair of them running simultaneously with different stations, and the students moved back and forth between the rooms depending on which experiment they were working on. The teachers (Paul and Dina) had planned this out ahead of time and it seemed to go really smoothly. The activities were engaging and were presented in the form of real-world scenarios- pushing a heavy shopping cart, collisions between cars, etc. 

Many teachers here, like as Dina, Giselle, and Paul Fielding, were actually engineers first before becoming teachers. The undergraduate degree doesn't matter too much- the teachers either got a one-year postgraduate diploma in teaching or a masters afterward. The diploma is being phased out and the only option for new teachers will be the masters route.

Billanook College feels like it's far removed from the city, but it just happens to have a large campus (with its own stream) and be situated next to a vineyard. It's an independent school, but it doesn't have an entrance exam, so it gets a wide economic cross-section of students. It has strong support services for students with learning disabilities and also for international students. One faculty member told me that while the campus is nice, their strength is in the programs they offer. The school has a day with five 65-minute periods on a 2 week rotation.

I observed a year 11 class that ran like a well-oiled machine. The students were running motion labs using inclined planes and trolleys (carts). They collected data via the Pasco Spark Systems. The only hiccup, which was really minor, was the transfer of the graphs to the students' Google Docs writeups. They have to take a picture with their device (iPads for years 7-9, BYOD after that (laptop and phone/tablet) and then insert it into google docs via drive. It worked fine and the students had an excellent handle on using the devices after having them for so long. Side note: Paul Fitz-Gerald's school had an interesting way to let the students know the expectations for how iPads were to be used during the lesson:

Too few students at my school use devices in this manner, so it's not really applicable, but I liked the idea.

There was 1 female student out of two classes that total roughly 22 students. Paul Fielding told me that the state average is 20% female for year 11's, and 10% for year 12 courses.

After school Paul took me to the top of Mount Dandenong, which was spectacular. We then had dinner with his wife, a linguist, and the school's career counselor. It was fascinating to hear their perspectives.