Friday, March 13, 2015

I Hate the Pyramid

As a teacher with a strong background in math and physics, I have always hated - nay, LOATHED the pyramid. You may know of it as the magic triangle, or sometimes as a "formula circle." I hate them all.

If you have never come across such a device, it is simply a way of determining how to solve for any of three variables in an equation where two of the variables are multiplied to give the third value. In the first pyramid above, if you wanted to predict volume (V) and were given mass (m) and density (d), you would use your thumb to cover up the V in the pyramid (what you want to predict). Doing so leaves m over d - indicating you calculate mass divided by density.

Want to determine mass? Cover the m, and you see that you would multiply density and volume, since they are side-by-side.

Is it easy? Yes. And that's why many students (and teachers) gravitate toward using them. My issue, though, is that their usage relies on memorization (you have to get the pyramid right before you can use it), and it removes algebra from the process. Sure, a pyramid works very well for "rearranging" an equation like V = IxR, but what about SA = πrs + πr^2? And don't even get me started on the complete lack of unit analysis...

When I was actively teaching concepts like Ohm's Law (in the circle, above), I never mentioned the pyramid, and made all my students rearrange the equations using opposite operations. I've always insisted that they practice the "hard" way, to better prepare them for the day they need to solve more complex equations. I've even been known to "boo" loudly (with a smile!) if a pyramid ever showed up on a student's work.

But now I'm letting the students choose how they learn concepts like Ohm's Law, and even though the majority of the resources I provide (including the textbook) show no sign of the pyramid, lo and behold, the dang things are showing up EVERYWHERE.

Because I'm emphasizing that each student learns his or her own way, I find I can't - and I don't want to - fault the students for using them. I don't encourage the use of pyramids - I won't even mention pyramids in a mini-lesson, and if a student asked me how to solve for a variable, I'll walk them through using opposite operations. But if the students have independently found a method that allows them to master the learning goal, then more power to them! Right?

Incidents like these are forcing me to step back and really focus on the actual learning goals presented to my students. I am asking them to accurately predict electrical resistance when given voltage and current, NOT asking them to correctly rearrange an equation. In that sense, it doesn't matter how they do it - they could even use trial and error - as long as they eventually do.

I'm not 100% sure this is the correct way to proceed, and I'm finding the algebra a tough thing to let go of. I feel my students might be gaining in the short term (by accomplishing the learning goal), but losing in the long term (less rigorous practice). What do you think? 

Tuesday, March 10, 2015

Classroom Makeover - Part 1

I'm fortunate to have been offered the chance to makeover my classroom, thanks to some funding from our school board and my administrator. With the shift from lecture-based teaching to student-centered learning in my classes, different spaces within the room were needed in order to better accommodate how different students learn.

I wasn't sure how to change things up, so I turned to the #BYOTchat crew and asked the experts. They had tonnes of great ideas, from different levels (standing areas vs. sitting areas vs. floor areas), movable furniture (modular desks), and creative spaces (white boards, projection screens for students to connect to). Click on that link above to see the archive of the chat if you are also looking for ideas.

The Original Room:


It's a science lab, with built-in lab benches on all four sides of the room (the front bench becomes the teacher's desk/bench). 

  • It's a big room (30 students easily fit with room to move about);
  • There are already outlets galore;
  • There is a working sink at the back of the room;
  • There is more storage than I need;
  • There is a counter along the back of the room (under the cabinets) where I already have four desktop computers.
  • The built-in lab benches cannot be moved or removed (since they have old water & gas lines in them);
  • The benches limit the creation of "spaces" - it's hard to get much into the corners;
  • This will remain a science lab, so flammable items must be kept to a minimum.

I'm by no means an interior designer, but together with the students, we came up with some ideas.

Drum roll, please!

After an unexpectedly early IKEA delivery yesterday, here is what the room looks like now:
"After" - part 1
Groups of students can continue to work at the large tables, which are now better positioned to get power. Two smaller table areas exist (one in the centre of the room, one at the very front of the room) for students to work in a group of two or on their own in a more focused setting.

The lab bench along the left side of the picture - which was previously unsuable - is now a standing/high chair area, ideal for students working with laptops. We took the doors off the cupboards so students won't bang their knees. The chairs can be moved to any of the lab benches as the students see fit, and I'm hoping to encourage some students to stand, while they work, on a regular basis.

The area at the centre-back is the most popular area at the moment - an area rug with bean bag chairs, cushions (more to come) and a coffee table for more casual working. I'll be picking up more cushions next week to add to the area. I spent some time marking there during my prep, and it was pretty cozy! There's a rule of no shoes on the carpet; I'll have to remember to pick up a carpet sweeper or small vacuum to keep it clean. Everything in this area is portable, so if we do a lab, it can easily be removed.

Still to come:

In addition to more cushions, I'll be picking up some small lamps to tone the room down a bit and offer an alternative to the harsh fluorescent lighting. I should have those once we're back from the March Break.

In time, all but maybe one or two of the large tables will disappear, replaced by modular tables that better suit the space. Students will be able to re-configure the desks as they see fit, depending on what they're working on.

One of the side corkboards will become a large white board, pretty much exclusively for student use.

The sides of the lab benches (brown in the photos) will be painted brighter colours, and our senior art class will paint a science-themed mural across the front of the room. I'm totally loving JMSS's science mural right now.

So far, the students seem to like the change. The room feels more spacious now, too, and it is much easier to move from group to group. It will be interesting to see how the students choose to use the different spaces, and how they customize spaces to suit their needs. Part 2 still to come!

Sunday, March 8, 2015


Tell me, class, what do we know about pioneers? 
(which pioneers? ANY pioneers!

They had it rough! They had to start pretty much everything from scratch. They might not have had all the tools they needed to get the job done, but they improvised, and they made do. They might not have had the knowledge they needed to succeed, but they learned - often the hard way - and they overcame their difficulties! Was being a pioneer easy? No way! But the amount of knowledge and skills they learned and mastered was immense, and in the end they were better off for their efforts!!

Over the past few weeks, we've been trying new things with our devices (both new-to-us as a class and new-to-us as a school) and there has been a lot of frustration. When things weren't working, when the connection was flaky, when webpages wouldn't load, when we didn't know what to click, I kept having to tell my students: we are pioneers.

Our journey has not been easy...

With the receipt of a class set of tablets from ORION, suddenly everyone was connected. Our plans seemed fairly simple: get the students connected with Google accounts so we could do things like share photos through Picasa, use Google Drive efficiently, and blog about our Genius Hour progress using Blogspot. 

But there was something I kept forgetting about the difference between our "simple" plans and reality:

It took at least a day to get everyone registered on their own tablet and connected to the school network (which was originally blocking all the unknown devices).

It took at least a day of troubleshooting to get everyone successfully on Gmail, as many of my students had never had an email account.

It took three days to get Blogger/blogspot unblocked at our school.

It took a week between the school board then telling me that students shouldn't have their own Google accounts (they should have board Google accounts), providing me with the new account names and passwords, and our students actually being able to log in.

This was when most of the frustration set in: issues with initially logging in, classroom icons not appearing, mail icons taking you to external apps instead of back to Gmail, me not being able to see Blogger (but my students could?), browsers being already unsupported for GAFE... many students started giving up. When they got bored, the games came out, and it took a lot of convincing to get people back on track and actually trying things.

"Break it," I'd tell them. "Break Google. Click on anything you can find and figure out what it does."

But then things slowly started to change.

One pioneer changed his profile picture, and many others followed suit. Yay!

Two of our pioneers discovered that typing in "" will take you to where students could access my class, which got around us not being able to get to the Classroom icon. Hoorah!
Using the tablets during Genius Hour
A silly trial assignment posted within the Classroom environment had students helping each other out with how to "complete" it. Sigh of relief!
Using the tablets to connect to online resources to help learn.

We discovered that (default for Blogger blogs) is still blocked, but (which takes you to the same blog) is unblocked. Phew!

Blogging with the tablets 
I played too - customized the header for our Google Classroom, and tried sending emails to my students through the board accounts. There was lots of public trial and error on my part, as well as me continually walking around and asking "hey - how'd you do that??" 

Our class' cover page in Google Classroom

Now we move forward...

Now that we are all connected, we are moving forward at a great pace. Students are consistently using their tablets to connect to our online resources, create blogs for their projects, and reach collaborative documents through our virtual classroom.

Getting everything set up was a painful process, but the students now demonstrate great familiarity with the tablets, and are starting to create amazing things online (which I hope to be able to share soon). They demonstrated resilience and ingenuity, and they started turning to each other for help, which was wonderful to see. 

While we're done pioneering for the time being, I'm hoping the students will be a little more likely to take risks with new technology in the future - a skill that is very much transferable as they become 21st Century learners.

Sunday, March 1, 2015

A Global Survey - Electricity Usage

I've been doing this BYOD thing for a year and a half now, and I'm much more comfortable working with students and their myriad of devices than I was when I started. I'll be the first to admit, though, that the bulk of what we do with the devices is access online resources that support the textbook and/or labs that we do in class.
Working on learning content.
Using an online circuit builder
In terms of the ever-present (in my mind, anyway) SAMR scale, it's pretty low. Sure, some of the resources we access are a step up from textbooks (like an interactive circuits website, or multiple choice quizzes that give you hints and immediate feedback), but I haven't really been harnessing the power of connecting through the Internet. Until now.

During the first semester, my colleagues and I created a grade 9 assignment on electricity production and consumption around the world. At its simplest, it could be a research assignment. At it's most complex, it could be a chance for students to reach out to other students around the world and personally compare their two countries.

For my class, I decided to break the project into four parts, extending it beyond our electricity unit and into our astronomy unit. The links will take you to each part of the project:
  • Part A: Research (including a global survey) on electricity production and consumption differences between countries;
  • Part B: Taking action by creating original resources (of their choice) based on what they've learned in Part A;
  • Part C: Research on light pollution around the world, and how this links back to the use (waste?) of electricity;
  • Part D: Citizen science as students collect their own data on light pollution in their area, and contribute to the Globe at Night project

Let me just say here that projects of this scale thrill me, but also scare the pants off me. This feels absolutely huge, and almost insurmountable. There are a lot of unknowns out there, but my #oneword this year was JUMP (as in, jump into trying new things, jump outside of my comfort zone), so let's go big!

After introducing the first part of the project, we discussed - as a class - what types of questions we could ask people (from any country) in order to gauge how much electricity they use. The students quickly agreed that "How much electricity do you use?" was too vague a question (though it led very nicely into a discussion of how electricity usage is measured and paid for).

Students worked on white boards in their table groups to brainstorm questions that could possibly go on a global survey. After a bit of time, they copied their best questions (as decided by the group) onto paper and handed it in.

The next day, I gave the table groups a copy of all the questions that had been submitted, and asked them to - again as a group - narrow the 36 questions down to the best ten that would go on the survey. That evening, I tallied up the votes, and created our class survey:

And then we tweeted. And sent the survey to friends on Facebook. And got our parents to send it to their friends. And tweeted some more.

After about a week of data collecting, we have 400 responses from 36 countries - and growing!

The students love seeing the responses roll in - every class starts with a glance at the spreadsheet on the board to see how many responses have come in since the previous class. Our box of pins is becoming depleted as we add more and more of them to our map.

We're not looking at the results so much right now (though the students are quite interested to see who doesn't have running water, or if anyone has left their email address to connect with us), but the discussion of countries has been amazing!
Our map, as of a few days ago. More pins have been added since!

Students crowd around the map in class trying to figure out where some of these countries are (Saint Vincent and the Grenadines??), looking up the capitals (where the pin goes), talking a bit about history and what makes a country independent (is Hong Kong the same as China? Are Wales, Scotland and England all the same country? Which country does Greenland belong to?). If a new country pops up on the spreadsheet during class, the students are quick to point it out. And celebrate!

We will keep pushing for data for one more week, and then delve into it for the projects. I'm looking forward to discussions about what the data means, when to exclude "dirty data," and where bias creeps in (and there's definitely a lot of bias in this survey!). We are also sharing the data with @jaccalder's math class who will help us by making charts and graphs demonstrating trends and correlations.

But for now, the science can wait. The students are getting a tremendous sense of what it means to connect with others around the world, and are opening their eyes to what all (and who all) is out there on the other side of the planet.

I am so grateful to every member of my extended PLN who has shared the survey with their friends, colleagues and their respective PLNs. I'm greatly looking forward to seeing what the students do with this new knowledge and how far they can push themselves to connect in return!

Saturday, February 7, 2015

BYOD in Science

When I started BYOD in a couple of my classes last year, I purposely chose two math classes. To me, the math curriculum was easier to break down into concrete learning goals, and to find resources that were tailored pretty much exactly to those learning goals.

But I struggled with doing the same in a science class. The learning goals are more nebulous - less a matter of being able to do a certain skill, and more a matter of demonstrating an understanding of a concept.

So I held off on changing over my science classes until this year. In first semester, I started experimenting with different formats in my Physics class, but this semester, I am entirely converting my grade 9 science class over to independent learning. And so far, I'm really liking it.

I'm playing with a new look to the resource page(s) my students turn to once they arrive in class. The way I had previously arranged the resources was functional, but not pretty or easy to navigate. The new format will hopefully make it easier for students to find the resources they want. I'm hoping it also encourages students to jump back and forth between resources, rather than approach them in a linear fashion.

Our new format.

Friday, during our 90-minute period, was our first real chance to try out the new format. There was initially a bit of confusion: students found it hard to choose what to start with. They were encouraged to master the learning goals however they liked, but losing the linearity of the original format led to worry about starting off on the wrong foot. 

Once the students actually chose their first activity, though, they jumped right in. It was a wonderfully busy and noisy class, with students all over the place!

Some students chose to work on learning the content first, through traditional methods (mini-note from me or the textbook), or using online resources.

Some students started to learn by playing (however before they could play with the Van der Graaf generator, they had to explain to me how it worked!):

What happens if the person holding the Van der Graaf generator
touches the person holding the metal tap?

 Some chose to start with a hands-on lab, experimenting with static electricity:
Bringing a charged ebonite rod near a stream of water.
The fabric attracts the rod after being rubbed together - what does that mean?

The ebonite rod repels the other ebonite rod after both were
rubbed with the same material - what does that mean?

Collaborating on the lab
On the whole, I think the students appreciated being able to start learning in their own way. Throughout the class I was peppered with questions to help students understand either what was happening in front of them during the lab, or to clarify what they were reading in the textbook. Just as in math, I found that a lot of the conversation revolved around what the students were figuring out together, albeit in different ways.

I'm looking forward to seeing how they progress with the rest of the unit, and whether the greater flexibility in how they learn the material helps them better understand the underlying concepts.

Sunday, January 18, 2015


I absolutely loved the frankness and honesty in @stoodle's blog post on Exorcising Teacher Demons@MrOrr_geek took this one step further and started #10GoodThings - a list of, well, ten good things that happened to him and his classes in 2014, to remind him (and others) that we are indeed fighting the good fight, and doing great things.

So here is my list. They are mostly BYOD/tech related because that seems to be my focus of late. I'm going to nominate fellow #rdsb21c bloggers and bloggers-to-be (@hpennie, @bauerE9, @henschsci, @MrJamesEady) to complete the challenge as well.

Here are my #10GoodThings from 2014

1. 2014 was the first year I started using Twitter to really connect with other teachers. Not just to say hi, but to collaborate on projects and have my students create something along with other students across Ontario. @PatGrew's Ratio Project and @MrOrr_geek's Pumpkin Time Bomb really stand out, as well as @s_m077's Skype chat between grade 3s and grade 12s.


2. I had great support from my principal and vice-principals on BYOD. Every step of the way, from applying for grants, to taking time to figure things out in class, to letting my students run around the school taking pictures of slopes, they've allowed me to experiment and grow. I'm very appreciative of that (and of them!).

3. 2014 was a banner year for attending conferences and non-board PD! Off the top of my head, I was able to connect face-to-face with colleagues at functions by Ontario Principals Council, STAO, STAO Congress, OTRK12, 2 EdCamps, and Manitoulin IGNITEd. It's tough being out of the classroom, but great to get out and discover new ideas.

4. Along with attending conferences, I also had my first opportunities to share my BYOD experiences and help other teachers get started with online pursuits.

5. I finally had the chance to teach true e-learning in the summer with an online Physics course. I had been wanting the opportunity to really test out D2L's vLE waters for some time.

6. I started overhearing good things - unexpected things - from my math & physics students that I'd never heard before. Some would tell each other that this was their favourite class, some would jump in to help a struggling student learn, many would say that they liked the pace, tone, and informality of our class. One student even told me that she likes ending the day with math because she goes home happy. I'm not pretending all students are in the same boat, but teaching-wise, I think I might be on the right track...

7. I became much more of a risk-taker in 2014, teaching a little more like a PIRATE both in how I deliver information as well as building up the excitement in my classes. My students are STILL talking about the mysterious build-up to our Hallowe'en activity.

8. In 2014, I learned to appreciate blogging a lot more, both as a reflection practice for myself, as well as taking the time to read other blogs (through #comcon and #blogamonth) and participate in conversations by commenting on others' blogs.

9. In the latter half of the year, our school's digital infrastructure was improved immensely, giving students and teachers much better connectivity. Slow connections and inconsistency in actually staying connected were perhaps my biggest frustrations while introducing tech into the classroom, and I'm happy to say it is so much better now. Now if I can just convince the powers-that-be to unblock youtube...

10. My husband (@christheij) started adopting and embracing technology in his own ways in his music classes in 2014. It was a really good year of developing ideas alongside him for our respective classes, and growing together as teachers. He has been a huge source of support, and he helped keep me sane throughout a crazy year.

What are YOUR #10GoodThings??

Saturday, January 10, 2015

Watching Students Struggle

Coming back from winter break, I found myself pressed for time in my grade 9 math class. We have just three weeks before the end of the semester, in which I need to squeeze one more unit (linear equations - arguably one of the most important concepts the grade 9s will take with them as they pursue higher levels of math), a unit test, a practice test for EQAO (don't get me started), the EQAO test itself (lasting two days) and the summative project.

We haven't had a snow day yet, but if we do lose a day because of one, this it going to be cutting things awfully close.

My instinct returning from winter break was to rush the students through the learning goals of this last unit - cover as much ground as possible - in what little time we have left. But I knew, too, that particularly with these linear equations, there needed to be a deeper level of understanding. 

I forced myself to slow down. Instead of assigning many small, quick learning checks, I assigned a a larger activity, forcing the students to also slow down. Forcing them to take their time and really understand what it was they were doing. Forcing them to not get the correct answer right away, but instead have to tweak and place in check what they knew as they went. 

The students found the leap to using equations to represent linear functions to be very hard. On Monday and Tuesday, I heard many students complaining about how much they "hate" this unit, and how difficult they find it. This has really been their first challenging unit in this course, and this is the first time all semester I have heard my students speak like this. It was disheartening.

To make matters worse (in their eyes), the activity I assigned them is in Desmos... which many of them haven't used before and were very hesitant about trying.

We had some pep talks in class, we discussed the value of being challenged and growth mindset ("This is hard!" they'd say; "Good! That means you're learning!" I'd say), and we talked about how the only way to get through this was to TRY things and to make mistakes - to take the time to play with Desmos and play with the equations. That things this challenging don't come immediately. To be honest, though, I didn't think they believed me.

Things started to change, however, on Wednesday of this week. Students started coming into class saying "I did it!!" They told me about how it took them one-and-a-half, or two, or two-and-a-half hours the night before, but they figured out Desmos and they got their initials done. They told me about how they understood this whole linear equation thing. And they told me all this with huge smiles. 

They started telling others in class that it wasn't that hard, but that they, too, HAD to play with it. They started helping each other, and creating things in Desmos together. Students would come up to me with their tablet to ask how to place a line or "cut" a line, and then figure it out on their own and literally cheer with joy. No longer afraid, they jumped into the rest of the learning goals of the unit, and are picking them up much faster than I would have expected.

Within a week, our class went from knowing nothing about linear equations, to being able to graph them (from an idea AND from an equation), figuring out the equation from a given graph, creating tables of values from equations and from graphs, and determining the equations of horizontal and vertical lines. I'm super proud of them for digging in deep and overcoming the urge to give up. I think they are also quite proud of themselves.

As teachers, we naturally want what's best for the students. In the beginning of the week, it was tough for me to stand by, watch my students struggle, and listen to them complain without jumping in to help. There were many times I really had to bite my tongue in order to do nothing but encourage them.

But taking the time to let them struggle paid off with huge dividends in the end. Something I definitely have to keep in mind the next time we tackle something new and difficult in class.