Sine Of The Times

The Value of Team Teaching

2011-12-17T22:43:00.001-05:00

Teaching is generally a solitary process. We work on our own and develop strategies that work for us but we rarely get to see what other teachers do in their classrooms. After the experience I had with team teaching this fall, I would highly recommend taking some time to watch another teacher in action or if you can to find a way to teach, even if it's just one lesson, with another teacher.

This fall I had a large grade 9 applied level class. The administration decided to split the class. In the time between the decision to split the class and the actual split a number of students decided that the course was too difficult and they switched out. By the time the second teacher was assigned to the class there were only 26 students left on the list. We decided that we would try team teaching the course. In the past when I have heard talk about team teaching it was always two or more teachers who were teaching the same course. The team teaching meant that the they would plan together and do the same work in their respective classes. That's not what we had in mind. We had a small number of students so we decided that we would keep them in one room and teach them as one class with two teachers. We essentially created a math class with two teachers. What more could a math student ask for?

Throughout our time together I was often amazed at how much I was learning just by watching my teaching partner. He has a wide variety of classroom management techniques. It was great to see those techniques in action. I wouldn't say that my classroom management is weak but like most things in life I think I have room for improvement. Throughout the semester I was able to observe a bunch of techniques that I was familiar with, but for whatever reason wasn't using. I think in some cases I had heard about the techniques but had never seen them in action. Seeing how they actually work in practice made a huge difference. I'm hoping that some of those techniques become part of my regular routine.

As a side note, since midterm we've had a number of students who have not been performing well in the class. They don't have the work habits to be successful and aren't putting forth a solid effort. We tried working with these students for a few weeks to help put them in a situation where they could pass the course. Many of them chose not put forth the effort. We decided a short time ago to offer the students who were failing an opportunity to get a credit at a lower level (a locally developed credit). We have now split the class in two and we could possibly have every one of those students getting a grade 9 math credit. This could potentially be an interesting model for student success.

If you get a chance, give true team teaching a try.

Know Your Audience

2011-11-25T21:38:00.001-05:00

CC Licensed Photo by o5com

Over the past couple of years it has been a personal goal of mine to improve my presentation skills. I found it hard to improve because it was difficult to get honest feedback from participants. Often the feedback came from participants I knew who would say things like 'Good job!'. This is all fine and good, but it's not particularly helpful in finding ways of improving. I also feel that people who attended my sessions may not have enjoyed them but were perhaps too polite to say anything at all. So, how could I truly improve?

I decided to make a conscious effort to watch presentations that I attended with a critical eye. I wanted to be able to leave a presentation thinking not just that a presentation was good or that it could use some work. I wanted to pinpoint what made the presentation good and what types of improvements could be made.

Today we had a professional development session about autism. The entire school staff was present as were a large number of people involved in special education from around the district and the community. The speaker was extremely knowledgeable about the topic, was well prepared and stopped her presentation a number of times to answer questions specific to what was happening at the school. Unfortunately, most of her talk was so advanced that I, along with others who don't have a special education background, were completely lost. It was clear very early on that she did not know her audience and wasn't able to adapt on the fly.

What did I take away from the presentation? When presenting I need to find a way to get feedback from the participants to gauge where they are. This will allow me to adjust the presentation as I go. I guess in the classroom this is what we call the 'student voice'. If students already know the material, move on quickly. If it's over their head, slow right down.

What tricks or tools do you use for gauging your audience?

"We're Only Students"

2011-10-15T07:40:00.000-04:00

"We're Only Students" was as comment I heard from one of my students about a week ago. I was asking my class to do something that was a little challenging and out of frustration and a little in jest this was her comment. I almost went into the traditional 'It's not that hard once you get down to it' speech, but I paused for a second and thought to myself that the comment needed a little more attention. I'm not sure if I paused because I was offended by the comment or I thought my students should be offended or because I thought they needed to think better of themselves. Certainly, had I made a comment along the lines of "You won't get this. You're only students", I can almost guarantee I would have faced a backlash.

My response to the class was essentially the 'don't sell yourself short approach'. You're not ONLY students. You ARE students. You have endless opportunities ahead of you. We talked about how they were the future leaders of governments, corporations, industries, etc. We talked about competition and how in the not too distant future they would be competing for spots at universities and/or jobs and how they can't just settle for good enough. I mentioned that if they wanted to be as successful as they could they needed to work as hard as they could starting now. They needed to seek out challenges rather than trying to avoid them. We also talked about pursuing their passions. My message was if they didn't start now someone else was already getting a leg up.

In any case it turned out to be a ten minute discussion, which was much longer than I had anticipated. One of the comments I overheard was "Wow, a motivational talk in math. Who would have thought". I guess some of them took the message to heart though I'm sure some of them saw this as just a ten minute break.

The Frustration of Learning

2011-10-08T06:12:00.000-04:00

Recently I needed to replace the shingles on my roof. I decided to go with a steel roof instead of shingles, figuring I could do the work and save on the labour costs. I had been told by many people that putting up steel was easy and it didn't take long. This confirmed my original thought and I ordered the materials.

Now I should mention that I'm much more comfortable, and competent at, pounding a keyboard to move bits than pounding in nails with a hammer. I began by stripping the old shingles, fixing the bad spots in the roof and strapping it. This process alone had taken a lot longer than what most people said it should take to do the entire roof. I was feeling a little discouraged but I was determined to do the work properly and later discovered that most of the people I had spoken with had much simpler roofs than mine.

As I worked I learned a lot about roofing and a lot about myself. I think my best learning came from making mistakes. Doesn't all learning happen from making mistakes? I would make a mistake and then get really frustrated about it. This didn't help much since as I became frustrated I was more likely to make more mistakes. I recognized that many of my students likely get stuck in this cycle. Most of my frustration came from the fact that I was being slowed down. I just wanted to get the job done. I'm guessing that students are often in the same boat. They don't really care about the learning they just want to get the job, work, assignment, etc. done. After a while I realized that my frustration was counter productive. I decided that it would be much more productive to view my mistakes as learning opportunities. This small shift in mindset changed my entire outlook. No longer was this a project that had to be completed in a hurry. It was a project that I was going to do right and one that I could take pride in.

I think that frustration is an important part of learning. I need to let my students know that, and I need to work to ensure that they know it's a natural part of learning. I need to encourage them to work past the frustration to get to the reward side. I have a feeling that if they can get to the reward side once, getting there again will be easier.

No Office Day

2011-09-20T06:18:00.001-04:00

Last week the principal and two vice-principals at my school decided to participate in 'No Office Day'. The idea behind the day is that administrators decide to spend the day in classrooms rather than in their offices. Our administrative team modified the day a little so that they could each spend a period in some classes. I was really excited to see this happening. I think that too often administrators get caught up in the paperwork, emails and dealing with the problem students and as a result don't have the time to see some of the great things going on around the school.

It was great to see the principals in a classroom chatting with students, asking questions about the work or life in general. It allowed the students to see that the principals are more than just school figure heads. It showed that they cared about the work in the classroom. It reminded me of Angela Maiers' TED Talk titled You Matter. By spending some time in the classroom the principals showed that all students mattered to them.

At the end of the day I thanked each of the principals for stopping by and informed them that the students really enjoyed the visit. All three of them said that they enjoyed the day and were keen to do it again. I hope it becomes part of their regular routine.

Do It Yourself Document Camera

2011-05-30T10:14:00.000-04:00

A couple of weeks ago I wanted to share information with my class from a textbook that we don't use. I didn't want to photocopy and I thought why not try to use a document camera. Our school only has one document camera and given my organizational strategy, it was the night before I needed it. I hoped that the teachers who normally used the camera were not using it the next day but I started thinking about a plan B just in case. I thought if the document camera were in use I could set up a webcam and point it at the book and have the image appear on the screen. It turns out that the document camera was not in use so I didn't need to worry about plan B.

I still wanted to pursue plan B in case I ever needed a document camera again. So a week ago I took a webcam and an old lamp and put them together to form an inexpensive document camera.

Here's a rundown of how I did it.

I started with a lamp that was adjustable so that positioning could be flexible.

From there remove the nut holding in the guts of the light so that you can remove them, as shown in the picture below. You'll have to detach the socket from the wire. This can be done by loosening the two screws holding the wires in place.

Trim the wires. I didn't remove the wire entirely since I wanted to use it to tie the camera in place.

Now that the wires are loose you need to ensure that the lamp can't be plugged in, otherwise you could be in for a bit of a shock. You can either cut the wire somewhere, or snip off the prongs. I was unsure as to how long to make the wire so I cut off the prongs. Failure to prevent the lamp from being plugged in could result in serious harm or death. Consider the safety of those around you.

Use a rotary tool to cut out a hole large enough to fit the webcam cable through. Put on some safety goggles while doing this. It's not worth losing an eye over a webcam. You may want to file off any rough edges since the cable for the webcam will be passing through here.

Pass the cable for the webcam through the hole and use the lamp wires to tie the camera on. Pull everything nice and tight so that it doesn't move around. I found that the wire for my lamp held everything in place. You may have to tie the wire to the stand if the camera moves around too much. I thought about finding a way to permanently attach the camera into the lamp, but I'm not finding it necessary. Perhaps there's some way to glue plastic to metal? If you have any good ideas feel free to share them.

Once the camera was setup it was a question of finding software that would allow me to display the video. The software that comes with the webcam can work but it often won't allow you to show the video full screen. So here are a couple of options. On a Mac try the QuickTime Player (File->New Movie Recoding then make it full screen). I tried iChat first but soon realized that iChat always gives a mirror image. Not so good for text. For Windows try FSCamView. It's a very simple program that takes the input from your camera and displays it using the entire screen. The quality of your video may very depending on the quality of your camera. An HD webcam may be worth the extra expense ($50 vs. $25).

Lighting may also be an issue. If so you may wish to consider an LED light. You can get some that plug into the USB port of your computer like this one or this one, or battery operated units, or even a solar powered light.

As I was searching for software solutions I came across a post where someone used an overhead projector (OHP) as the stand. I'll have to dig around the school for an old OHP that doesn't work and try it out. On second thought, I bet nobody would notice if I used the OHP that collects dust in my room.

I really enjoyed this little DIY project. The most exciting part for me was saving a ton of money by doing a little bit of work. It may finally be time to build the wiimote interactive white board.

Open Doors vs. Closed Doors

2011-05-21T22:58:00.000-04:00

The other day I had the opportunity to work on a project with a colleague. We spent the morning working in the library at the school. We finished up the project a couple of minutes before lunch and as I headed back to my office I noticed that every classroom door I passed was closed. There was nothing special happening at the school that day, no particular reason the doors seemed to be closed. As I noticed this I wondered if most teachers in the school regularly teach with their doors closed. Then I began to wonder what, if anything, teaching with your door open or closed says about you as teacher? I starting to think this could be a could statistics project. Have students wander the halls daily, tallying the number of open doors vs. closed doors then have students perform so statistical analysis to see if there are any types of relationships between when doors are open versus when they are closed.

I personally teach with my door open. I do it for two reasons. The first is that I enjoy the flow of fresh air that results in having the door open. When I teach with my door closed it feels as though the air in the room becomes stale. I'm not sure if there is in fact any difference in the air quality but that's how it feels.

The second reason I teach with my door open is that I want my class to be an inviting place. I want teachers, administrators and even students to feel as though they can stop in at any time. I want teachers and administrators to stop by to see what we're up to or to share an interesting story or lesson. I want students to feel that they can stop by for extra help or to share their math struggles and successes. It's exciting when a senior student comes by for extra help or wants to share how well they did on a test or assignment when I'm teaching a junior class.

Do you, generally, teach with your door open or closed? How come?

Angry Parabolas

2011-05-04T11:11:00.001-04:00

As a way of connecting quadratic functions to something my students would be familiar with I decided that we should play a game. Not just any game. I wanted to focus on one of the most popular games available for mobile devices. So I hooked my phone up to a projector and fired up Angry Birds. Most, if not all, of my students were familiar with the game and couldn't believe that we were playing it in math. I heard comments such as "Are we really going to play this?", "Is this a joke?", "What's the catch?", "You're going to link this to math aren't you?". If nothing else they were interested in what the link to math was.

I had a couple of students come up and try the game. Once they had a chance to play I gave it a try and fired the bird high into the air so that it made a beautiful arch. I didn't hit a single obstacle and my students thought I was completely incompetent at the game. They sincerely offered suggestions about how I could improve. Eventually they realized that I had no intentions of hitting anything. I explained that the interesting part about the game is that it leaves behind a nice trail showing where the bird had been.

I took a screen shot and fired it up on the computer. We labelled the parabola and discussed some terminology. I didn't feel the need to write out any definitions. They seemed to get the ideas. It was funny to hear students helping each other by referring to the game in their explanations.

The game provided a good introduction to the unit and I wondered how I could take it further. My first thought was how cool would it be to have students write a simplified version of the game? They would learn the math, a whole ton of problem solving and some programming. I wasn't prepared to do this since I thought it would take up too much time. I may however consider using Sam Shah's technique of modifying a program in the future. Perhaps I could write the program and they could modify it so that it worked properly.

My second thought was to have students determine the equation that modelled the path of the bird. I created a Geogebra file with the image as the background and a grid laid on top of the image. I had students determine the equation at their seats first, then I had a student come up to board and move the sliders around to reveal the equation.You can find a link to the Geogebra file here.

I'd like to find a good way of determining the equation of the function that will allow the bird to hit a certain location and use this information to improve game play. I can see some technical challenges here. I'll have to think about this for next time.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

What If Math Were an Elective?

2011-04-17T07:12:00.000-04:00

Dan Meyer made a very simple statement on Twitter that really had me thinking. His statement was:

If I ask myself this question before bed, I don't sleep: "What if math were an elective?"

It turns out I was unable to sleep as well. The question had my mind going in many directions. The first of which was how would this change the teaching of math? My first reaction is that there would be a lot fewer students taking math. Currently in Ontario students are required to take 3 math courses. Many of them don't like math and won't take a minute more than they need to. My thinking was that the teaching would need to change to engage more students. We would have to show them how useful and exciting math can be. Get them to crave more. How do we do this? By providing them with engaging problems that they can relate to, which is easier said than done. It's a lot of work but it's something to work towards.

The other questions I had were: how would this affect students? Would they have enough basic mathematical knowledge to get through life? What effect, if any, would it have on their problem solving skills? How would this affect society as a whole? How do I as a math teacher ensure that I'm making a difference?

Unfortunately, I have a lot of questions and very few answers. I'm not discouraged by this since it's questions like these that allow us to continually improve. Perhaps we should all teach our courses as though they were electives. My guess is that students would get more out of them. I think I've just set a new goal for myself: teach as though my classes are electives.

What questions do you have? Do you have any suggestions for making math more meaningful?

Setting Personal Learning Goals

2011-04-07T21:04:00.000-04:00

One of the big things across the province right now is learning goals. A learning goal is what the students are expected to accomplish by the end of the class. The goal is explicit and is written in student friendly language. It should be posted somewhere at the beginning of the class and left visible throughout the class so that students can monitor how well they are meeting the goal throughout the period. This isn't anything new, the process has simply been formalized and reiterated.

Just as we have learning goals for students I think it only makes sense for teachers to have learning goals. These should be goals that are set periodically to help a teacher improve his or her learning. The learning could be in any area. Examples might include wanting to improve group work, learning a new method of presenting a lesson, learning a new technology, connecting with other teachers more regularly or anything else. These goals can help teachers guide their learning just as they do for students. I don't think it's necessary for a teacher to have a learning goal every day but it may be useful to set one for a week, a month, a semester or even a year depending on what the goal is and how it is to be achieved.

My goal at the beginning of the school year was to improve my presentation skills. I have presented to the staff at the school numerous times and each time I did I felt like the presentations became more effective. After each presentation I wanted to present again. I was hooked. I decided that I wanted to present at a number of conferences so that I could refine my skills in this area. My goal wasn't to improve my methods of delivering my classroom lessons, but I think I may have improved there as well.

I submitted proposals to present at two conferences early in the school year. The first was a virtual unconference. meaning that I was presenting virtually to an audience from around the globe. The biggest challenge here was trying to figure out how to present without really getting a read on the audience. The audience was small and the presentation was alright. After the presentation I reflected on how I could improve and looked forward to the next presentation.

My second presentation was at the ECOO conference in November. This is the premier educational technology conference in the province. One of the first things I thought of after my proposal was accepted is 'what am I doing presenting at this conference? What could I possibly offer these very savvy teachers?'. As the presentation drew nearer I realized that I was likely doing some things in my class that at least some of the participants were not aware of. Once the presentation was complete I wished that I could have another chance since there were a few things that I wanted to tweak right away. I reflected and made note of the things to improve.

The next two presentations were somewhat unexpected but since I was looking for opportunities I followed up by submitting proposals. One of the proposals was for the Eastern Ontario Staff Development Network. I presented two sessions on mobile learning. The room (although small) was full and we had to turn people away. The presentation went extremely well. I felt like I had finally mastered presenting. The feedback I received was very positive. I even had teachers asking where they could find the presentation since they couldn't attend.

My final presentation came at the request of an assistant superintendent who had visited my class and liked how I was using technology to engage my students. She asked if I could present to the district principals on 21st Century Learning. I decided what better way to show what I was doing in class than to bring along some students. The presentation was only 30 minutes but in that time we were able to show some of the tools that could be used and gave participants an opportunity to try some of them. For me the best part of the presentation was the student involvement. It was so much more powerful for the students to show what they had learned and for them to show the principals how to use the technology than to simply have me speaking. We all received a nice letter from the assistant superintendent expressing how well received the presentation was. This letter made us realize just how valuable the knowledge that each of us possess can be to others. There was some talk at the end of the session about presenting to school staff or even students. The students I had brought along with me were so excited about this possibility.

The presentations have been great learning experiences. I'm happy with my progress towards my goal. Unfortunately, I don't think it's a goal that I can ever check off any sort of list. There's always room for improvement. If you want to get excited about teaching and learning make sure that you see both sides. Be a part of both teaching and learning.

Hockey as a Metaphor for Learning

2011-03-03T20:56:00.002-05:00

As I played intramural hockey with some teachers and students this week I couldn't help but think how the learning process on the ice seemed to be the ideal way to learn. I wondered how that process could be transferred to the classroom.
The intramural hockey program was started by a teacher at the school five years ago as a way to improve the skill level of staff and students. The goal was to really develop a love of the game. The group of players is extremely diverse. There are boys and girls from grades 9 to 12 as well as teachers, all with varying abilities. When the program started I was a complete novice. I had never played hockey before and really wasn't a good skater. Some of my team mates (and opponent) play very high levels of competitive hockey.
The goal of the program is to help all of us become better players. The atmosphere is always very positive and all players are very supportive of their team mates as well as their opponents. The better players often setup the weaker players and provide suggestions and feedback. Your better opponents will often give you an opportunity to try a shot, a pass or a move, while your weaker opponents will work hard to prevent you from doing any of the above. As the weaker players try to outdo each other, their skills improve. Improvement also happens as the weak go up against the strong. The strong seem to provide just enough support, but will also challenge you so that things aren't too easy. Finally, the strong players will challenge each other so that they will improve as well.
Wouldn't it be great if our classrooms allowed for the type of collaboration that is happening on the ice. The strong students would be able to provide the weaker students not with an answer to a question, but just enough support so that the weaker students could be successful in understanding the content. The weaker students could work hard in an attempt to outdo each other, while the strong could continually challenge each other. Perhaps the most important part of this setup would be that the teacher is a learner as much as the students, learning and trying new things and benefiting from the knowledge and expertise of the students.

Wolfram Alpha As An Instructional Tool

2011-02-22T07:39:00.000-05:00

I have been very impressed with the power of Wolfram Alpha as a teaching tool. When I first started using it I would show something in class with it, refer to it and encourage students to check the site out on their own. Since I've discovered Wolfram Alpha Widgets, I've made more explicit use of this great tool.

Last week I was reviewing operations with fractions with a group of students who have struggled with fractions for a long time. Rather than just showing them the operations with fractions and giving them a worksheet, I quickly reviewed the operations and showed them this widget, which will not only perform the operations but will also show them the steps required to get to the answer. I sent them to the computer lab with a small number of questions and encouraged them to work on a problem and then to check it using Wolfram Alpha. My students loved the immediate feedback they received from Wolfram Alpha. One student came to class the next day so excited that Wolfram Alpha was able to help her get through her homework. It's a great tool that adds another dimension to the classroom.

In addition to being able to find widgets you can modify any widget that you find or create your own widgets. I'm beginning to experiment with how to create good widgets that help students gain a better understanding of the concepts I'm covering.

Exam Time

2011-01-29T22:39:00.000-05:00

Exam time is one of my favourite times of year, not because I enjoy administering a 30% final exam that frightens the heck out of students, but because I think exams bring out the best in some students.

The two or three weeks leading up to exams can be a very telling time for students. Many come to the realization that they won't pass or get the mark they were hoping for. Unfortunately, the vast majority of those students fail to do anything about the situation. This is not what makes exams a pleasant time. For me, the joy comes from that small percentage of students that decide that the last few weeks is the time to really make a difference. They're coming in for extra help at lunch and after school, they're studying on their own, they're catching up on work they've missed, they're helping their friends who chose not to get extra help. These are the students that have realized that they control their destiny. They have realized that it is not I who determines who passes or fails. I simply report the results. They have realized that they have more control over their learning and their marks than anyone else. They are ready for change.

This year was particularly exciting for me. I had record numbers of students in my room at lunch. Teachers and students would walk by my class and think that there was a class going on. I even had students from my upper year classes helping those in lower grades. The best part about whole experience was that all of the students who were in for extra help realized the relationship that exists between time spent on learning and how well they understand the material. Many of these students truly learned how to learn, which to me is far more important than mastering the content.

Local Collaboration

2010-12-30T23:10:00.003-05:00

Today I had the opportunity to work with a math teacher from another school. We spent the afternoon playing with Wolfram Alpha. Our goal was to play around with widgets to learn how we could use them to help students with their understanding of math concepts.

That's right two math geeks spent an afternoon collaborating during their vacation. It was great. We both learned a lot from each other and a lot that neither of us knew. I really enjoyed working with a teacher that I have a great deal of respect for, but never get to work with. How do we make this sort of thing happen more often? How can we harness our professional development time to make more connections like this? The last time I had an opportunity to collaborate with other teachers within my district was four years ago. I find it odd that I connect with teachers around the globe more often than I connect with teachers within my own district. Somehow we need to use our professional development time to allow for collaborative exploration of ideas that will advance education in all subject areas. After all, if we hope to teach our students to be 21st century learners, don't we need to become 21st century learners.

What does your school or district do to allow for collaborative professional development?

Also, if you're interested, here is a sample of what we were working on today. We were trying to get make it easy for students to use Wolfram Alpha as a computer algebra system. The widget allows users to enter an equation and then enter the inverse operation that would take them to the next step. The process can be repeated until the equation has been solved.

Looking For Wrong Answers

2010-12-05T23:05:00.000-05:00

I have, in the past asked students for wrong answers rather than right answers to my questions. When I've done it, it's usually because nobody knows the right answer or how to find it. So I ask for wrong answers to start the thinking process. When a student gives a wrong answer I ask why it's wrong and then we try to narrow down the correct answer from there.

I've been reading Dan Meyer's blog for a while now. He's a big supporter of asking for wrong answers but he doesn't just ask for them when nobody knows the answer. He asks for wrong answers all of the time. I tried the technique last week before asking for the correct answer. I was blown away by the quality of wrong answers I was getting. Here's the graph we looked at:

We had just calculated the slope of the blue to be -1. I added the red line to the graph and before asking what its slope could be I asked for what its slope can't be. I originally expected a lot of ridiculous answers. I was pleasantly surprised.

Here are some of the responses I received:

Can't be negative 1, since the slope is different from the blue line (nice segue into slopes of parallel lines)
Can't be zero since it's not a horizontal line
Can't be -1000 (a little silly but nailed down that our solution needed to be between -1 and 0)
Can't be undefined

The best part about these answers is that they were mostly from students who are afraid to answer questions for fear of being wrong. There was no more fear when I was asking for wrong answers. This tool just moved to the top shelf of the toolbox.

Blogging With Students

2010-11-29T22:47:00.000-05:00

My district has just begun a blogging pilot project. There are about 20 teachers involved ranging from elementary to secondary and across a wide variety of subject areas.

I wanted to get involved for a number of reasons. Perhaps the most important is that I strongly believe blogging is a skill that many of our students will need to use later in life.

The second, more immediate reason, is that I want my students to express in words what they understand and don't understand about the math they are doing. If they can think about what they don't understand, they have a better chance of being able to rectify the situation. I also want them to talk about how they learn best, what study habits they have and how they can improve.

On Thursday my students began writing their first blog post. I wanted to make sure that all of the technical details were taken care of so I booked out a lab and had them write a short post on how they planned to prepare for the upcoming test. Within a minute four of my students had explained that they don't actually study for tests, what should they write.

This blogging process may be more fruitful than I imagined. I never would have guessed that I would learn something about my students before they began writing. I can't wait to learn more.

Group Work

2010-11-12T06:58:00.000-05:00

I have never been a big fan of group work in a math class. I think it's mostly because I'm not good at coordinating it or making it effective.

I'm currently involved with coaching project where a group of teachers are helping each other become better at their practice. One of my goals through the project is to improve the way I use group work in my classes. Last week I assigned group work and it failed miserably.

The task I gave was a simple one. I gave students a distance vs. time graph which displayed two different bicycle trips. The students had to give a commentary of the bicycle trips. Without any sort of creativity or group work the assignment could have been completed in a period (or at the very least finished up for homework).

My colleague suggested that we spice up the assignment by having students create a performance that included a commentary on the bike trips. We left it open-ended on purpose to allow for a wide variety of submissions (live performance, videos, animated videos).

Generally speaking, the results were terrible and I reaffirmed the reasons why I tend not to give group work. I'm not blaming the failure on the students. I'm blaming myself for not being able to set things up effectively.

Here are some of the things that I noticed:

We need to work on presentation skills. I assumed that they had these already.
Most of the class time I gave was wasted.
Most of the groups had 1 or 2 people do all of the work, even though I offered suggestions on how to divide the work.
Technology problems were great excuses for not getting things done on time.
Rarely were all of the group members present, which became an excuse for not doing any work since the absent student always seemed to have the work.

All of these things made me realize that the time spent on the assignment didn't yield a good return on investment.

Here are some things that I've thought about for improving:

I need to be explicit in addressing presentation skills. Talk about it on a daily or weekly basis, model good presentation skills, talk about when I do things wrong, etc.
I have no idea how to address the issue of wasted class time.
I also have no idea how to address the fact that some students didn't pull their weight. I had them complete self-evaluations and evaluations of their group members but that didn't seem to help.
I need to lay some ground rules to let my class know that they need to have a backup plan in place. The failure of technology does not excuse you from having to present.
I need to teach them how to share files, etc. so that the absence on one student doesn't cripple the entire project.

I may have jumped into the deep end a little too quickly. Perhaps I should have started with a smaller task that could have been completed in class, or even a small portion of the class, and had students working in pairs instead of larger groups.

Please help! What do you do to make group work effective?

Learning From A Student Teacher

2010-10-11T21:57:00.001-04:00

I've had the great pleasure of working with a student teacher, Justine, for the past five weeks. She is completing a four month practicum at the school. In order to give Justine a diverse experience, the math department at my school decide that it would be best if she worked with a number of different teachers. She's working with three different teachers and I'm fortunate enough to be one of those teachers.

Justine spent the first couple of weeks observing in my grade 12 university bound math class. She helped students who had questions and taught the occasional lesson. As we approached the end of the first unit I asked her if she would be comfortable teaching Unit 2? I wanted her to plan and present the entire unit as if it were he own class. I remembered back to my own experience as a student teacher and how useful it was to be able to try new things and to feel like the class was my own.

So far Justine has taught for just over a week and her progression has been incredible. I'm amazed at how much a person is able to learn when they are fully submersed in a given subject or topic. I honestly believe that the best way to learn is by doing. This is certainly true for something like teaching but I think this can be generalized to learning in all areas. I'll have work at finding more hands-on and engaging activities for my students.

Watching somebody else teach has allowed me to think a lot about teaching. Why don't we as professionals do this sort of thing more often? I think by watching others we can gain so much insight about how others teach and the tools and tricks they use. Working with a student teacher has allowed me to think about the good things I do, the bad things I do and how I can improve. It's great to see new ideas, different approaches and unique methods. I guess sometimes I get bogged down with the routine of teaching and find that I don't often think about all of the mechanics. Having a student teacher has not only forced me to think about all of the little details but has also forced me to question why I do thing the way I do. As a result I'm rethinking some of my practices and hope to make some improvements.

If you haven't already guessed, I seeing learning with a student teacher to be a two-way street. It's an opportunity for the associate teacher to share some knowledge and experience while the student teacher has an opportunity to share creativity and to question existing practices. I can't wait for more learning this week.

New Game, New Tools

2010-09-26T22:22:00.000-04:00

Thanks to Twitter and Kristen Fouss, I came across this blog post last spring. The post describes how to play Trasketball, a fun way to review before a math test. I filed the game away under "Use At First Opportunity". It seemed like the game could be fun and yet still provide some good learning opportunities.

Last week my grade 9 class was ready to review for their first test. What a great opportunity to try Trasketball. As I was setting up the presentation with the questions I couldn't help but think that it didn't seem like there were a lot of questions and I was worried that my students wouldn't get enough practice. I didn't let that sway me and I went ahead anyway.

I had a couple of reasons to involve another class. I ended up with this class about a week ago as a result of the splitting of another class. I thought why not get the other half of the original class in on the game as well. Although we could have all packed into one classroom and played the game it would have been much too crowded.

The second reason for involving another class is that I'm currently part of a team at the school exploring the use of video conferencing. What better way to start with video conferencing than with the class next door, with students who would be comfortable with the teacher and the other students in the class. If you're interested in the technical details I'll document them at the end of the post.

Photo by Maik Pereira

We divided the classes into groups of four (each person got a letter M, A, T or H) and numbered the groups in both classes. The group ones, although in different classes, were working as a team to get the most points. The same was true for the other pairings.

The game went like this: I posted the question which showed up in both classrooms. Everyone worked on the question and could get help from their group. My colleague next door, Kate, choose a random letter out of the word MATH. The person in the group with that letter came to show Kate or me their work. If the work was right they received a point and could shoot for either two points from the two-point line or move back and shoot for 3 points. The cameras in the classrooms were pointed at the basket looking towards the shooter, a backboard cam of sorts. Students from both classes were able to watch the shooters from both classes. The score was tallied on the screen so that everyone could follow along.

How did it go? I was quite pleased. Although I didn't think there were enough questions, every student did every question. I was amazed that everyone was engaged for the entire period. Although I assigned fewer questions, I would say that the overall productivity was much greater than I had I simply given work out of the textbook. I was also very pleased to see that my students' math skills were far superior to their basketball skills.

Did we need a video link to the class next door? Absolutely not. Did it help keep students engaged? Probably not that much. Why do it then? I'd like to eventually bring some guest speakers into the class using video conferencing. These guest speakers might talk about how they use math in their jobs and hopefully answer questions from the class. Before trying with a guest speaker I thought I'd try within the school. Thanks Kate for being such a good sport about the whole process.

This is more for my future reference than anything, but if you're interested in the technical details read on. We setup and tested the equipment the night before. Despite this we still ended up with an audio hiccup in the morning. We hooked up a simple web-cam, a set of speakers and a projector to the computer in each room. Since our district has licenses for Adobe Connect, that's what we used. One teacher was signed in as the host, the other as a presenter. I loaded the slide show into Connect and had it displayed on the right side of the screen. Both videos were shown on the left half of the screen. The score was shown on a Connect Whiteboard at the bottom right under the slide show. I ended up moving windows around a lot so that the questions were large enough. Next time I would spend a little more time setting up the layout so that I was happy with it for the entire presentation. We recorded most of the presentation so that we could learn from it.

Just before we started I sent an email inviting the principal and the two vice-principals to join us either in person or virtually. I was happy to see that all three were able to join us virtually at some point throughout the presentation.

Notes for next time:

Get the groups cheering for each other, shoot baskets in specific order so that it's easier for them to remember who they're working with.
The answer key should go to both teachers instead of being displayed on the screen to stop groups from cheating (not that it happened).
Find a way to minimize the delay in video

Why Go To Class?

2010-07-28T23:36:00.000-04:00

The Virtual Conference on Soft Skills

Like most (if not all) math teachers I constantly hear from many students about how they hate math. Hearing this time and again is quite frustrating and I find myself wondering how can I change these attitudes. I haven't found the magic bullet but I seem to have found a few things that may help.

Last semester I taught a number of students who hated math and were very open about it. Not only would these students tell me they hated math but they would also tell me that they loved being in my math class. This didn't make any sense to me so I asked them how they could hate math and yet love math class. The response I received was that class was fun and they didn't want to miss it. When I reminded these students about how much they hated math they simply repeated how much they enjoyed the class. This got me thinking. How could someone who hates math so much like coming to class so much? I probably should have worked a little harder to get meaningful feedback about what these students liked about the class. In any case, I tried to think about all of the things that I might do to make a class enjoyable. Here's a short list.

Take an interest in students: Be interested in what they are doing both in and out of school. Many students will be excited that their teacher cares about what they do.

Use humour: Many students sit in a desk all day bored to what seems like near death. Try to spice things up a bit by adding some humour. A small joke here or a silly word problem there can make a big difference.

Create a safe environment: Let students know that it's alright to take risks. Let them know that all answers are acceptable and that it's alright to be wrong. Try to build up their confidence so that they are more willing to take risks, answer questions in and out of class and help others. Students should know that they are in an environment where they should feel comfortable and respectful of each other.

Have fun: This one is the most important to me. I mean this in a couple of ways. Fist, be excited about what you do. If students see an excited or crazy teacher every day hopefully some of that excitement for math will rub off on them and they can start spreading the excitement. The second way to have fun is by...well...just plain having fun. Organize a class-wide spirit day. See how many other students in the school your students can convince to participate. The spirit days can be math based but certainly don't have to be. Organize a potluck breakfast or lunch or get students to bring in a couple of bucks and buy some pizza. Have students turn a Christmas carol into a math song. The sky is the limit. These are the things students will remember.

These are some of the reasons that students may want to come to my class. I'm not saying that these things will turn students into lovers of mathematics. But it seems to get them to come. They seem to enjoy themselves and hopefully they will learn a few things along the way. The next time I hear of a student who hates math but enjoys my class I'll find out what makes it enjoyable and share my findings.

What's Wrong With Free Software

2010-06-06T22:10:00.000-04:00

What's wrong with free software for educational uses? I'm not talking about free software with trial versions or free software that's full of spy-ware. I'm talking about quality open source software such as Linux, Open Office, Moodle, Gimp, Audacity, Blender, Scribus and Geogebra to name a few. There are literally hundreds, if not thousands, of open source titles that we could be using in education. The use of open source software would allow schools, districts and governments who fund the purchase of software to save what seems like a ridiculous amount of money; money that could be better spent on hardware or anything else for that matter. The savings aren't just a one time occurrence either. Not only do you save on the initial purchase you also save on future upgrades.

Another good example of high quality, free software is Google Apps for Education. Although Google Apps isn't open source it is free, ad-free, easy to use and could still save schools a truck load of money. The nice thing about Google Apps is that it's a cloud based service which means no installation, no maintenance and it's accessible wherever there's an internet connection.

One of the biggest advantages of using free software is that students are not limited to access at school. They can use the tools at home or anywhere else they choose to work. Doesn't it make sense to provide students with the tools they need to learn when they want and where they want?

Many people I've talked to about this issue say that it's important to teach students using the industry standard (i.e. MS Office) so they will already be familiar with the software once they get out into the workforce. This to me seems like a poor excuse. I strongly believe that we should be teaching students life-long skills that are transferable. I'm confident that when I teach students to use a spreadsheet in one program they will be able to figure out to use all other spreadsheet programs. The other issue I have with this line of reasoning is that the industry standard today may not be the industry standard tomorrow. In the current climate of rapid technological growth, open formats and the open web I'm not entirely sure there is an industry standard anymore.

Many IT departments seem very reluctant to move in this direction and those that do are willing to adopt open source software seem to be providing it as a duplicate service alongside a paid service. I realize that there are issues involved moving from the 'industry standard' to something else but those issues can be worked out and surely it's worth working out those issues given how much money is at stake.

iTunes Song Sales and Exponential Functions

2010-05-13T21:35:00.000-04:00

Earlier in the year I was looking for some information about using iPods in the classroom. At the same time I was teaching the exponential functions unit in my grade 12 course. One of the pages I came across was this iTunes Song Sales graph. Despite my excitement for iPods I stopped what I was doing and integrated the data I had found into my class. My thinking was that this is data that students can relate to and hopefully it would keep them interested and help them see how math is used in the 'real world'.

Here's what I had my students do:

a) Describe the shape of the curve.
b) Why does it look the way it does?
c) Model it with a function.
d) Can we expect this trend to continue?
e) If not what can Apple do to increase its revenue. This question led to some interesting discussion about what Apple should be doing in the future (including selling books) before the iPad was announced.

There's not much to it but it just gets students thinking about where exponential functions appear in real life and who might care about them. Next time I might get students to do some research to find their own 'real life' exponential situation.

One of the interesting tangents of this lesson arose when a student asked "Why would anyone buy music when you can just download it for free?". We had a good discussion about why it's important to compensate content creators for the enjoyment of their work. We also talked about Creative Commons and how some creators choose to release their products for free and encourage others to use it or even change it. I love days when I end up teaching more than just math.

Quadratic Functions With Video

2010-05-04T21:59:00.000-04:00

There are some lessons that I know students are just going to hate. Often times they'll put up with it but I feel like I'm doing them a disservice. I want to find a way to make these lessons more engaging.

One such topic is having student determine the function that models some form of quadratic data. I find that many students get lost in the wording of such questions and get bogged down by the details. I thought I would introduce a video to see if it helped with their understanding. I showed my class the video below and asked them to determine the function that models the height of the ball at any given time.

I played the video on the interactive white board and had a student come up to the board and put dots on the board to show the location of the ball. Once the video was finished he drew a smooth curve through the points. My question to the class was how do we determine the function that models the situation? I was amazed how engaged the students were. I received a ton of answers: We need to find the vertex. We need a set of axes. We need the 'a' value.

The video and the one question I asked produced the buy-in I was after. It was great. The nice thing about this lesson is that later in the unit when students struggled and asked for help they would say things like "Oh right, this is what we did with the video isn't it?".

As an added bonus we were able to practice a couple of times just by shifting axes around, which also reinforced the idea that the 'a' value was the same because we were talking about the same curve.

I realize that the problem is still somewhat contrived. Ideally I'd like to have a situation where students feel compelled to solve the problem and end up using the math to do it. Nobody really wants to know the function that models the path of the ball, but it was a situation they could relate to and was a step in the right direction.

Back-Channel Chat During Test

2010-04-24T22:48:00.000-04:00

About a week and a half ago I read Royan's post about Test Taking with the Backchannel. My first reaction was "Is this guy crazy? You can't do that on a test". As I read the post I started to think that it was good for Royan to try this but it's not something I would ever do. By the end of the week I was planning how I could incorporate a back-channel for one of my tests. I just kept thinking about the amount of information that I would be able to gather from my students based on the questions they asked and the answers they gave (assessment for learning). It seemed like the right thing to do. Coincidentally, a few days before the test, one of my students asked if we (as a class) could do the test together. She was joking but she was very pleased to hear about the chat.

Here are the logistics. Not everyone in my class has a hand-held device and the school doesn't have wireless. Using the back-channel in my room was out of the question. I booked a computer lab and we wrote the test in there. Not ideal but it worked. I thought about using Twitter and had we done the test in the classroom that's probably what we would have done. Since we were at the computers I created a Moodle chat within our course and that's what we used for the back-channel.

The day before the test I informed my class that they would be able to (and were encouraged to) use the chat for their test. We modelled asking good questions and providing good answers (guiding but not giving the answer).

My predictions of how the test would go, which are probably no surprise:
a) My top students would do a lot of question answering and may ask the occasional small question.
b) The middle of the class would ask lots of questions and occasionally answer a question or two.
c) The bottom of my class wouldn't contribute much to the chat.

There were a couple of surprises. The first was one of my top students who had good conceptual understanding but couldn't quite put the nuts and bolts together. Not only did she provide some great help to get students started but she also answered in a way that was guiding but not too helpful. In fact, overall I would stay this was true of most answers given.

The second surprise I had was that some of my mid-mark students provided much more assistance than I had anticipated. Again the help was good help. I was very pleased.

It's unfortunate that prediction c) was in fact bang on. Unfortunate because those students are the ones that have the most to gain from this type of test. I would hope that if we did this enough they would start to see the value and buy in.

Would I do this again? Definitely. In fact, I think I would try to have all applied level tests this way. The students in this class are the types of students that don't spend a lot of time thinking about the questions. When doing a test on their own, if they don't know how to start they give up. This doesn't allow me to see what they really know. If they can get a hand starting, at least I can see how much they actually know instead of seeing a blank answer. Don't get me wrong. I probably wouldn't use this strategy for all classes. I'm not sure how I would feel about using a back-channel in a grade 12 university bound class. I'm not sure how cooperative students would be given the competition for scholarships and entrance to university.

I would love to hear your comments.

How to Motivate the Unmotivated?

2010-04-19T22:30:00.000-04:00

A colleague and I had the chance last week to introduce grade 8 students to Moodle. The purpose of the visit was to provide students with a quick introduction to the high school's online learning environment so that they would feel a little more comfortable when they arrived in grade 9.We gave a quick tour of some of the courses that would be useful to all students, such as the Library and Student Services courses.

Once the tour was finished I led students through an interactive unit price activity based on Dan Meyer's idea. We were working on a very tight time line so we worked through the activity as a group. The students seemed very engaged in the discussion. They were participating and asking great questions. I outsourced the unit conversions to different groups (about 6 or 7 students each doing the same unit conversion). I told students how to use Google to do the conversion. Later they converted to a unit rate.

We did this presentation a total of three times at two different schools. I felt, as you might expect, that each presentation was better as the day went on. I also found that participation in the outsourcing seemed to drop. In fact in the last presentation an entire group didn't do their calculations. I was absolutely floored. Here was an interesting (or so I thought) math activity that was accessible to all and there were a ton of students who chose not to participate. I don't think it was because they couldn't. I think it was more that they wouldn't.

The above may not be fair to the last group that we presented to so in their defense it was the end of the day. Perhaps they were thinking 'Who's this strange guy teaching us?' or 'this isn't for marks so I don't need to do this'. In any case I left at the end of the day wondering what I did wrong? How could I fix it for next time so that everyone would participate? Then I started thinking about my own classes. Why is it that some students in my classes choose not to participate or do the work? How can I motivate students that don't seem to be motivated?

I know that there are no easy answers to any of the questions but I've realized that the questions need some pondering. My goal over the next while is to work at finding ways to motivate and engage students who aren't typically motivated or engaged. If you have any ideas please share them.