Thursday, December 30, 2010

Local Collaboration

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.

Sunday, December 5, 2010

Looking For Wrong Answers

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.

Monday, November 29, 2010

Blogging With Students

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.

Friday, November 12, 2010

Group Work

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?

Monday, October 11, 2010

Learning From A Student Teacher

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.

Sunday, September 26, 2010

New Game, New Tools

 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

Wednesday, July 28, 2010

Why Go To Class?

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.

Sunday, June 6, 2010

What's Wrong With Free Software

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.

Thursday, May 13, 2010

iTunes Song Sales and Exponential Functions

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.

Tuesday, May 4, 2010

Quadratic Functions With Video

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.

Saturday, April 24, 2010

Back-Channel Chat During Test

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.

Monday, April 19, 2010

How to Motivate the Unmotivated?

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.

Tuesday, April 13, 2010

TEDxOntario Ed

I had the opportunity last week to view TEDxOntarioEd. For those of you not familiar with TED talks the idea is that speakers who are passionate about a subject will give a talk based on the theme 'ideas worth spreading'. TEDxOntarioEd was focused on education and how we can make changes for the better.

As I watched the presentations I kept thinking about what a great idea this was. Here I was sitting at home watching some top notch speakers share their ideas about improving education. I truly was in awe. I couldn't help but wonder why every teacher in the province wasn't watching. The event was extremely well organized, full of great ideas, entertaining and downright fun.

For me one of the best parts of the night was the back channel. There were so many great comments posted on Twitter to @TEDxOntarioEd that I felt there really was a sense of community among the participants. Although I was at home it felt as if I was surrounded by other educators. The only thing I would change for next time would be to create a satellite location so that the experience could be shared with others in person as well as on Twitter. Hopefully a satellite location would also allow teachers who wouldn't normally be a part of an event like this to participate.

I would like to thank all of the organizers for their time and effort. Great job. I look forward to the next one!

Saturday, April 10, 2010

iPods as Learning Tools

Apple sent me two iPod touches and a MacBook to test out at school for the period of 1 month. Unfortunately, the one month period included spring break as well as Easter break. That meant that one month turned into about twelve school days. We made the best of the time we had with the devices.

One of the first things that people ask when they find out I want to use iPods in class is 'What apps will you use?'. I get a kick out of that question because the iPod is about so much more than just apps. The iPods that I had were not connected to the Internet (no wi-fi at school) but I think that's where the power of these mobile devices really lies. I think it totally transforms the classroom. Rather than having a class of 1 teacher and 30 students, mobile devices make it so that you have 31 students (including the teacher), 1 facilitator (the teacher) and access to a seemingly unlimited number of subject experts for all subject areas. iPods and mobile devices allow the classroom and learning to be opened up beyond the four walls of the physical classroom. How many times do we get asked questions we don't know the answers to? In a math class you might be talking about finding the volume of a barrel of oil. A student may ask what the current price is. This can suddenly become a lesson in research. Have students find the cost of oil. Why are they getting different answers? Who's right? Why? Instead of shrugging the question off as not important to the lesson, geometry students can learn skills that are critical for all 21st century learners.

In addition to accessing subject experts or current information, iPods can be used as a device to consume and even create content. The obvious use here is podcasts. This is where I focused my time with the iPods we had. I created podcasts that would help students prepare for the provincial literacy test (here's an example). I took the print material that we had, which wasn't very appealing to high school students, and turned it into a video podcast that they could watch anytime, anywhere. Students listened to the podcasts in class as they were preparing for the test. If they had to write a news report they could listen to the podcast about news reports. They could pause it as they worked, start over when they were done to ensure that included all parts of the news report or just listen to it on the bus as a way to remind them what needed to be included. There are tons of podcasts out there that would suit just about any subject area. As an extension to this students could create podcasts to show their understanding of the content or to help others understand.

It doesn't just have to be podcasts that students consume. Imagine the school newspaper or course notes available on the iPod. Imagine a school created app that students could use to access important information and documents relevant to their school. This is not new! There are schools doing it. In fact the app could be developed by students in the computer science (CS) class. Heck why not teach the CS students how to use the iPhone SDK so they can learn CS and produce content that can be shared around the globe?

Now...onto the apps. I didn't use a ton of apps but found some that would be extremely beneficial.

Math Games: I downloaded a ton of math games. When students were finished their work they could work at improving their number sense and problem solving skills.

Graphing Calculators: I tried a bunch of them. The ease of use and resolution is far superior to the TI-83.

Stanza: A simple ebook reader. Takes away the stigma that reading books isn't cool. Nobody knows you're reading a book. This is an easy way to engage reluctant readers (especially boys). They get hooked on the device.

International Children's Digital Library: A collection of children's stories from around the world. Great for classes studying children's literature.

Story Kit: Allows the user to read a story and then modify the story. You can also start your own story from scratch an include your pictures. Once you're done you can share your stories with others.

Quick Office: Open and edit office documents on a variety of hand helds.

Voice Memo: Good for creating audio podcasts right on the iPod.

Google Earth: Great for geography classes

This is just a very small sample of the apps that could be used in classes. For a more detailed list check out

I really believe that the iPod can change the way we teach. It is a cost effective way to ensure that our students become true 21st century learners. It's extremely engaging and is the ultimate tool for differentiated instruction. I truly believe that all schools (if not all students) should have mobile devices in order to help students get the most out of their learning.

Tuesday, April 6, 2010

How Not To Teach Statistics

I had to teach statistics to my unmotivated grade 11 students. I thought I'd try to make things interesting. Textbook questions for a unit like this are typically boring and unrealistic. I decided that as a class we would create a survey that was interesting to teens, post the survey online, have everyone share the link then analyze the results. To me this was a good way to make the material interesting and relevant and was also a way to teach some digital media skills.

We created a Google form that would house the questions. The survey answers we're automatically dumped into a spreadsheet, where in theory they could easily be analyzed. I shared the link to the survey with my students through Moodle and they could share it using their preferred methods.

The trouble with data sets is that they are rarely very clean. Many of the questions generated by students in the class used a scale (poor, good, very good, excellent). This data was clean and would provide good graphing opportunities. I also wanted students to have numerical data. How else can you find measures of central tendency or measures of spread?  We did create some questions where the answer should have been numerical (How many hours of television do you watch per week?). The trouble is that many of the survey participants either didn't enter a number or entered numbers that were unrealistic. After the first day of releasing the survey we had 16 responses, six of which were unusable. I decided to scrap the project and we headed back to the textbook. We discussed the problems with surveys so that we could all learn from the situation.

I'll have to rethink this activity for next time. Ideally, we'd have a Wii in class and could generate a ton of data for a given game: scores, time played, levels reached, points/second, player biographics, etc. We could then analyze that data. Add a Wii to the wish list.

Wednesday, March 31, 2010


While listening to the radio last night there were a ton of stories about the hike in long-term interest rates here in Canada. These stories generated a lot of buzz around mortgages. Many experts were saying that homeowners should lock their variable rate mortgages into a fixed rate mortgages.

One of these brokers caught my attention. He suggested sticking with a variable rate but making the payments as if you were on a five year fixed mortgage. This would pay down principal a lot faster. Here's the math...He said that on a $300 000 mortgage this method would result in a savings of $8000/year. My first thought was 'I wonder if that means that on a $150 000 mortgage your savings would be $4000'. It was a very simple question as I was driving, but I quickly realized how useful it could be when talking about exponential functions and to see how much students have understood. It's also a nice way to show students how the math they're learning relates to everyday life.

The question could simply be: Would a mortgage of $150 000 (or $600 000) result in a savings of $4000 (or $16 000)? Why or why not?

Monday, March 29, 2010

Cluttered Desk or Something to Ponder?

I've been teaching for a decade now. Today I had a moment when I realized just how much things have changed in that decade. This is a picture of how my desk may have looked on a given day:

This is what my desk looked like by lunchtime today:

I did have to group everything so that it fit into the shot, otherwise there would have been a whole lot more clutter in the picture. I notice two things about these pictures.
  1. My desk looked a whole lot tidier back then. I hate to imagine what this picture will look like 10 years from now.
  2. The tools I use have changed dramatically.
Point #2 had me thinking about the tools I will use in the future. Just to be clear I still use most of the tools I used 10 years ago and today's display was unusual. However, I do see myself using more and more tools. My hope is that by expanding my toolbox I can  make math more interesting and engaging for students. I think this is working since one my students made a comment along the lines of "I usually hate math, but this is a lot of fun" as she was leaving today. I also hope that I can provide my students with skills that will help them in the 21st century. I want them to be able to blog, edit images, participate in online communities, etc. If we don't teach them these skills who will?

What tools do you think teachers will be using in the future? What 21st century skills (if any) should we be teaching students in addition to the curriculum?

Thursday, March 25, 2010

Let Them Create

I asked my students to create a public service announcement for math class. They had the choice of doing an audio or video file. Much to my surprise all of them chose to do a video. I was a bit nervous about having students create videos in a math class. I was concerned that their videos would be entertaining but wouldn't have a lot of mathematical content. I set some guidelines for them and much to my amazement they are using the math in their videos. In fact many of them are doing more calculations and including more math than I had expected.

My students are just loving the project. It's such a departure from what they're use to. It nice to see them coming to class eager to do math and work on their videos. I'm definitely a convert and will have to do more projects like this.

Monday, March 22, 2010

iPods in Class?

I am extremely excited about using the iPod Touch in class. I think they can be an incredible learning tool to all students in all subject areas. I see iPods as a way to bring the outside world into our classes at a very reasonable price. I have been trying to convince my school and district of the value of these devices, but as of yet I haven't had much luck. I managed to get a couple of iPod Touches from Apple on loan for a period of one month. I'm hoping that in that month I can show students, teachers, administrators and parents the value of mobile devices in the classroom.The best thing about these devices is that we don't have to buy an entire class set. Many students are coming to class with this technology. Let's provide some to the students that don't have access and put the ones that are already in students' pockets to good use.

I have two routes that I am going to pursue.

a) In my low-end math class we've used water conservation as a context for the math that we've studied in this unit. I've decided that I'm going to assess the unit by having students produce a public service announcement (PSA) in either audio or video format. The PSA will have to contain some mathematics to show that they have understood the content. Students creating audio PSAs will use the iPods to do it while students doing the video PSAs will use video cameras. I know that I could book a computer lab to do this but it seems like such a waste given that the different groups will be at different stages at different times.

b) I teach in a province that has a province-wide literacy test for all grade 10 students. I will prepare audio/video tutorials that can be loaded onto the iPods to help students prepare for the test. The students can use this material as they prepare for the test. They can pause it, rewind it (do you still call it rewinding on an MP3 player?) or listen to it again. The iPods can then be handed out to students who need some remediation. I think that the real bonus here is that the delivery method will be engaging.

If you have any other ideas about how to use iPods in a classroom please feel free to share.

Tuesday, March 9, 2010

A New Take on Slope

I haven't taught the basics of slope for a few years. Rather than use the tried and true method of drawing graphs on the board and finding their slopes I thought I'd take pictures around the school of lines and we would find the slope of those lines. It was a very small difference but the images seemed to capture the attention of many of my students. Many of them commented on where the picture was taken (Are those the stairs at the North end of the school?), some were even curious when I took the pictures.

After a quick demo of slope using Geogebra I started with just an image an asked how we could find the slope of a slanted microphone. Someone quickly pointed out that we needed a grid. We overlaid the picture with a grid and counted the squares for the rise and the run. On the next image we introduced a coordinate system and the formula for slope so that we didn't have to count the squares. The end result was something like this.

I wanted students to find the slope of the roof for this church. Somebody asked if they had to do both sides. We discussed how they thought the results from both sides would be related. They were then asked to confirm their guesses.

Overall most students were tuned in. I think there were a few that thought I was babbling and wanted me to get to the traditional lesson. It make take a few lessons like this for them to realize that this is the lesson.

Wednesday, March 3, 2010


I had a Smartboard installed in my class a week ago. Before I get into too much detail I should mention that I've been using a Smartboard on wheels for the past month so it's not as though last week's addition totally changed they way that I do business. I must say that what I like most about having an interactive white-board is having a projector permanently mounted in my classroom. Now if I want to show a quick video or do a quick demonstration I just turn on the projector and I'm in business. Before it was such as hassle (I could go on in depth about the hassle but will spare you the details) that I often decided that the gain wasn't worth the effort.

I think that the interactive white-board is a very neat idea but I'm not entirely sure it's good bang for the buck. Yes my students love coming up to the board to use it. Will the novelty wear off? I'm guessing probably. Yes it's great to be able to capture everything I've done in my lesson, export it as a PDF and upload it to Moodle for students to view. Is it worth the expense? Time will tell.

There are other companies that make interactive white-boards and devices that turn a regular white-board into an interactive white-board.  Mimio is one of those companies. For the price of my Smartboard (and the installation) we could have purchased almost three Mimio systems. Don't get me wrong I do like having a Smartboard but I feel guilty that my colleagues don't have one. I have extended an open invitation to my colleagues to kick me out of my room so that they can use the technology with their classes.

 As a side note we had four teachers in from a neighbouring district to see how our school is using Smartboards and Moodle. They are looking at using both technologies and wanted to learn from our experience. They were very curious about the details of Moodle and to learn all of the ways it could be used. It's great to be able to collaborate like this. Thanks for coming guys.

Thursday, February 25, 2010

Math Journals in Groups

I've never been a really big fan of using journals in math class. I think my dislike stems from the fact that the few times I've tried it I always had a large percentage of students saying "I can't do this" or "I know how to do the work but I can't explain it". As a result of the students being frustrated I too became frustrated and gave up.

I recently attended a differentiated instruction session where I was reminded about math journals. This time I wanted to make them work. I decided that I would train my students to be good journal writers. I figured that on past attempts I just gave up too early. I also decided that I would use journals not only to let me know what students understood but also to let students understand what they needed to work on. I know that this sounds obvious but in the past I would hand back journals, students would look at their mark and put them in their book never to look at (or think about) them again.

This time students were to write a summary of right angle trigonometry. They needed to tell me when it was used and how to use it. I collected the the journals and graded them immediately. I handed back the work to the weaker students and withheld the work of the stronger students. The stronger students became my subject experts. I paired strong students with weak students. The strong students had to explain the concepts to the weaker students. I then posted four problems to work on. The experts were to walk the weaker students through the first problem. The rest of the problems were worked on individually, but the students could check with each other to see how things were going. The next day I had all students redo the journal article.

How did it go? I think most students seemed to enjoy the experience. They didn't enjoy the journaling at first but seemed to enjoy the collaborative approach. When students rewrote their articles there was far less complaining. I even had some students ask if we could do more of this type of work.

Tuesday, February 23, 2010

Math 2.0 Meet

Over the past three or four months I've felt as though I wanted to do more in my math classes. I wanted some new strategies to engage my students. I came across a Math 2.o meet offered through the Community of Expertise in Educational Technology (CEET). The conference was a week long event where teachers shared their ideas and resources relating to teaching and technology. Every day of the week I looked forward to seeing what had been contributed and what thinking about what I would be able to contribute. The conference allows guests. Just choose to login in as a guest to see what you missed. I think I need to do more of this type of networking and collaborating. I also think it would be a valuable tool for many teachers who aren't even aware of these possibilities. It would be great if all of the teachers in my district could be a part of an evolving online community.

If this type of learning interests you sign up for CEET's Literacy 2.0 Meet or their Cell Phones in the Classroom meet.