What If Math Were an Elective?

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

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

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

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

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

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

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.