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.

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.

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?

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.