PBL for Engagement and Empowerment in the Mathematics Classroom

Yes, I am a huge LOTR fan but can’t help feeling a little like Sam Gamgee and stating, here at the end of all things, “Well, I’m back.”  It has been a very stressful year for many reasons, one of which was dealing with the new curriculum in our Geometry class.  May zoomed by so fast that I didn’t even have time to think about what I could post.  Here are a few comments.

We definitely wrote and planned for too many problems.  Unfortunately we did not get to the end of the curriculum which had volume and surface area of three dimensional solids.  We feel OK omitting this mostly because in general, students have seen this material before.  It was much more important to include a solid foundation of Trigonometry and exposure to arcs and angles in circles.

We have resigned ourselves to the fact that some students really didn’t like this method of teaching.  We did course evaluations and some students were pretty frank about their feelings on how this class was run.  However, the good thing is that almost for every student who didn’t like it, there were 2 or more that did.  Also, even the students who didn’t “like” it, wrote that they came to appreciate the teaching method.

I also had had my class video recorded one day in order for me to reflect on my teaching. I was amazed at how much work was getting done without my knowledge.  But I was also amazed at how much of other behaviors goes on in my class without my knowledge.  I highly recommend having a class videotaped at least once in your career.

I also would like to reflect on how important attitude is to the success of the student in this course.  I know I’ve said this before in my blog, but I think that once a student has buy-in and investment into the process, it is truly an amazing thing to experience and watch.  However, that can be three months for most students, 6 months for others, ( for a smaller minority and for a few, it just doesn’t happen. 

I’ll use the example of a student, Bob, who has not been able to take down his barrier of pessimism and bad attitude.  Just last week, at one of our last classes of the year, Bob could not control his anger towards the class and stormed out of the room when the bell rang.  I am sure that this anger was not necessarily directed at me, but most obviously directed at himself for not being able to accept his own responsibility for the lack of work put into this course.  However, on the final problem set, I happened to observe Bob describing to some members of his group how to find the area of a sector of a circle, without prior knowledge of a formula.  I was very proud and smiled at him quietly.  He smiled back.

Another student, I’ll call Sam, had real reservations about a team final exam.  She said in class one day,”I just feel badly for my group because I don’t think there’s much I can contribute”.  She seriously did not see what she might bring to a group discussion of a problem.  However, afterwards, while I was looking at the course evaluations, I could tell Sam’s by her handwriting and noted that she said “I was surprised at how much I had to add to the discussion.”  I believe this was a turning point for her, and may have been a place where her confidence in her abilities has changed for the better and for good.

There’s so much more that I could say and my hope is to somehow organize my thoughts from this blog so that I can form chapters in a book.  Hopefully, I can affect more than just the classrooms at my own school, but possibly model what is possible at any other school.  I would like to thank my two colleagues who embarked on this challenge this year with me.  They were continually an inspiration and without them, this would not have been possible.  Also, I owe a debt of gratitude to the head of my school for allowing us the freedom to “think outside the box” with our curriculum .  The autonomy and respect she afforded us and the faith she had in our abilities really was a support throughout this year.

And so I come to the end of this blog (at least for this year), I hope if anyone is reading this that they leave me comments so that I can give further information that might be helpful.  Thanks for reading!!

The constant hum of November is over and the bright rush of the holiday season of December are upon us at my school. The group of geometry teachers that I work with are all settled in for their “long winter’s nap”. Well, OK, not really, but that’s something of what it feels like. We have passed the “three month” period of teaching with problem-based learning and it seems that most students, but not all, have caught the fever. One of my colleagues, whose class was still clearly retaining a negative feeling toward the class and how it was taught decided to do something drastic one day. She went into class, after a day before where the students had actually been rude to each other, and asked each student to go around the table and say one positive thing about this course. Was she taking a risk? Most definitely, but for this teacher it paid off. The students all had different things to say:

“I like that it’s OK to be wrong in this class.”

“I like that we can share our ideas and don’t have to have the homework all right every day”

“I like that my opinion matters”

These were just some of the comments that she shared with me. I saw a weight lift from my colleague when she told me this and I feel like it was a turning point not only for the students, but possibly for her as well. I have the utmost respect for the two teachers who had faith in my ideas and theories around PBL and who were brave enough to take a chance on this curriculum with me. They both are pioneers in this method at our school and it has taken a toll on them this semester. But, no matter how down they got about the classes, they still believed that what they are doing is in the best interest of the students. We clearly have a strong team of dedicated teachers working on this project and I feel very lucky to have them.

So, as the kids say in the car, “Are we there yet?”. Have things settled and we won’t have issues with students for the rest of the year? Are we at our best in our teaching with PBL? Do we sit and rest on our laurels? Well, first we take a break and relax. Then we meet at the beginning of the new year and start again.