Category: In the classroom

PBL facilitation from a Yogi’s Perspective

This fall I was asked to do a small workshop for my department about PBL since almost everyone will be teaching a course that has some component of problem-based learning involved in it. I think for some department members it was somewhat daunting, but I had so much respect for those who were trying something new. It takes a lot of courage to step out of your comfort zone – especially in your own classroom.

I don’t think my professor, Carol Rodgers, would mind me borrowing her yoga metaphor and adapting it to PBL. I use it often when talking to teachers who are nervous about falling short of their ideal classroom situation or teaching behaviors. I think this can happen often, especially when learning best practices for a new technique like facilitating PBL. There are so many things to remember to try to practice at your best. Be cognizant of how much time you are talking, try to scaffold instead of tell, encourage student to student interaction, turn the questions back onto the students, etc. It really can be a bit overwhelming to expect yourself to live up to the ideal PBL facilitator.

However, it is at these times that I turn to Carol’s yoga metaphor. She says that in the practice of yoga there are all of these ideal poses that you are supposed to be able to attain. You strive to get your arms, legs and back in just the right position, just the right breathing rhythm, just the right posture. But in reality, that’s what you’re really doing – just trying. The ideal is this goal that you’re aiming for. Just like our ideal classroom. I go in everyday with the picture in my head of what I would want to happen – have the students construct the knowledge as a social community without hierarchy in the authority where everyone’s voice is heard. Does that happen for me every day? Heck no. I move the conversation in that direction, I do everything in my power for that to happen, but sometimes those poses just don’t come. Maybe I just wasn’t flexible enough that day, or maybe the students weren’t flexible enough, maybe we didn’t warm up enough, or the breathing wasn’t right. It just wan’t meant to be. I have exercises to help me attain the goal and I get closer with experience. That’s all I can hope for.

So I tell my colleagues who are just starting out – give yourself a break, be happy for the days you do a nearly perfect downward facing dog, but be kind to yourself on the days when you just fall on your butt from tree pose. We are all just trying to reach that ideal, and we keep it in mind all the time.

Asking “True Questions”

The school year is upon us and it is with great excitement that I look toward this new school year. I just sent off the first draft of my dissertation proposal, we just got our edited version of geometry text back from the printers, and our newly edited trigonometry text is hot off the presses as well. It always seems like there is a fresh energy surrounding the beginning of the school year that emanates from the students and is just contagious – even after twenty years of teaching.

I recently read a great essay entitled “Questioning Authority” by Charles Bingham in his book about relational authority (SUNY Press). In it, he discusses Gadamer’s view on questioning as an act that “breaks open the being of the object” and “revealing the questionability of what is questioned.” Basically, Gadamer believes that a true question is one that is asked only when the answer is not already determined – it may “sow the seeds of its own answer” but the questioner is really asking about something she truly doesn’t understand. So the philiosophical question that Bingham poses is just this – can a teacher ask a “true” question? It seems that for the most part, in a mathematics class teachers, including myself, generally ask questions that they previously know the answer to and have an expectation of a response. This is really how we teach and make sure that we are fulfilling our curriculum and students are “learning” what we need them to learn.

However, Bingham posits that we can ask “true” questions if the experience of the students is that they are “true.” In other words, one must look at the intention of the question posed by the teacher – if the teacher hopes to “break open” the subject matter as can happen with a true question, and if it experienced that way by the students in the classroom, then in the students’ expeirence it is a true question. Math teachers can ask questions in a true way, questions like why did you choose that method to use? what other problems does this remind you of? Do you prefer this method or that solution? Describe your reasoning process for the rest of us here. Why does that prove your statement? What’s the contradiction in what you just said? and many others.

Think how differently the teacher-student dialogue would be if math teachers posed true questions throughout the class period. Today in a faculty meeting, an English teacher colleague of mine had us all read an Emily Dickinson poem (much to my dismay) and then everyone was able to raise their hand and say one part of the poem that was confusing to them. This was totally acceptable that without any explanation of poetry or review of Dickinson’s works, we were able to creatively and openly express our confusion and process of “not-knowing.” I wondered how acceptable this would be to my colleagues in a mathematics lesson. How many of them would’ve expected a review of some algebra and then an explanation of the problem before questions were allowed. I then wondered how different our education system would be if the questioning process in mathematics classes was more like that in the English class.

The Consequence of Larger Classes

It’s very interesting to see how larger classes affects the effectiveness or productivity of a class that is based in a PBL curriculum. This year my classes are a tiny bit larger than they have been in the past. Generally, the class size has been between 12-15, and this year one of my section is as large as 17. I do think that this affects a students’ ability to get their questions answered, focus on listening to a student description of their process, see which process is correct, take good notes, and even to show respect when others are talking. It is honestly difficult enough to create a sense of community of learners with a small class – but what can you do with a larger class?

In my workshops, I have always promoted group work and discussion about the problems, but I am finding that difficult to manage as a facilitator, and when left to their devices, oftentimes students cannot facilitate a discussion themselves (even the most focused students). What I have found effective is putting them in deliberate pairs at the board to discuss their solutions. Why at the board, you may ask – why not just have them sit at their desks and show their work they did in their notebooks? Their is definitely an advantage to the physical act of getting up out of their chairs and writing (showing) the work again on the board that gives a sense of ownership for the work. It also gives a sense of scholarship when two are working together in discussion at a board (picture Charlie and Amita on Numb3rs working on a problem just writing in down on paper – not as dramatic). Students can sense this themselves. Students being at the board also gives the teachers a broad view of who’s working and who’s not – the work is all public and with a quick scan, you can see what is being done (and more importantly, what is not). In my experience, students have shown a lot of excitement when a solution has come to frution at the board – a lot more than when sitting at desks or the table.

It is the comraderie in a community of learners that grows when working together for a common purpose and there is nothing better than sharing ideas and problem solving that does that in PBL. Of course, you surely need one thing – enough board space!

Busily preparing

I am finishing up my spring break from teaching and I was very busy with a great deal of doctoral work during this time off. I worked on a lot of this website and edited some papers. Currently, I am preparing my presentation for a conference this coming Friday in Cambridge – it will be my first presentation of the research I did last fall on discourse in the PBL classroom. Those who read my proposal commented that they found it interesting, so I am hopeful that it will be well-received. I am looking forward to attending this conference simply to experience a research conference and prepare myself for perhaps a professional conference in the near future.

I had a wonderful conversation this week via Skype with a school in California that has implemented Phillips Exeter’s PBL curriculum this year. It was fun to discuss with their department some of the ups and downs of this year. Interestingly, many of the common obstacles that other schools have faced were what this school brought to the table in that conversation. Hopefully, they have found their stride and will continue their great work into the coming year.

I have got my forums up and running (well, my husband has) and hopefully we will begin some great conversations soon. I look forward to hearing from all of those who have been in contact with me about PBL in the past years and how they are all doing.

Winter into spring

Hello reader – hopefully you have found this site easily. I am writing here at the beginning of March, as I sit down to fulfill about 6 goals written down on purple post-its stuck to my computer. I have many issues that I would like to address here in my first blog entry, but not knowing the issues that are on the readers minds is of concern to me. I would love to hear from people that I haven’t heard from in a long time – those from my summer courses, or those I have seen in workshops, etc. If you have thoughts, please let me know.

I will be creating forums based on topics that people inquire about or have interest in. My goal is to have this site become a resource for teachers who are interested in PBL or transitioning their school to PBL curriculum.

So for now, I am looking forward to seeing how my school will do this spring with the advent of our new Algebra II/Trig PBL curriculum. This will be the first semester that we utilize the trigonometry portion that we wrote last summer and it will be interesting to see how it goes. The students with which we will be using this curriculum did go through our geometry curriculum, so they do know what they are getting into. I wonder how they will react.

Hopefully, with spring will come new life, goals fulfilled (including my paper getting out to a journal), and new challenges faced as well. If you have a new challenge that you are facing in the utilization of PBL curriculum or movement towards it, please let me know!