Returning from a week-long conference is always invigorating for me – not for the reasons that many people think. I do appreciate the great feedback I get from my “teacher-students” that I interact with during the week who are so extremely eager to learn about PBL – this truly invigorates me and allows me to do so much work over the summer myself. However, what I always look forward to is how much I personally learn from the interactions with my students that week. At this point, PBL is so popular in its use in mathematics classrooms across the country, although people see me as an expert in the field, I gain so much from the questions and process of those who are learning that it is so useful for me to move through that process with them all the time. I believe this is why they call it “professional development”! So I just wanted to give a HUGE shout-out of thanks to everyone who took my workshops, came to my Cwic sessions, had conversations with me or interacted in some way – it might have been one of the best professional weeks I’ve ever had!
Since that week in New Hampshire, I’ve done a lot of reading, editing of my own materials, and catching up with my own work. I recently read a blogpost on edutopia entitled “The Importance of Asking Questions to Promote Higher-Order Competencies” which stood out to me as something that we talked a great deal about in my own PBL classes, although this blogpost was not specifically about PBL or math at all. It was written by a professor at Rutgers University in the Psychology Department, Maurice Elias, who is part of the Rutgers Social-Emotional Learning Lab, and made me wonder if he had done any work with Cindy Hmelo-Silver, who is also at Rutgers and does work with PBL in Psychology. The concept of asking questions is something that we discuss and practice in my workshops because Hmelo-Silver says that it is a characteristic of an experienced PBL teacher to ask probing questions that are metacognitive and at a higher-order level. Interestingly, the four areas that Elias discuss are often not linked to higher-order thinking (for example, yes/no questions) so I thought I might take his “Goldilocks” example and try it through the lens of math PBL. Elias’ four questioning techniques are 1)Suggest 2) Ask a Closed Question 3)Ask an open question and 4)The Two Question Rule.
The idea of “suggestion” is one that I always tried to stay away from since student voice and experience is first and foremost in my mind as a pillar of the PBL pedagogy. Allowing students to make first attempts at making those connections on their own I believe takes precedence over critical thinking skills of choosing from alternatives. However, that concept of making a choice between alternatives is important as well and might be a very good skill to have them practice every now and then deliberately. I think I will begin to try this in class. The next time when it seems like no one has an idea or when the student at the board is going in the wrong direction, I may decide to say something like “Should Joe go with the method of completing the square or factoring here?”
The second idea of asking the closed question (yes or no) is also one that I have always tried to stay away from. In my experience it’s kind of a conversation staller, but the way it’s explained by Elias in his blogpost is actually a very interesting twist on the closed question. It takes a yes or no question but embeds an opinion in it, so almost forces a justification of the closed question with the yes or no. It makes the teacher find a way for the student to continue (well, the teacher must make sure the student follows up). So for example, if the teacher asks asks, “Do you think the quadrilateral is a rhombus?” it might seem very obvious that a student could just say yes or no and the conversation could just end there. Everything I’ve read about closed questions say that you should not phrase the question that way but be sure that the question has within it some interest in the student’s opinion. “Why do you think it’s a good idea to argue that this quadrilateral is a rhombus?” (Which is a closed question in disguise but opens up the conversation).
Then there’s the Open-Ended Question (or what Bingham calls a True Question) which I have written about before. I talk about this in my workshops as well and real open-ended questions are questions that the teacher doesn’t really know the answer to. I love Bingham’s analogy of trying to predict with your students what the sum of two dice will be (the answer) but trying to keep the dice rolling for as long as possible without knowing the answer.
What’s an example of this type of question in mathematics? This is a tough one because as we know so well, there are definitely right and wrong answers in mathematics. However, we can ask questions like “Why did you chose that method?” and “What do you think of Sara’s argument? Do you agree with her?” These types of questions can make mathematics teachers very uncomfortable but we can keep the box wiggling for great deal longer than we could before with these questions and they allow us to work towards the CCSS Mathematics Practice Standards of persevering and critiquing other students’ work.
Elias’ Two Question Rule isn’t just as simple as asking a follow-up question, but makes the assumption that students want to see if when you ask a question the first time, you really wanted to know what they wanted to say. For example, in most mathematics classrooms, students are accustomed to the I-R-E form of dialogue which is short for Initiation-Response-Evaluation (Teacher-Student-Teacher) where the teacher generally knows that answer that they want for the question they have asked (kids know this, they’re not dumb). So when the same old kids do the response part of this, instead of just doing the evaluation part, why not blindside them and actually rephrase the question and ask it again in a different way, or ask one kid themselves individually in order for them to know that you really want to hear from them? I think that’s what Elias is talking about. (or even better don’t use IRE, break that darn habit, I know I’m still trying to!)
We had some great fun during my workshops role modeling and just trying out different ways of questioning the mock student who was at the board – it’s hard to break old habits. But the more we are aware of what we are trying to do and do it deliberately, the more important it becomes and bigger agents of change we can be as well. If you have any thoughts on these questioning techniques in math PBL classroom – please let me know