PBL for Engagement and Empowerment in the Mathematics Classroom

Well, it was an interesting meeting. When PBL is discussed in such a cut and dry way, it’s really hard to argue with. The presentation went smoothly with a number of questions afterwards. I felt like people listened, but I’m afraid that they brushed off a great deal of the philosophy because it is so abstract. Many advisors had good questions though about assessment, handling different types of learners and the such. This coming weekend is our parents’ weekend and I needed to give them a reason to relax and things to say to parents if they have concerns.

I think the hardest thing about talking to the whole faculty at our school about PBL, is I’m always afraid that externally they support it, but internally they really haven’t bought into it. Most tradtionalists really believe that math should be taught in a way that allows for exact, direct instruction. One parent wrote me an email and said that this type of thinking was too much to ask of teenagers. I guess my answer to that is that they have been asked to think creatively and critically in English and History courses so far. Why is it different for math? I think that people are in the habit of the way they have learned all their life. It really is a cultural problem that it is acceptable that people have problems with math. I mean, all over the country there are programs to help illiterate people – Literacy Volunteers of America, etc. When is the last time we heard about a volunteer group that makes sure that people know basic math? It is unheard of (and quite the social stigma) to not be able to read, but is strangely accepted if people did not understand math. One of my fellow colleauges even asked how it was that we could require our students to be able to retrieve prior knowledge in such a random way. I really thought that was a strange question. Yes, this person was speaking as an adult who is much farther removed from high school math, but at the same time, hopefully she has been using some of the skills she learned in math class all her life? If not, what a pity.

I’ve uploaded the powerpoint presentation that I used at the meeting this week. Hopefully it will be heplful to someone.PBL Explanation and Justification

Well, next week I am addressing our whole faculty at a meeting on the issue of why we changed our geometry curriculum to a PBL curriculum. I’m trying to decide whether or not to get technical with them or just to basically give them very basic ideas. I could easily talk for an hour just about the pedagogical reasons behind the instructional design of PBL. I could talk for another hour about Jo Boaler’s research and why PBL seems to work best for girls. I can give them tons of tables from my graduate classes that describe the difference between a recipient learner and the low level thought processes that go with that, and the self-regulated learner and the high-level processes that go with that? Do my colleagues want to hear all of this? Well, guess what, I have the floor so I can talk about what I want to!
So what I’ve done is started to compile a powerpoint presentation that does include all of the background information. I’m going to start with the ideas behind PBL, then move to the advantages it gives for girls’ learning. I’m going to talk about how we changed the problems and assessment strategies. How does this work for girls who might not conisder themselves good at math?

Finally, I think I’m going to give each faculty member who wants one, a hand-out with bullet points to discuss with visiting parents on parents’ weekend just in case there are some that are concerned about that. I’m working on another post right now that includes the ideas of parents’ concerns. Hopefully, the presentation will go well next week and the value of this type of teaching might be shared.

I continue to feel very lucky that my administration supports this change fully.

So the first graded exercise (aka test) which we are choosing to call “problem sets” this year has happened. many students received grades that were lower than they are used to getting. What are some reasons that this could happen?

first, it is the first test with a new teacher. Generally, every year it takes students a while to figure out what teachers are looking for in their work, what kinds of questions a teacher will ask, and how best to answer them.

second, it is the first test in a course that is supposed to be geometric, but we are teaching it from a very algebraic standpoint. So, although many students go into “geometry” thinking, oh it will be different from algebra – it does not give students who struggled with algebra skills like slope, equations of lines, factoring, etc. any leeway, as traditional geometry texts or courses do.

third, it’s not what they are used to as a “test”. Since we are trying to assess problem solving skills, it seems logical that our graded exercises are not simply just repeating material that they are shown in class. We are trying to assess the growth from a recipient learner to a very self-regulated one. How does one do this in a fair way? One of my colleagues really struggled with what she interpreted as sacrificing her own standards of grading. We had a long talk about what we are trying to assess with problem sets. If our overarching goal is problem solving, then we need to praise risk-taking and attempts at problems that are not totally done right. I feel that no student should earn a failing grade who makes attempts at solving problems. This is a very fine line for some teachers.

I assess weekly with “quick quizzes” which are more to manage students’ daily skill-level of the content discussed that week. Every other week they have a “problem set” that is a larger grade, and whose main goal in assessment is for the students to practice independent problem solvers. Of course, this is frustrating for the girls in the beginning. It is a very different type of “test” than what they are used to.

In general, I do see a direct correlation between participation in discussion and good grades on problem sets AND growth in their independence. I am honestly continually assessing students on a daily basis. We also require journal writing which is reinforcing topics and recording the process of their own problem solving. It is encouraging to see growth, but it is also frustrating to sense some of their continued bad attitude towards me.

This summer two colleagues and myself started a project to change our traditional geometry curriculum to a Problem-Based-Learning Curriculum. We teach at an independent school and the geometry course has mostly 9th and 10th graders in it. We had the support of our school head, and my experience with PBL from a former school that were pushing us forward. I feel that this is a pretty radical change for a lot of people, but do feel that the experience is worth writing about and recording. It is not supported by the whole department.
As the school year started, it was clear that some students were feeling the “uncomfortableness” that almost always comes with trying a PBL curriculum. For many reasons, students end up feeling lost, frustrated, disorganized and without focus. this generally takes a good 2-3 months of working with the kids to get them past the “out of my comfort zone” feeling that they have. Generally, though students are not afraid to talk about their feelings. Interestingly, in my class initially students kept their thoughts to themselves for about a week and a half. There didn’t seem to be much going on in class that they didn’t like, and they seemed to be trying the homework with minimum effort, but trying nonetheless. then it happened….

One Wednesday morning, the dam broke and all of their fears, frustrations, anger and emotions came flooding out. They yelled at me, calmly spoke to me, gave examples of what they needed and more. As I felt my mouth become bone dry, I started giving my usual speech about why I teach this way. Problem-solving is the overarching goal of mathematics education. What I want you to leave this class with is not knowing the pythagorean theorem or how to use it. I want you to leave with the confidence to know that if you don’t know how to solve a problem, you know how to use the resources at your fingertips, and know how to delve into the knowledge that you already have in order to find the best solution that you can. I spoke about the goals of using problem solving skills all throughout your life. They seemed to hear me, the mood of the class changed and things picked up in the rest of the period quickly.

My colleagues also were having similar conversations with their students. But there was a hum beginning on our campus about this change. I heard a few advisors who didn’t know what to say to their advisees who were complaining about it. I felt very frustrated that my colleagues in other departments didn’t feel comfortable coming and asking me about it. I received only one specific email from a parent that was worried about her daughter. There was also an email sent to my head about me and how she was in full support of this change. It is very helpful that she believes in it too. (that’s an understatement)
During the third week of school, I observed my other colleagues and noticed a few things. One of them was at the end of the spectrum where she might have talked a bit too much, but honestly, I thought she was doing a pretty good job. Highlighting the important topics that came up, but letting the kids struggle with the problems together. It seemed very fair and productive. The other colleague was trying to stay out of the conversation a little much. I could see the level of frustration rising in the students as she would ask question after question, but not tell them if they were right or not. I admired what she was trying to do, but in the beginning it was pretty important to earn their trust and confidence in the teacher. So I spoke with her and tried to show her that it was important to speak up a bit more. I think she will work with it a little more. I need to encourage them to come see me teach more too.

I will try to keep up with this blog so that I end up with a record of the successes and failures of this year’s transition – hopefully to say that we will do it again next year.