Teachers who attempt a problem-based learning lesson may be discouraged from trying it a second time if the experience doesn’t go the way they had hoped. Even if teachers are committed to its implementation, they may be unsure of what steps to take next.
As a district math coach, my challenge has been successfully demonstrating problem-based learning in academically diverse classes. I am frequently unsure of what to expect as I go into unfamiliar classrooms to work with a variety of students. An interesting problem that achieves wonderful results in one class causes frustration and anxiety in another class that appeared similar on paper. These struggles have led me to come up with four C’s that I believe teachers should focus on to improve their success with problem-based learning: communication, curiosity, critical thinking, and content knowledge.
Insufficient communication skills is a problem from remedial classes where students have low self confidence to honors classes where students may believe that only numerical answers matter. When students are uncomfortable asking questions or expressing what they know it is very difficult to move forward. Math Practice 3 of the Common Core State Standards explains it well as students must be able to “justify their conclusions, communicate them to others, and respond to the arguments of others.”
Fortunately students love to talk (perhaps not currently in math class) and with the right environment and teacher encouragement, this can be worked on. Students need to feel that their classroom is a safe place to state their opinion. Strong explanations need to be recognized as much or more than correct answers. Teachers need to become masters at asking the questions that facilitate rich math conversations (Fawn Nguyen shares a great example here where she facilitates a conversation that helps students explain what they know and explore further). Transitioning students to this environment does not happen overnight but the rewards are worth it.
Somewhere along the line, many students lost their desire to wonder about the world, how things work, and life in general. Without speculating on what is causing this, I have observed that this abandoned curiosity poses a significant challenge to student engagement during problem-based learning. Many students are unfortunately too comfortable being spectators in the math classroom, and rekindling their curiosity will help them persist through challenging problems.
So if lack of curiosity is a problem, how do you teach people to wonder again? I don’t have a perfect answer, but my current best guess is showing them interesting multimedia and having them come up with questions. Dan Meyer’s 101qs.com website is a fantastic source of this kind of resource. Who can look at the penny pyramid or enormous sink hole and not want to know a little more? What if you began every class with a picture and had students come up with a question to share with their classmates? I believe that over time their curiosity would grow, and if you reached a point where they just had to know more, then you know you are getting them back on track.
The critical thinking process is rarely comfortable or convenient. Many students do not like the struggle, yet most successful people excel at it. Perhaps Dan Meyer best summarized critical thinking’s importance during his TED talk when he stated “What problem have you solved ever, that was worth solving, where you knew all of the given information in advance? Or you didn’t have a surplus of information and you had to filter it out? Or you didn’t have insufficient information and had to go find some? I’m sure we all agree that no problem worth solving is like that.”
What I have found to be the main problem is that students are overwhelmed by the abundance of information and lost without the explicit directions they have been trained to expect. We have to retrain them how to think for themselves. Geoff at emergent math has a very helpful blog post that includes his five step approach to implementing problem-based learning. I have found his step 2 “Students brainstorm ‘Knows’, ‘Need to knows’, and ‘Next steps’, all the while being guided by the facilitator to generate the intended learning outcomes.” to be very useful in developing students’ critical thinking. I strongly agree with his recommendation for using a Problem Solving Framework to help students build these skills.
In a textbook, problems are neatly arranged so that students have been introduced to all the content knowledge they will need to solve it. If they have forgotten anything, they have convenient examples to reference that will help them get back on track. With problem-based learning, students work around a real-life math application involving a variety of interconnected skills that may not have been covered.
Teachers may need to facilitate conversations to help students identify the prerequisite knowledge and skills. This may require several cycles of pausing the problem-based lesson, reteaching necessary content knowledge, and returning to the problem. The key difference here is that students should be the ones to identify their deficiencies, request the new knowledge, and assess whether they have learned it by immediately being able to apply it to their problem-based lesson.
It is important to note that students are not the only ones who will need strong content knowledge. One of my favorite aspects of problem-based learning is sharing the wide variety of solutions students come up with. Often times students find approaches I hadn’t considered. This is where strong teacher content knowledge is critical. At a minimum, teachers’ content knowledge must be strong enough to understand students’ diverse explanations. Ideally teachers’ content knowledge is strong enough to help students make connections between the various approaches.
To prepare, teachers should consider multiple solution paths to every problem-based lesson they implement. It may help to save student work for future reference. Also realize that students may come up with an answer you will need more time to think about. It is OK to tell a class that you haven’t ever seen a student approach the problem in that way and want more time to think about what the student wrote.
In conclusion, my hope in sharing this reflection is that teachers who are refining their practice with problem-based learning will realize that it is a valuable process that benefits students and takes time and patience to implement. If you have any thoughts on what I wrote or feel that there are other “C’s” worth focusing on, please let me know in the comments.