When I first thought of problem-based learning(PrBL) students need to solve a real-world problem. I thought about the innovation challenges where students are designing items to solve a need for a community or person. I thought about design thinking workshops where students engineered a plan to fix the cafeteria seating. I think about the Anatomy and Physiology class where students are solving case studies (Punahou, 2011). I thought about my own class Design of Emerging Technology (DET) where some students design a project to solve an issue they see (mail sensor, sensors for low stock items, light that changes based on heart rate). These are all real-world problems and fall under the umbrella of Project-based learning in my mind. In fact, some of my students in DET would create art installations and be more project-based. Then I read Krall’s (2012b) statement “we need to define what is an “authentic mathematical experience”. A mathematical experience to me is something that promotes mathematical habits of mind.” This got my mind thinking about the best math lessons I have taught and how some of my former math colleagues teach mathematics.
I look back on the last few years of my teaching mathematics. Often we would grapple with a problem and figure out how to solve that problem. This could take a day or two to determine. Students would learn via discovery and build their critical thinking skills. I agree with Krall (2012b) “lectures suck”. The more that teachers can act as facilitators and allow students to explore their mathematical concepts, the more critical thinking students develop. I love understanding the importance of stripping away the made-up scenarios and actually looking at some good math problems (Krall, 2012b). This was always a challenge for me, I hated making up problems that were not real. I think that this is why I liked teaching Statistics. I could easily develop problems that they could look at that are about real life and enhanced my students’ mathematical minds.
Krall’s edgier brownie pan lesson (2012a) demonstrates a great inquiry-based lesson. The problem is based on a real-life situation, “Can we make an edgier pan or a pan for people who like only centers?” Students first have to decide a metric for “edginess” (Krall, 2012a). This is having them develop some mathematical arguments for this metric as well. I have always struggled at the high school level with how to balance the content of mathematics (such as Pre-Calculus) through PBL. A PrBL approach allows the content and a way to help students develop independence, inquiry, and the four C’s (Larmer, 2014).
When I think about PBL, PrBL, and STEM, I realize there are many ways that critical thinking is developed in classrooms. The NGSS provides a guideline for STEM teachers to develop the practices, content, and relationship to other STEM disciplines. PBL allows for the multi-disciplinary approach that allows teachers to pull from other subjects such as English, Reading, and History. I can see how the approaches for inquiry-based take time, being able to touch on many concepts would assist in the lack of time teachers always mention. I think of my own daughter’s 2nd grade Komodo Dragon book. The teacher developed expository writing while researching reptiles and writing about their life cycles. This simple project gave my daughter a chance to do science, writing, reading, research, and art. It touched on many of the standards and provided them with more learning than just spending x amount of minutes in each of these subjects. I think that when we begin to combine STEM with units developed through PBL students begin to engineer and discover more about the world around them. They start to become inquiry-based learners. They begin to question the world around them and look for supporting valid evidence to support their own reasoning and thinking.
References:
Krall, G. (2012, January 7). Can we make an even “edgier” brownie pan? What about the “perfect” brownie pan? Emergent Math. https://emergentmath.com/2012/01/07/can-we-make-an-even-edgier-brownie-pan-what-about-the-perfect-brownie-pan/
Krall, G. (2012, May 24). Isn’t problem-based learning easier than project-based learning and 10 other myths about PrBL. (“Real or not real”). Emergent Math. https://emergentmath.com/2012/05/24/isnt-problem-based-learning-easier-than-project-based-learning-and-10-other-myths-about-prbl-real-or-not-real/
Larmer, J. (2014, January 4). Project-based learning vs problem-based learning vs X-BL. Edutopia. https://www.edutopia.org/blog/pbl-vs-pbl-vs-xbl-john-larmer
Punahou School. (2011, August 22). Problem-based learning [Video]. YouTube. https://www.youtube.com/watch?v=J63e_YSntuo
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