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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