Last week, a reading referenced George Kuh’s idea of experiential learning. Where learning can mean something more than just memorization; instead, learning is like an *adventure*. A common thread between this description of learning and the examples presented in* A New Culture of Learning, *is the idea that learning should be more holistic. It shouldn’t just stop at simply learning facts by rote and regurgitating them back at a teacher.

There is discussion on shifting away from lecture, and instead, focusing on creating an environment where students are free to explore and interact on their own to learn. I believe that when the initiative to explore (and learn) is given to the students, they become more engaged and in turn, more invested in what they are experiencing. When it works, this is a powerful technique to teach students, not only information, but the process in which they obtain it.

In this environment, failure is not only encouraged, but it is *required *to explore the boundaries and constraints of the environment students are placed in. The ability to reiterate and experiment without the fear of failure is natural learning at its finest. And it is through that failure where students begin to innovate.

But that’s the trick, how do we make it work? In certain contexts, it is clear that this form of teaching is better for students. You can tell people what happened in the past, or you can design scenarios where students live through it themselves. However again, I’m thinking about how this connects back to teaching mathematics. Can we create that environment of exploration when it comes to higher level mathematics?

I took MATH 3114, Linear Algebra, with Professor Wawro my first year at Tech. Professor Wawro does research in Math Education, so unsurprisingly, her class was not a typical. She set up the topic of diagonalization in a way where we almost “stumbled” upon it by our own exploration. We were presented with a problem before us, and through the process of solving it, we unknowingly described the technique for the change-of-basis matrix. Looking back, this was really the only example of “exploration” in teaching mathematics that I have experienced.

Now, I think it is important to see the strengths of lecturing as a technique as well. I was very glad to see this article about someone who, while not a full proponent of lectures, still finds lectures helpful in certain ways. I really appreciate someone acknowledging both sides to the argument. I’m not sure about fully *replacing* current techniques with these new ideas, but rather, to use new techniques to support the classic techniques that we use.

Perhaps because I’m so focused on thinking about how to teach mathematics that I, myself, am missing that bigger picture, the holistic framework of learning.

My final thought is on the connection between video games and learning. Reading about learning theories in video games brings reminds me of a youtube channel I stumbled upon two years ago called Extra Credits. Among other game-related topics, they created videos discussing games in education. Some topics include gamification of education, agency in education, and also include some small case studies. While their videos aren’t necessarily deep, they are an interesting watch for those who have dabbled in video games in the past.

Thank you for your thoughtful post. I think you bring up a good point that we in GEDI have come across many times – the importance of holistic versus the importance of specific fields. I do want to say that it is also tough to not pit them against each other, however I also realize that don’t need to. I think it really depends on how bird’s eye view you want to get and how specific too. For my profession, it really matters that we take the global context into consideration and then intentionally figure out the specifics. Maybe you can try that and daydream about how that would look like in Math Education. Unfortunately, what happens is that we limit ourselves because we know we have existing structures in place and we’d rather add on instead of reinvent. In some cases both can be applicable, in others we just limit the possibilities. Hopefully as the semester goes on you’ll get some more ideas. And YES we will talk about Gamification too!

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I really enjoyed reading your post! I totally agree with your point focusing on creating an environment where students are free to explore and interact on their own to learn. I mentioned it in class last week, but in my field that is the only way to learn. At a certain point you max out of what you can learn by lecture and you have to go out in the field to see geologic features. Also, many of the labs include hands on exhibits that are necessary to engage students. I absolutely see your struggle with trying to create that environment in math. I genuinely don’t know the solution, but you have all of the pieces there and are already thinking of how to create a learning environment, so that’s already the right direction to be going!

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Last summer, I was one of the instructors of the Summer Bridge Program for students entering the College of Science majors. This three-week program is designed in a way to teach the problem solving and mathematical modeling solely through activities in a way that brings the examples and ideas from different sciences that use mathematics to students. Although, I admit that mathematics is not always a tool for science, up to certain level, teaching math in the context of science helps students make sense of it in a deeper way and also provides the opportunity of implementing the student-centered learning in a math course.

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I was glad you brought up the point about failure. So many of my students are very concern about getting As. There focus is on that letter rather than improving their work or understanding. Students benefit so much more in the long run, I think, if they do poorly on an assignment and get the opportunity to rework or rewrite it. (Of course I’m thinking about papers or essays.)

I think you are right to be thinking about what we read in the context of the discipline you teach. I’m doing the same thing. I think the example of presenting a problem and having students stumble across the method on their own is a really good idea.

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I agree it must be difficult to consider how math should be taught differently. Maybe the approach needs to move towards team based learning. You may enjoy this video: https://www.youtube.com/watch?v=gW_M426V2E0.

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