There’s a famous line that many people use when they describe teaching. “Tell me and I’ll forget, show me and I’ll remember, involve me and I’ll understand.” I’ve always loved that quotation. I’ve tried to base my teaching style on it, like most teacher’s I’ve met or worked with have as well. But it wasn’t until recently that I actually knew what that meant. Or how powerful it can be.
Think of your class. What do you see? Do you see lethargic faces, students with their heads down, and only your top 10% answering your questions? Or do you see all students engaged; regardless of level? Do you see students talking about math in a productive argument? I can tell you that in just a few months, I have transformed my classroom from the first classroom example to the second.
Over the last years I have offered a course about inquiry-based learning to graduate students. These students are usually teachers that are working full-time in their own classroom while completing their professional licensure and master’s program. In this blog I will explain how I run the course and, more importantly, you can read about the journey to inquiry of two teachers that worked with me this semester.
This blog shows two different videos, one from Stanford University (CA) and one from Cornell University (NY), in which undergraduate students work on the Pennies and Paperclips task from Discovering the Art of Mathematics.
In this blog we invite the reader to think deeply about professional development opportunities for faculty. The focus of this professional development is to improve teaching by including more inquiry in the mathematics classroom. Our hope is that faculty developing professional development will use some of our ideas to create new opportunities that lead to transformational change and deep conceptual learning about teaching.
In this blog, Julian Fleron describes how he uses mathematical art to make his students think about racism, sexism, etc. Together with his students, he created a powerful piece of art to show that how we view each other depends on where we stand.
There were several things I didn’t like about grading...I didn’t like agonizing about the exact number of points to give, grading homework felt more summative than formative to me and I wasn’t sure if students learned from my written comments. I was also confused about the fact that a “B” could look many different ways. Then I read the book “Specifications Grading” by Linda B. Nilson. While this book doesn’t focus on mathematics it gave me lots of ideas and the goal to change what I am doing...
In this blog, Phil Hotchkiss describes his experience in teaching a "first year only" mathematics for liberal arts course. He explains several components of his course and uses students quotes to show the positive impact on his students.
My goal for this blog post is for you to get a sense of my philosophy and approach to one of the most enjoyable courses I teach; as well as to highlight how an IBL (inquiry-based learning) approach to the course is fundamental for the learning goals that I and my institution have for the course. You can download some of my explorations.
I have seen in the classroom how students’ conceptual understanding grows out of getting lost, feeling confused and making mistakes. Yet at the end, I still tend to “tell” students to not make mistakes anymore or at least not to repeat mistakes. How? By assessing their learning with presentations, tests, written homework, and final exams using rubrics that give the highest score to the work that has no mistakes... So how can I avoid sending mixed messages and create better rubrics and assessments?
Changing the mindset of our students, helping them understand how our brains work, how we actually learn is incredibly important for any mathematics class, from Kindergarten through graduate school. Since there is a lot of wonderful material, including blogs and videos, already published about this topic, I will use this blog to just present some of the main resources.
In this blog, Brian Katz is connecting beautifully the issues of equity and teaching using inquiry. He also promotes a special edition of PRIMUS which focuses specifically on inquiry-based teaching and learning.
In this blog, guest writer and aspiring teacher Lauryn Zaimes describes her insights into the intricacies of teaching with inquiry gained while videotaping a semester of Calculus. I hope that reading her experience will motivate practitioners like you to ask students to video tape your class sometime. While Lauryn clearly learned a lot from her experience, I learned at least as much!
This Fall (2016) the 13 students in my honors mathematical explorations class embarked on the journey of understanding some mathematical ideas behind maypole dancing. In this blog you can find some videos about maypole dancing, student work proving our conjectures and a beautiful writing project by Sarah Dunn about mathematics, running and maypole dancing.
Sarah Dunn, student in the Honors Learning Community for "Mathematical Explorations" and "English Composition," reflects on connections between the challenges of running and grappling with the mathematics of maypole dancing. She sees connections in the role played by community support, the thrill of venturing into the unknown, and the passion in pursuing a personal challenge.
We have long believed that our students enjoyed working on challenging mathematical problems and that after taking our classes they could find mathematics to be beautiful. However, we needed more than anecdotal evidence of this. Data from surveys administered from 2013-2016 provide evidence that our curriculum materials and our pedagogical tools have a significant impact on our students.
I believe that one learns best using inquiry. Therefore the guiding principle of our workshops is to not lecture about how to teach using inquiry but to facilitate activities what will lead the participants to discover the teaching ideas themselves. Since we don't have video clips (yet) from most of our workshops, we invite you to read this vignette.
To help our students better understand the process of doing mathematics and how even great mathematicians need to struggle with ideas before solving a problem, we show our students the video, The Proof, a NOVA special about Andrew Wiles proof of Fermat’s Last Theorem. The students’ responses to the video have shown some remarkable depth and recognition of how different the process of doing mathematics really was from what they had experienced.
Solving the Rubik’s cube was one of the main themes in my Mathematical Explorations class this semester. My students believed for most of the semester that they would never ever be able to solve the cube. Watching them overcome this belief was powerful for all of us. One of the main goals of my course is for students to change their beliefs about their mathematical abilities and to become more persistent, confident and creative in problem solving. And the Rubik's cube does just that.
Instead of describing a particular teaching technique, this (shorter) blog will expose you to many ideas that come up for me around teaching a specific topic, salsa rueda, in a math for liberal arts class. I will tell you why I love to include dancing in my math classes and show you videos and student work from my math and dance class. Maybe you also want to give it a try some day?
Informed by discussions with our students, this month’s blog invites you to consider the connections mathematics has to the common core, the liberal arts, and important goals of reports like the just-released Common Visions Report. Julian Fleron also uses this context to describe the logo for our project and to touch on its symbolic role in these connections.
I believe that students need to take risks in the mathematics classroom: the risk to not know (yet), to make mistakes, to speak up when something doesn't make sense, to ask for support, etc. In my experience this creates the environment that allows students to learn. If we ask our students to take risks, shouldn’t we, the teachers and facilitators, do the same? I find it easier for my students to be vulnerable when I have modeled what that could look like.
We present the following case study as a way of illustrating the power of inquiry-based learning to transform how we think about what we know and how we know. It challenges us to reconsider the nature of teaching and learning in mathematics. Julian Fleron describes how he and his students explore triangle patterns.
What we know changes several times in the story of Rascals’ triangle. And each time the matter of what we know is inextricably intertwined with how we know it.
Math Explorations showed me how much there was to learn in the world of mathematics. I had been contemplating the idea of pursuing a career as a teacher. Seeing the difference in how math is taught in high school and how it was taught to me in Math Explorations pushed me into thinking about how I could help kids in high school learn and appreciate math. I was convinced that this was the direction for me, so during my next semester I declared a Mathematics major with a certification in Secondary Education.