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.
Although I enjoyed and appreciated mathematics, I was not compelled enough by the mathematics of high school to make it my major. This soon changed as I took my first college-level mathematics course, Math Explorations.
Hello, my name is Nicholas Taliceo and I am senior at Westfield State University. I’m a Mathematics major and I love it. I’ve had some amazing experiences – I’ve attended and presented at numerous conferences including the 2015 JMM conference in San Antonio, TX, and had the opportunity to experience undergraduate research, just to name a few. Interestingly, only a few years back, I would have never thought that I would be doing what I’m doing now…
The primary audience of Discovering the Art of Mathematics is mathematics for liberal arts students. The scope of the project’s work continues to expand to include audiences that are more and more diverse. Here we describe the project’s connection to Mathematics majors. What we have found is that Discovering the Art of Mathematics has great value in recruiting mathematics majors AND our view of our Mathematics major has been deeply informed by our work on this project.
This blog is part of our guest blog series: Dana Ernst is an assistant professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ. We met him at the IBL workshop a few years ago, where we noticed that besides being a committed cyclist he knows a lot about using IBL in many different classes. Dana is co-author of the wonderful blog Math Ed Matters .
We met Angie Hodge at the 4-day IBL workshop run by Stan Yoshinobu 3 years ago. Besides competing in 100 mile long trail runs (yes, really!) she knows a lot about teaching IBL in calculus and in larger classes. Angie teaches at the University of Nebraska, Omaha. She also co-authors a wonderful IBL blog Math Ed Matters with Dana Ernst.
In this blog we tell the story of the different surveys and assessment tools we have used since 1997
to measure the impact of our materials and teaching style. You will find the actual
surveys, the full reports (and summaries) and our current ideas and efforts.
Matt Jones is sharing some of his technology ideas for the IBL classroom with us: "A few years ago, I got involved in a professional development project for middle school mathematics teachers where all of us were using iPads. Partially as an outgrowth of that project, I started a blog called The Math Switch . In this post, I am going to detail the workflow that emerged in the first year of the project."
Steven Strogatz' wrote a blog post about what it was like to be a beginner at teaching through inquiry. This second part contains his experience of teaching a Mathematics Exploration class at Cornell University using ideas from "Discovering the Art of Mathematics":
Last fall, for the first time in my career, I tried a new way of teaching. Instead of lecturing, I gave my students puzzles and questions to explore together in small groups. What happened over the rest of that semester turned out to be the most astonishing, uplifting experience I’ve ever had as a teacher.
Steven Strogatz writes about what it was like to be a beginner at teaching through inquiry. This blog contains his impressions of the "Discovering the Art of Mathematics" workshop held at Cornell University in summer 2014:
"This experience gave me powerful insight into what it must be like for students in an IBL classroom. It made me realize the importance of providing a safe and nurturing space for the math explorers I was about to start working with in just a few days."