The need for more active involvement of mathematics students in the learning process is well documented. Involvement occurs through the use of inquiry-based learning. The curriculum materials that make up Discovering the Art of Mathematics (DAoM) reverse the typical lecture dynamic by being built on guided-discovery investigations.
DAoM materials focus on investigations, tasks, experiments, constructions, data collection and discussion prompts rather than transcribed lectures and worked-out sample problems followed by banks of routine exercises. The transformative impact this has on students in MLA classrooms can be seen clearly in the classroom vignette, student quotes, and videos shown below.
Perhaps the best way to understand the depth and powerful impact of our project is to read what the students have to say about their experiences. The following student quotes, collected during the project, are typical responses received as part of student journals, essays and reflections. Many more student quotes can be found in our quote library »
This course challenged me to think in ways that I don't usually think, and it helped open my eyes to the world of math. It actually seems interesting.
The class was fair, and you really had to use your brain.
This class taught me how to think independently about not only math but other subjects and everyday problem solving.
This course is a breath of fresh air. It helps me understand why math professors enjoy math so much. I see the fun in math now and how beautiful it can be. I had a lot of fun with the projects we created. I also enjoyed the amount of help I received from working in small groups with my classmates. I would recommend this class to anyone who currently has a negative attitude towards mathematics. This class could change their opinion, just like it did for me.
I will sort of miss this class -- most of the chapters of the book are interesting -- I'll keep the book for the fun of it.
Math Explorations taught me what mathematics really is. It is an art form.
When I figured out how to cut my own shape out I was actually excited. I actually had fun in doing it and was really proud of myself for being able to do it.
The focus on active student involvement, student responsibility for learning, and decentralized role of the teacher is fundamental to this project. Without models or experience, such fundamental restructuring of one's mathematics classrooms can feel uncomfortable, foreign and daunting. Video clips from DAoM classrooms provide access into this culture of student discovery and inquiry.
Caption: A small group interaction with their professor as part of investigations of the areas of polygons on a geoboard in relation to the number of pins contained within the polygon and those falling along the boundary. Mathematically, these are first steps towards the (re-)discovery and proof of Pick's Theorem. The students wondered which pegs actually lie on the boundary formed by the rubber band. Pedagogically, notice how the teacher works hard to support the students, drawing their attention to particular aspects of the geoboard. It seems he has a certain path in mind, given where the students are. Not all the hints are connecting with the students. In their attempts to describe the different patterns they see, the students realize that they can be grouped depending on the slope of the side of the triangle.
Powers of i
Caption: This video clip is from a section of Mathematical Explorations, our Mathematics for Liberal Arts course. In this clip the students are exploring the pattern formed by powers of i and one of them turns to Prof. Hotchkiss as the authority for correct answers. As you watch this clip, listen to her questions and how Prof. Hotchkiss responds to them using inquiry-based questioning techniques.