The images and videos in the Art of Mathematics media library showcase the active student involvement in our classrooms and the decentralized role of the instructor. You can browse the most recent images and videos shown below or search for specific examples of student activities, *e.g.* search for "Pick's Theorem" in videos to watch a small group of students investigating the areas of polygons on a geoboard.

# Media Library

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## Pages

Multiple search terms will be joined with AND by default. You can also enter OR to widen your search, *e.g.* searching for maypole OR salsa will return all results containing either maypole or salsa. To reset or clear the search, delete all terms and click update again.

## Pages

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.

Multiple search terms will be joined with AND by default. You can also enter OR to widen your search, *e.g.* searching for maypole OR salsa will return all results containing either maypole or salsa. To reset or clear the search, delete all terms and click search again.

I enjoyed the comparison between art, music and math because it gave me a glimpse at how mathematicians see math. It took music, which is something I can closely relate to, and math which is something I am not passionate about and it allowed me to see what it would be like if music were taught in the same fashion as math is.

The fact that it was never easy to find an answer to the problem made me want to find it so much more. I would sit at my table with my three classmates and work so hard on one problem until we got the guts to ask for help. But we were so personally determined to get the answer ourselves that we almost did not want to hear what we were doing wrong. And even when we asked for help, we were never told the answer. Rather we were given suggestions to turn different corners to possibly find the answers there. It taught us to think for ourselves. And it taught us so much more than just the way to get the answer to certain problems. The worst feeling in the world was to look up at the clock and realize that class was over seven minutes ago and you still have not figured out the solution. Yet the best feeling was when you figured out a solution and could not stop smiling for the rest of class because you had figured out that one question that had been pushing on your shoulders since the first time you read it.

Usually I absolutely dread going to math class. I think it is because I have the negative mindset that I am just going to fail. This class has helped me widen my horizons and see that I do have the ability to succeed in math.

One of my favorite projects in this course was the string art project. I believed this assignment to be very creative and quite contrary to any of my previous history in a math course.

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.

In my previous math classes, proofs were something I memorized and forgot because my teachers didn’t give me the chance to experience the fun in math. In my high school math classes, I felt dumb because I couldn’t memorize all the equations for the tedious amount of textbook problems we were assigned. When I came up with my own proofs to math problems in my math explorations class, it made me feel smart and important.

Math Explorations taught me what mathematics really is. It is an art form.

This class taught me how to think independently about not only math but other subjects and everyday problem solving.

I went in to this class saying, “I’m not good at math,” and I left this class saying, “I can do math.”

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.

I never would have discovered .999… and 1 are equal to one other, I would have never made such beautiful string art and learned the mathematical principles considered with it, I would have never been able to study a famous mathematician, and learned so many essential things about life in general, without this class. The ability to do conjectures and proofs, to discuss things in a more expanded light, to be able to write out how I got something and truly know why, are qualities I didn’t have before this class.

I always knew that I would see science or art or literature in real life, but no math class ever taught me that I would see mathematics in real life. Even now I catch myself seeing fractals or hearing about math things in songs.

As a student at Westfield State University, this course has had a profound impact on me. I have always had trouble with math and it has helped me look at it in a different light. It is now possible for me to look at mathematics as an art and something that is worth to explore.

Instead of falling asleep listening to lectures I was able to solve problems and make conjectures.

Math Explorations was undoubtedly the strangest and most enjoyable math class I have ever been enrolled in. I was engaged throughout the entire class and for once in my life not dreading math class when it came around.

Like I said before, I have hated math my entire life. I never had a love of math, not once in my life. I can sit here and say taking Mathematical Explorations, and the proofs we learned and the concrete material may never change my life. However, the **way** I was taught will affect me for the rest of my life.

…We were never told the cookie cutter way of finding an answer. We struggled, using trial and error and our own thoughts to find the answer to the problem. Yes, it was insanely frustrating. I cannot tell you how many times I wanted to throw my notebook out the window, or at my teacher (sorry Professor, it’s the truth). However, when I finally figured out the answer to the problem, I have never felt smarter. Here I was in math class, a subject I feared my entire life, feeling invincible. That’s right, invincible. For the first time in my life, I felt like I was fighting for my education. That is how you feel when you’re really learning.

In mathematics in the United States today, the focus is more of throwing a ton of information of steps and procedures for solving certain math problems and, completely disengages students from exploring solutions to problems on their own through experimentation and observing data to independently create a solution… School boards have completely made math a subject of throwing information at students, using the information to solve a problem step by step, expecting students to memorize the given steps for every type of possible problem for multiple subjects, and then determine a student’s future of continuing education on their ability to memorize all the tedious steps they were told.

…Math is no longer a student-engagement subject. Students are not give the time or encouraged to experiment with a math problem and find patterns for solving it.

…It is very difficult for me to look at a non-basic math problem and be able to know exactly what I have to do to solve it because, I have no personal experience of figuring out how to handle the type of problem through my own understanding.

…[In this course] I was encouraged and guided to engage in making the discoveries and understandings for myself. The techniques for how I found my solutions were very clear to me because, I was the one who found a pattern and applied the pattern to generate the solution. I have gained my own personal experience with mathematics that has changed my view on the subject completely.

I came home one weekend and I was discussing with my mother (She's and elementary teacher.) about your rule of answering a math problem in a complete sentence. I thought that was ridiculous and tedious. My mother then went on to explain that that is how math is being taught today. I finally understood your expectations from that point on.

From Math Is Still and Unnecessary Evil: "As you can see by the title of my paper, my feelings towards math have not really changed since the beginning of the semester...Maybe I'll try being a little more open-minded when it comes to my next math class.

When this class first started I thought I was going to run into the same problem I've always had with college math courses. I have gone into my past two math courses with a good attitude each time. By the end of a month each of the classes I had practically given up in...I love this class, I can't say enough about it.

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.

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 intimidates so many people, including myself, because of the way it has been taught in previous years and not one of my math teachers before now has asserted that it's not that hard if you take your time and not to move on until you're sure you understand. In my mind, the mathematical dogma and attitude from teachers that didn't seem to care if I really understood killed it for me.

I feel (although I shouldn't) that I have to prove to you and myself that I can do this and that I'm as smart as we think I am...This is what the class is about; writing math out and even if Einstein was in this class he'd be in the library with me for three hours so I'm going to get back to it now.

I've never had an affinity for math and I was so surprised by how easily I understood all the concepts we went over during the semester. I think that if all math classes were taught in the systematic and comprehensible way that this one was there wouldn't be so many people that don't like math...What I thought was really great was the fact that my mother, who teaches fourth grade, got some ideas from the text how to teach certain themes to her students in concrete terms they could understand.

I have to admit, I have never had a class like this, where learning is the most important factor.

I've done more math in this class than all of high school.

Deep down inside I know that I am a math struggler and this was by far the most that I have ever comprehended. Thank you, I had fun!

I described math to my family and they could not believe that I was actually enjoying the class. Because they know that I have had math phobia since sixth grade.

As the semester is about to end, the many weeks that I spent in your class were very educational, yet stress free. I have worked hard, like you said we would, but I feel that I really do understand the material and think that maybe all these years that I dreaded math and thought I was not good in it have changed.

No one had to be shy about asking questions and if you helped out a fellow student you felt smart, like you had learned something in a math class.

This course has gotten rid of my cynical point of view about math and taught me that it can be a beautiful subject.

I used to think that mathematics was all about adding, subtracting, multiplying and dividing numbers and letters and that I would never have any real use for it at all. This class has really made me more optimistic towards mathematics.

I can't say that my feelings about mathematics have changed. I think that this course was just an exception. I can still remember back to taking math tests in high school...

I really said these things to a friend when he asked about the class. So, believe it or not, you were right, I did end up liking the class. You win.

It made it less mundane than an ordinary math class with a professor mumbling into the blackboard and not really helping any students.

I had originally thought that my professor would be that of the likes of my Algebra 2 teacher. She had made us feel humiliated in front of the class if we did not know the answers.

I've always been good at math but I get board with courses like precalculus. Since I don't have any interest I don't want to learn it. What's unique about this course is the material we study actually means something to me. I can see how it's applied in the real world. That's interesting to me.

This class was truly unique. It was unlike any other class I have ever had. I had fun during class, and I learned from it at the same time.

I thought that the teacher would just stand up at the board and write a bunch of stuff that I wouldn't understand and then we would have a big test on it and I would fail. To my surprise, it was nothing like that.

I feel if math is taught like this in elementary schools at the national level the sky is the limit for us.

I will go into my next math course with a positive attitude, as opposed to the attitude I displayed when I entered this course.

Never in my life have I ever written a sentence in math. Since I am an English major, writing has always come a lot easier to me than math. It was wonderful to be able to express my thoughts on the subject...

I was somewhat impressed with the course from the beginning, but now I must say this is definitely the best math class I have ever taken.

The course uses both the teacher and the students to teach the material and this is very helpful to the students.

This is a class that you don't mind going to, because it does not put you to sleep.

I have always enjoyed mathematics and my view has not changed. I have never enjoyed a math class as much as this one though.

Now at the end of the course I feel like this is not a class to take lightly and that if you don't do your work then you'll get a bad grade.

All of my life math has not been one of my specialties and I have always dreaded going to math class. I wish that my elementary and high school teachers could have adopted your style while I was in their classes.

Non-mathematically, the course gave me a chance to organize my thoughts and answers to be clear and understandable. For instance, the write ups at the end of each section are monotonous but, the complete sentences remind me of how and why I got a specific answer.