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.
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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.
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The emphasis is on bringing out clear ideas. I have never had to write complete sentences for math class, or type out the homework. Typing out and writing out sentences takes just as long as studying for a test or quiz. I learn more, to get my ideas across and they are more clear.
Maybe I'll learn more instead of trying to cram information into my head and not remembering the next day.
I can tell right now that this mathematics class will be very different from any math class I've ever had.
My teacher seems pretty cool too. He actually talks to us as people and not just 'some students'.
As I wrote out the final math problems I was surprised how much work I put into the assignments throughout those few weeks. I believe tests wouldn't reveal that much.
Today we discussed the DNA possibilities in the O.J. trial. It is kind of funny how we really didn't understand how large 250 million is.
The math we're doing is like tricky math. It's no algebra or geometry, it's more complicated, more fun.
I'm really impressed with how we are graded in this class. That says that with hard work and class participation everyone will be able to get a good grade.
It's alot more work than I thought it would be. It's better than having a test though.
Maybe for the first time in my life I'll get better than a 'C' in math.
I must say that this is quite a strange math class, but I like it.
Well, it seems strange to write a journal for a math class, but this doesn't seem like an average math class.
It seems like it's going to be a lot of fun, and it seems like it might be easier than an actual class, but I'll probably learn more.
I still feel very confident and having a good attitude about the class I am willing to put alot of time and effort to get a good grade knowing that you set up the class in a way in which we as students can succeed makes me feel at ease and a willingness to work hard.
I wish I could write you that I wanted to become a math major now, but that isn't the truth. This class was definitely better than trigonometry or calculus that I took in high school. Meaning more fun. I learned things that I might actually use in life sometime. But I don't think it was easier... You know what I mean? Math has always been hard for me, I've had to put in more effort than anyone just to get by.
By making the course available to students, we are given a chance to broaden our mathematical horizons. Much of the material involves creative thinking and common sense, so the average non-mathematician is given a shot at math success, thus building confidence for future mathematical endeavors. My past mathematical experience, I'm sorry to say, is nothing short of horrid.
...it will help me make math fun for my children. I can also see how a person can love math and I respect that.
This course showed me a different view of math. It worked with objects and figures rather than numbers. I thought in logic rather than in numbers.
I used to consider math was just a number course and nothing else. Now I see it as an art and a class to be creative in.
I was happy to come to class every day and that says something about the course.
For once in my life I think that mathematics doesn't have to be awful.
When I first came to this class I anticipated the worst. I was sure this class was going to be like every other class: I would probably just pass with the help of a patient tutor. However, this class wasn't like that at all, in fact it made me realize that I am not as bad in Math as I thought I was. I was allowed to ask as many questions as I needed to understand the ideas involved. I actually began to enjoy the subject that I had for so long despised. I began to see and understand why math was so important.
The topics we covered were cool, for once I enjoyed doing the work because it was interesting. I have trouble doing things I'm not interested in.
Your unique way method of teaching and class formation made it an interesting class to attend. The time went by fast and the work was interesting.
I realized that math is much more than what we have been exposed to in elementary school, junior high, and high school. I've realized that there is a lot of intellectual thinking involved, it is not just right and wrong numerical answers. I never really could understand how people believed that mathematics was an art but now I see how reaching an unsolved conclusion could give such a great feeling of accomplishment.
Overall I thoroughly enjoyed the class, and I dislike math a little less because now I see it can be interesting.
I guess I have an appreciation towards mathematics. I understand people devote their lives to finding the contrasting rule to a law or formula and I think that's cool.
My attitude toward math hasn't changed that much except for the fact that know I can appreciate how some people, like yourself can have such a passion for mathematics.
Hopefully I'll be able to tell my children how fun and interesting this class was and more importantly how much I learned about what mathematics really is.
When I first heard you say that math "was beautiful" I thought you were a little strange. However, now after experiencing what math can really do mentally and physically, I can say that math is beautiful when you are taught right.
These ideas of math are part of everyday life, but society doesn't take in the true meaning and significance of math.
Math can be fun and exciting if you teach students to "understand" something rather than just memorizing it.
Thank you for this wonderful class and experience.
The first thing I noticed as I walked into room were the benches. Already I was put at ease because the traditional '5th grade' desks were not there. Then when we were handed the survey and I was some of the questions regarding our feelings about math, I was excited because I knew we were having a teacher who cared as much about our feelings as he cared about numbers and equations.
But like I have told you I would have rather taken tests. Nothing against you or the class that is just my preference.
I really like the way this class is set up this semester. I like working things out with people at my table. We work well together which helps. I do wish that the Professor would teach a little bit more, but then again, I don't know what he could because it's all in the book. I do like it when he'd read things as passages from books, articles, etc.
This class reminds me somewhat of my high school math classes. In high school I never understood what the teacher was talking about. So during class I would look at the lesson in the book and teach myself. I didn't mind doing this. That's when I liked math. In college I've taken to classes and had trouble with them. All they did was lecture. This class brings me back to the ways when I liked math.
The Math in this class is something I've never experienced in any other Math class. Most of my Math classes were always problems with numbers that a calculator could figure out. There were never problems that involved much thinking.
This math class, much to my surprise is very different. My views and hopes are slowly changing about math. I now feel a little more confident in my abilities.
For a guy who is reluctant to give math a chance I must admit that classes like Mathematical Explorations help broaden the minds of students like myself.
The lack of tests and homework in this class is a refreshing change. I am used to studying page after page of formulas and tables in math class. But this class is different and I like it. When math is shoved down my throat I cannot learn. The "pressure thing" again. I learn better when I can see the process step by step.
It was a nice break from the do-it-know-it-or-fail type math course in high school or any other arithmetic course. Granted, I have to know these skills and be able to do them without much difficulty. But it was good to be able to take a course that really just shows math as a form of art and (dare I say it?) philosophy.
You've shown how someone can see beauty and passion in mathematics. Your passion for mathematics really is inspiring considering the fact that most of my past math teachers didn't really care. They didn't have that fire in their eyes that you have. You want to share what you know and expand on it.
I now appreciate my father's intellect for being an engineer. I used to think he was boring for knowing all this math, but I now see that his thought process goes well beyond just numbers.
When I first came to class in the beginning of the year you were always talking about how math was so beautiful. When I heard you say this I was like, what is this guy talking about? But as the year went on I started to think about the beauty of math more and more. Math is pretty beautiful! Math is everywhere, it is in all art work and designs. I love art and I love to draw and paint, so I guess math is beautiful to me also.
When our class began doing work in Chapter 11 [Discovering the Art of Mathematics - The Infinite], I thought I was in hell. Your handout was much more difficult than the book [Mathematics: A Human Endeavor by Harold Jacobs]. At that point, although it was a good thing, I thought it was going to be too hard and wanted to go back to the book. However, after spending time on Chapter 11, that challenge is exactly what I needed. It was in Chapter 11 that I gained my appreciation for the differing levels of infinity and some of Zeno's paradoxes. It was not until we went back to the book at the end of class that I realized that the book was no challenge at all. It was the challenge that I received in Chapter 11 that helped me to appreciate mathematics.
One of the most surprising things about this class is that I actually like being here, which is weird because every other math class that I have ever had has sucked and been boring.
I do like the fact that this class isn't boring. I tend to want to understand the work because I can't get into something if I am not actually doing it. When professors teach math generally they show you how to do something on the board when half the class is doodling in their notebooks and then they expect you to be masterful at it on a test.
This is who I was meant to be
It all started in the beginning with Mobius bands,
When we began using everyday math with our hands.
It instantly opened up my perspectives on how I view life,
For the first time I felt a sense of sharpness, like a knife.
I honestly started to view things differently,
Or at least, with a sense of pure, complete decency.
But that... that, was just the beginning.
As we moved forward with our assignments in class,
I began looking at everyday things with an open mind, at last.
When we faced those difficult challenges every day,
"I can do it. I won't give up. I'll expand my mind!" I would say.
I began to realize that maybe math was an interest of mine.
For the first time, this class literally made me shine.
I would get so mad sometimes, I would want to give up.
I never did though; I used the phrase that relates to a cup.
"It's a glass half full, not half empty" I would tell myself.
Eventually, I was able to put my worries up high away on a shelf.
I swear it was like a breathe of fresh air.
That moment I realized this class and I were a perfect pair.
No matter how much of a struggle it was,
I will never regret the mistakes I made... just, because.
Because I now know how to face academic challenges,
The class literally took away all of my regrets and salvages.
In the beginning I thought I was going to fail,
But that didn't stop me... I decided I was going to set sail.
This class was one hundred percent a turning point,
I can't stress enough, I'm happy I wound up in this joint.
I never would have expected this from a class,
But wow... I finally feel a sense of being free, at last!
Everything from the Mobius bands, string art and Maypole dancing,
Each topic made me stronger, and now I feel like prancing.
I know how to look at obstacles with a different state of mind,
It really is something that's truly one of a kind.
Thank you, Dr. for never giving up on me,
One day you will see, this is who I was meant to be.
If ever in the future I meet a mathematician I won't say something corny like I can't balance my checkbook.