We did learn some good practical application concepts about calculus, and WE WOULD BE VERY COMFORTABLE PRESENTING THIS PROJECT IN A GROUP ATMOSPHERE. [...] The project was an interesting application of the concepts presented in class, but not entirely realistic. IT WAS DEFINITELY BETTER THAN THE CONE FILLING PROBLEMS ON THE AP TEST. It would be nice to expand this topic into a class discussion, with real-life examples instead of more variables. [Matt Danzeisen]
"at least in our case, everyone in the group worked very well together and all got something out of pooling our ideas to solve this problem" [Emily Chiang]
The aspect about the project that I liked the most was the fact that it showed us a real life example of how calculus is actually applicable in life...Since it was a word problem, we had to figure out what was being asked of us. Then, we had a little difficulty in figuring out how to go about finding the answers. But, once we got started, things moved fairly quickly [Christine Ellis]
I did enjoy the project, although it wasn't terribly difficult. There were several intricacies that made it thought-provoking, but that was good. [Rob Lewin]
ALTHOUGH IT MAY SOUND BAD, I LEARNED THAT CALCULUS CAN BE INTERESTING. In my old high school, we basically memorized everything and didn't really knew what meaning it had. [...] I think that each group should have a balance of people who really know what they're doing and those who have more trouble. This way, each person in the group can benefit from each other.
I think that the project was interesting. It showed a real application of the techniques that we were learning. It made the abstract calculus I learned in high school into something more tangible and realistic. I THINK THAT THE PROJECT CONCEPT IN CALCULUS CLASS IS EXTREMELY IMPORTANT TO TRULY UNDERSTAND THE VALUE AND MEANING OF THESE TECHNIQUES. [Connie Liu]
Solving the problem went pretty well. It was more challenging, but working in groups helped because someone else could help you out where you got stuck and vice versa...some techniques [which we used] have been routine for many years, yet when it was time to [rigorously] explain them it was difficult. The groups seemed to work well together. Everyone seemed to contribute and listen to suggestions that others made. (It seemed that while some people were working on one part of the problem, others were checking if those methods were correct -- in other words the group members seemed complimentary) --Laura Oremland
I liked working as a group on challenging problems. I learned how to
apply many variables and equations from written text to mathematical
equations. I also learned about how to justify each step I did.
Our group worked really well together. We all shared ideas and weren't afraid to state our minds if something went wrong. WE WORKED EFFICIENTLY CUZ WE ALL THINK DIFFERENTLY AND CAN SEE DIFFERENT SIDES TO A PROBLEM. [Laura Rossier]
WHAT I LIKED ABOUT THE PROJECT WAS THAT IT WAS A BIT CHALLENGING, NOT TOO EASY TO SOLVE, AND TRICKY.[...] I think that the idea of helping Houdini to solve one of his incredible stunts is appealing. The project introduced me into more depth with the material because there was no common guideline to follow, we had to think about how to solve the problem. [Juan Zurita]
Doing this project I was able to see and use calculus in a more practical and visual atmosphere. We did get stuck on part b but we were able to find the answer easily after we thought about it for a while. [...] I FOUND THE PROJECT TO BE INTERESTING. IT TAKES YOU AWAY FROM THE EVERYDAY ATMOSPHERE IN CLASS. IT ADDS A DIMENSION AND LOOK TO CALCULUS. IT REQUIRES THINKING INSTEAD OF MEMORIZATION. IT WAS LIKE A BRAIN TEASER. I DEFINITELY FELT IT WAS BENEFICIAL. [Kiuk Han]
I enjoy[ed] seeing how calculus can be used to apply to situations in the real world. The most difficult part of the project was to organize our thinking with so many variables and equations floating around.[...]The project was interesting, for a math problem. I wouldn't go so far as to characterize it as "fun", but I didn't really mind having to work on it [Matt Christianson]
I personally had a really nice time working together with my group on the Houdini project. The problem itself was fairly interesting and definitely served the purpose of demonstrating simple practical uses of calculus.
I found it interesting to work with other people on the project just as researchers might do (of course, on a much much smaller scale)
IT WAS NICE TO SHARE THE WORK FINALLY IN MATH. I had a good time with it. I DEFINITELY FEEL MORE COMFORTABLE KNOWING THE INTERPLAY BETWEEN MERELY SOLVING A PROBLEM GIVEN AND DERIVING SOLUTIONS FROM BASIC INFORMATION GIVEN. THIS WAY ONE CAN SOLVE ANY PROBLEM once you know the relationships between volumes, distances, intervals and rates of change. I AM LOOKING FORWARD TO THE NEXT PROJECT [Emph added -HB]. [Jigyasa Chander]
I THINK EVERY TIME I SOLVE A PROBLEM OUTSIDE A MATH TEXTBOOK, IT REINFORCES MY UNDERSTANDING THAT CALCULUS IS USEFUL. [...] We brainstoirmed quite well together -- we bounced ideas off each other to mutual advantage. [...] [The Houdini Project] definitely grounded my understanding much more substantially [Louise Siddons]
worked really well together. We got to know eachother well, too, so we were able to be completely open about what we thought worked and didn't work. I think we worked very efficiently, too. We systematically went through each section, everyone stating their disagreements as we went along. [...] The project was interesting because it showed how calculus can be applied to real life situations. [Melissa Rethy]
Harel, I enjoyed the project. I thought it was a great rate of change problem that involved a thorough understanding of calculus. I didn't think that it was too hard but as it turned out, my group primarily used my calculations, for they told me that they didn't understand some parts. I therefore explained the parts that they didn't understand to them. We were able to meet as a large group a few times and in small groups at other times. [Appendix for Phil] For the most part, we cooperated well, but there were times that we were in disagreement but we worked things out. Everyone contributed, but not equally. Laura did most of the note-taking, I did most of the calculations, Phil did most of the typing, Connie made the diagram and made inputs whenever possible. I THOUGHT IT WAS A GREAT PROBLEM. It really tested our knowledge of calculus. I felt that we had to water down our writeup. It might be fun to explain the project in class. I generally have a hard time dealing with disagreement, but I learned from this project that it really is not good to be stubborn. [Nathan Jauvtis]
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