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Thursday, May 28, 2009
CRUSADERS UNITE!
Related Rates Vid
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Question by Jamie
Slides by Jamie
POISONED BIRD!
Jamie's Bird Got Poisoned
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Question by Bench & Zeph
Slides by Zeph
TROUBLESOME PETS!
Troublesome pets.
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Question by Bench
Slides by Bench
BREAKDANCING BENCH!
Bench Can Breakdance?
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Question by Zeph
Slides by Jamie
Zeph's Reflection
1) Why did you choose the concepts you did to create your problem set?
Our Developing Expert Voices project puts a major emphasis on applications of derivatives and integrals: related rates and optimization for the applications of derivatives; solids of revolution and accumulation functions for the applications of integrals. We decided to focus our questions more on the concepts and less on the mechanics because that is what our exam would be like. For example, antidifferentiation was its own unit in the course. Since antidifferentiation is all mechanics, we decided to not create a question that puts a major focus on antidifferentiation. Instead, the antidifferentiation unit is scattered throughout the questions: Integration by Parts can be found in the Poisoned Bird episode, while Method of Substitution (Reversing The Chain Rule) can be found in the Crusaders Unite episode.
We also focused on those types of problems we have difficulty with. We looked at our BOBs (blogging on blogging posts found on our blog) and pinpointed our strengths and weaknesses in each unit and formed a question for our project based on those strengths and weaknesses. I remember we were iffy on how to solve optimization problems, so we decided to create a question based on optimization while incorporating material from another unit as well. By basing our questions on topics we had trouble with, practicing them improved our understanding of those topics.
2) How do these problems provide an overview of your best mathematical understanding of what you have learned so far?
We have chosen questions that would cover the majority of the course by creating questions that are similar to the free-response questions found in the Advanced Placement Calculus AB Exam and making sure that the variety of questions we created are diverse in terms of the concepts they ask. The amusement park question, for example, is a famous question that was asked on a previous exam which involved a rate flowing in and a rate of flowing out. The rate of flowing in and the rate of flowing out could be the rates at which people enter and leave the amusement park. Our Flood of Beetles episode has similarities to the amusement park question.
Our project’s theme is the views of mathematics, which can be viewed in at least three ways: graphically, numerically, and symbolically. Analogous to Mr. K’s favourite teaching tool—the block of wood, the block of wood represents the questions and each side of the block of wood represents one of the views. By being able to see and understand each view, we were able to gain a better understanding of the question that is being asked of us. This is shown in our Poisoned Bird episode, where we had to find the solution to the rate of poison via slope fields (graphically), Euler’s Method (numerically), and separation of variables (symbolically). Our young adventurers realize this in the Last Leg of Their Journey episode.
3) Did you learn anything from this assignment? Was it educationally valuable to you?
From this assignment, we practiced our time management skills. Everyone in our class is taking more than one AP class and everyone had other projects to work on, so timing was important. Since this was a teamwork project, we learned how to give and take, knowing that “we are all in this together” and everyone is “in the same boat.”
I find this project educationally valuable since it allowed us to explore many of the topics of the course and our strengths and weaknesses and practice our interpersonal and project management skills. By pinpointing our strengths and weaknesses and getting help from other team members, we are able to be better prepared for the exam.
Our Developing Expert Voices project puts a major emphasis on applications of derivatives and integrals: related rates and optimization for the applications of derivatives; solids of revolution and accumulation functions for the applications of integrals. We decided to focus our questions more on the concepts and less on the mechanics because that is what our exam would be like. For example, antidifferentiation was its own unit in the course. Since antidifferentiation is all mechanics, we decided to not create a question that puts a major focus on antidifferentiation. Instead, the antidifferentiation unit is scattered throughout the questions: Integration by Parts can be found in the Poisoned Bird episode, while Method of Substitution (Reversing The Chain Rule) can be found in the Crusaders Unite episode.
We also focused on those types of problems we have difficulty with. We looked at our BOBs (blogging on blogging posts found on our blog) and pinpointed our strengths and weaknesses in each unit and formed a question for our project based on those strengths and weaknesses. I remember we were iffy on how to solve optimization problems, so we decided to create a question based on optimization while incorporating material from another unit as well. By basing our questions on topics we had trouble with, practicing them improved our understanding of those topics.
2) How do these problems provide an overview of your best mathematical understanding of what you have learned so far?
We have chosen questions that would cover the majority of the course by creating questions that are similar to the free-response questions found in the Advanced Placement Calculus AB Exam and making sure that the variety of questions we created are diverse in terms of the concepts they ask. The amusement park question, for example, is a famous question that was asked on a previous exam which involved a rate flowing in and a rate of flowing out. The rate of flowing in and the rate of flowing out could be the rates at which people enter and leave the amusement park. Our Flood of Beetles episode has similarities to the amusement park question.
Our project’s theme is the views of mathematics, which can be viewed in at least three ways: graphically, numerically, and symbolically. Analogous to Mr. K’s favourite teaching tool—the block of wood, the block of wood represents the questions and each side of the block of wood represents one of the views. By being able to see and understand each view, we were able to gain a better understanding of the question that is being asked of us. This is shown in our Poisoned Bird episode, where we had to find the solution to the rate of poison via slope fields (graphically), Euler’s Method (numerically), and separation of variables (symbolically). Our young adventurers realize this in the Last Leg of Their Journey episode.
3) Did you learn anything from this assignment? Was it educationally valuable to you?
From this assignment, we practiced our time management skills. Everyone in our class is taking more than one AP class and everyone had other projects to work on, so timing was important. Since this was a teamwork project, we learned how to give and take, knowing that “we are all in this together” and everyone is “in the same boat.”
I find this project educationally valuable since it allowed us to explore many of the topics of the course and our strengths and weaknesses and practice our interpersonal and project management skills. By pinpointing our strengths and weaknesses and getting help from other team members, we are able to be better prepared for the exam.
Jamie's Reflection
1) Why did you choose the concepts you did to create your problem set?
I believe we came together and distributed questions from different units fairly, based on what each person could handle and based on our strengths. Even though, mathematically, I may not have done the most, I think it was really challenging since I decided to take on a question that reflected my weakness in class. That questions had to do with related rates. I think this was the whole point of the project, because we sort of act as students and teachers at the same time. We were supposed to challenge ourselves and our understanding by facing these problems and learning their patterns by nothing else but practice. You can't really get to know a question really, unless you make one yourself.
I believe the fact that we were prepping for the AP exam also played a big factor on how we chose our questions. We most likely chose challenging questions of diverse topics in calculus and made questions that could possibly show up on an AP exam so that we could practice.
2) How do these problems provide an overview of your best mathematical understanding of what you have learned so far?
Our questions consisted of almost every possible essential unit in calculus. From related rates to integration by parts, solids of revolution, and optimization. These were some of the hardest concepts that the course provided, but we chose to do them. It's not about taking the easy way out. Practice makes perfect. How are we supposed to practice if we don't "face our fear". Because of this practice, I think it deepens our understanding for the topic and that we learned from each other on both how to do these problems elegantly and efficiently. With a lot of time invested, I believe we tried our hardest to fulfill that, and may not have mastered these types of questions completely but know enough about them to recognize their patterns.
3) Did you learn anything from this assignment? Was it educationally valuable to you?
This was our last ever DEV project and honestly I'm so happy it's finally over. We were given countless extensions and I'm quite disappointed in myself because I think I could've done way better.
I feel like the quality of my work isn't as high as I would like it to be but I suppose I'm just too hard on myself. I just feel like I could've done so MUCH more with it given the amount of time we had to finish it. Doing this DEV though forced made me force myself to explore the concepts of calculus to my breaking point.
Being in two groups was really stressful and caused a lot of problems for not only me but my other group members as well. Having to finish one DEV is hard enough let alone finishing two. The experience did teach me a thing or two that wasn't math related. I really did learn to work in cooperation with my group members and the value of responsibility. It was my sense of responsibility that made me not want to give up on all the work for my two DEV's. I didn't want to let my group members down and I should have taken into account how much responsibility this is.
I believe we came together and distributed questions from different units fairly, based on what each person could handle and based on our strengths. Even though, mathematically, I may not have done the most, I think it was really challenging since I decided to take on a question that reflected my weakness in class. That questions had to do with related rates. I think this was the whole point of the project, because we sort of act as students and teachers at the same time. We were supposed to challenge ourselves and our understanding by facing these problems and learning their patterns by nothing else but practice. You can't really get to know a question really, unless you make one yourself.
I believe the fact that we were prepping for the AP exam also played a big factor on how we chose our questions. We most likely chose challenging questions of diverse topics in calculus and made questions that could possibly show up on an AP exam so that we could practice.
2) How do these problems provide an overview of your best mathematical understanding of what you have learned so far?
Our questions consisted of almost every possible essential unit in calculus. From related rates to integration by parts, solids of revolution, and optimization. These were some of the hardest concepts that the course provided, but we chose to do them. It's not about taking the easy way out. Practice makes perfect. How are we supposed to practice if we don't "face our fear". Because of this practice, I think it deepens our understanding for the topic and that we learned from each other on both how to do these problems elegantly and efficiently. With a lot of time invested, I believe we tried our hardest to fulfill that, and may not have mastered these types of questions completely but know enough about them to recognize their patterns.
3) Did you learn anything from this assignment? Was it educationally valuable to you?
This was our last ever DEV project and honestly I'm so happy it's finally over. We were given countless extensions and I'm quite disappointed in myself because I think I could've done way better.
I feel like the quality of my work isn't as high as I would like it to be but I suppose I'm just too hard on myself. I just feel like I could've done so MUCH more with it given the amount of time we had to finish it. Doing this DEV though forced made me force myself to explore the concepts of calculus to my breaking point.
Being in two groups was really stressful and caused a lot of problems for not only me but my other group members as well. Having to finish one DEV is hard enough let alone finishing two. The experience did teach me a thing or two that wasn't math related. I really did learn to work in cooperation with my group members and the value of responsibility. It was my sense of responsibility that made me not want to give up on all the work for my two DEV's. I didn't want to let my group members down and I should have taken into account how much responsibility this is.
Bench's Reflection
1) Why did you choose the concepts you did to create your problem set?
The Derivative and the Integral are the 2 major concepts of Calculus. So we tried to show as much of those as possible by using their many applications such as optimizing the volume of a box and accumulation functions. Also we wanted to show the concepts more than the mechanics because the AP exam itself measures understanding of concepts rather than how well the mechanical stuff is.
2) How do these problems provide an overview of your best mathematical understanding of what you have learned so far?
What the group tried to do was to work on questions that we were best at. We chose to do that because that would make the quality of the set of questions as high as possible for us and whoever is going to read it in the future. Some of us had questions that involved a weakness but we continued and actually got better at the concept. I remember hearing from Jamie complaining that she didn't feel good about working on the question involving related rates. Now after all of this is over, she feels much more comfortable with the concept. Even if the question wasn't a weakness, it still increased our understanding of the concept.
3) Did you learn anything from this assignment? Was it educationally valuable to you?
I didn't really learn anything new that was related to Calculus but I did increase my understanding of Calculus. Well I guess that can be considered learning something new. It took forever to make the functions for the optimization and differential equation questions.
For the optimization question, I was playing with the different parameters of the polynomial function. I was trying to make the shape of the function the way I wanted it to be. So I changed the parameters one at a time but as the number got more larger negatively and positively, the changes began getting more exaggerated. All of this experimenting with polynomial functions got me kind of frustrated. Once the general shape of the function was discovered, I was relieved and continued playing with the parameters to make it into a larger scale.
Differential Equations was a strength of Zeph and I, but when it came to thinking of a function, the tables were turned. It turns out that we were strong with the mechanics and some concepts. We weren't strong with understanding the differential functions and how to make them. It took a while and we agreed on a function that involved a cool trick. I won't talk about the trick here, it is your job to find out by reading the question.
------------------------------------------------------------------------------------------------------------------
To be honest, this project was such a hassle. The math part was enjoyable and useful for reviewing for the exam, but the presentation part killed me. The amount of filming and editing required was nothing I've ever done before. It's funny how I'm making this sound horrible.
The effort I put into the math was very helpful towards reviewing for the exam. Getting to work with other people on the questions was helpful as well because it allowed me to sometimes see another angle of a question. Making our own questions was quite entertaining because we tried to make the numbers fit the scenario, but most of it came out unrealistic.
Video Editing took a lot of my time. Time that I could have used in working on the questions. There were many difficulties but I learned how to fix them. Slideshare was messing up on me, telling me that my slide show had 700 slides, which made me use up even more time in fixing the slides.
Overall, I had fun. I think my group had fun.
The Derivative and the Integral are the 2 major concepts of Calculus. So we tried to show as much of those as possible by using their many applications such as optimizing the volume of a box and accumulation functions. Also we wanted to show the concepts more than the mechanics because the AP exam itself measures understanding of concepts rather than how well the mechanical stuff is.
2) How do these problems provide an overview of your best mathematical understanding of what you have learned so far?
What the group tried to do was to work on questions that we were best at. We chose to do that because that would make the quality of the set of questions as high as possible for us and whoever is going to read it in the future. Some of us had questions that involved a weakness but we continued and actually got better at the concept. I remember hearing from Jamie complaining that she didn't feel good about working on the question involving related rates. Now after all of this is over, she feels much more comfortable with the concept. Even if the question wasn't a weakness, it still increased our understanding of the concept.
3) Did you learn anything from this assignment? Was it educationally valuable to you?
I didn't really learn anything new that was related to Calculus but I did increase my understanding of Calculus. Well I guess that can be considered learning something new. It took forever to make the functions for the optimization and differential equation questions.
For the optimization question, I was playing with the different parameters of the polynomial function. I was trying to make the shape of the function the way I wanted it to be. So I changed the parameters one at a time but as the number got more larger negatively and positively, the changes began getting more exaggerated. All of this experimenting with polynomial functions got me kind of frustrated. Once the general shape of the function was discovered, I was relieved and continued playing with the parameters to make it into a larger scale.
Differential Equations was a strength of Zeph and I, but when it came to thinking of a function, the tables were turned. It turns out that we were strong with the mechanics and some concepts. We weren't strong with understanding the differential functions and how to make them. It took a while and we agreed on a function that involved a cool trick. I won't talk about the trick here, it is your job to find out by reading the question.
------------------------------------------------------------------------------------------------------------------
To be honest, this project was such a hassle. The math part was enjoyable and useful for reviewing for the exam, but the presentation part killed me. The amount of filming and editing required was nothing I've ever done before. It's funny how I'm making this sound horrible.
The effort I put into the math was very helpful towards reviewing for the exam. Getting to work with other people on the questions was helpful as well because it allowed me to sometimes see another angle of a question. Making our own questions was quite entertaining because we tried to make the numbers fit the scenario, but most of it came out unrealistic.
Video Editing took a lot of my time. Time that I could have used in working on the questions. There were many difficulties but I learned how to fix them. Slideshare was messing up on me, telling me that my slide show had 700 slides, which made me use up even more time in fixing the slides.
Overall, I had fun. I think my group had fun.
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