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.