{"id":44,"date":"2024-04-30T01:35:22","date_gmt":"2024-04-30T01:35:22","guid":{"rendered":"https:\/\/blog.richmond.edu\/emma-brashear\/?page_id=44"},"modified":"2024-04-30T01:46:29","modified_gmt":"2024-04-30T01:46:29","slug":"calculus-ii-final-reflection","status":"publish","type":"page","link":"https:\/\/blog.richmond.edu\/emma-brashear\/calculus-ii-final-reflection\/","title":{"rendered":"Calculus II Final Reflection"},"content":{"rendered":"

This semester in Calculus II, I feel as though I have really integrated my learning between biology, chemistry, and calculus. One aspect that highlights a clear connection between the disciplines is through the calculus labs. For example, in Lab 3<\/a>, which was for the qPCR analysis, we graphed the data for the cycle numbers and the log of the ng gene. The only way we were able to graph this was because of the calculus techniques. We had to use calculus-based equations to find the slope and intercept of the data, for example. The resulting graph was especially useful in explaining our results. It was so helpful that it was even showcased on our research poster that we presented at the A&S symposium.\u00a0<\/span><\/p>\n

Another example of this integrative learning is through graphing chemical equations using calculus programming. Lab 7<\/a> really highlighted how enzymatic reactions occurred over time. Funnily enough, this was a topic that I had struggled to grasp before this lab. Once completing this lab, however, I felt like I had a much better understanding of the topics. For example, the graph that included both the Vmax and KM values really helped illustrate the relationship between concentration and time. Overall, these labs both helped solidify and explain many of the concepts that are occurring in the natural science side of this Endeavor course.<\/span><\/p>\n


\n<\/span>One concept that I really struggled with in Calculus II is Euler\u2019s method.<\/a> Even though I completed this lab in class, I still had no clue what Euler\u2019s method was or how to put it into a spreadsheet at all. The first time that I submitted the lab for Euler\u2019s method, Aidan Hills did not even grade it because I was so lost. After reviewing Euler\u2019s method on my own, I reattempted the lab, just to feel more confused than before. I still did not get it. So, I eventually went to office hours to discuss the overall topic of Euler\u2019s method. Even though I think I understand the principles of Euler\u2019s Method now, I still don\u2019t think I will ever understand the lab. And that is okay.\u00a0<\/span><\/p>\n

Through this process, I developed a lot of adaptability and resilience. For example, I learned to fully utilize the resources that I have, whether that be through Khan Academy videos or through visiting office hours. I also learned that I should go to office hours sooner rather than later, especially when I seem to be repeatedly not grasping a concept. I also learned that it is okay to adapt and take your losses when you need to. I realized that I needed to fully get the other topics in Calculus II in order to make up for not grasping this one. This is an important life lesson to cut your losses when you can.<\/span><\/p>\n

One portion of collaborative learning that I have learned to love is team quizzes. At first, it was difficult to learn how to collaborate with three people, especially when we all got different answers to the problem. Now, however, I love team quizzes. They are a great way to both check my work with my peers and also work as a team to fully come up with solutions. For example, in Team Quiz for LT 14<\/a>, each one of our team members contributed a different aspect to the solution. For example, I found all the derivatives for the functions and their values when x equals 0. Then, Ryan remembered the exact form for the Taylor\u2019s Series. Then, Yvonne was able to use this information to come up with our full solution. Without all three of us, we never would have come to a full answer.<\/span><\/p>\n

Another portion of collaborative learning that I have really engaged with is sharing my work on the board. In class, there are opportunities to share our thinking with our peers. I try to always put my work up at least once during a class period. Even though this sometimes makes me nervous to put myself out there, I realize that even sharing a wrong way of thinking can be helpful. It is better to share what I have and explain how I got there, so that everyone can learn from my mistakes. Along this same line, I also love participating in whole class discussions. If there is ever a controversy on how to solve a problem, I love to put in my opinion, because I know that this is both a learning opportunity for myself and for my classmates. <\/span><\/p>\n

I feel that throughout the semester, I have really improved my communication of quantitative information. Last semester, I would rarely use words in any of my math problems. This semester, I have learned the importance of using both words and numbers within my solutions. This is necessary for both assessments and whenever I do practice problems or homework. For example, in CP LT12 LT13 LT14<\/a> from the first semester, I only have numbers, making my thought process hard to follow. This semester, however, I learned how to use words to clearly explain my different steps throughout a problem. For example, in CPLT1 and LT3<\/a>, I use a full sentence to explain why I would use integration by parts for this issue. This is much different than in my previous work, where I would only write the numbers and that was it.<\/span><\/p>\n

I think that communicating quantitative information is also a big area of growth for me to work on. Even though I have greatly improved on my ability to use both words and numbers in my explanations, this is not a skill that I consistently use throughout every problem I solve. I think it would be really beneficial for me to continue to use this technique, regardless of how many people may see my work. It would also be good for me to follow my thinking when looking back on my own work. But, it would also be equally beneficial when sharing my thinking with the class, for example. It is already difficult to understand a person\u2019s thinking when they are just writing on the whiteboard, so it is best if I write words as well so that everyone can understand my logic. <\/span><\/p>\n



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This semester in Calculus II, I feel as though I have really integrated my learning between biology, chemistry, and calculus. One aspect that highlights a…<\/p>\n

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