Growth and Development Reflection
Student Led Comment (Semester 1)
Dear Ms. Gonzalez Coloyan,
I really appreciate all that you have done to make this a great math class. This has been the best semester of math that I have ever had. In your class I have made made work that I am proud of.
For example, I am most proud of the board game, an interactive infographic, that I made and presented during the Mind the Gap symposium. I had to collect data and display that data in a way that would be interactive. I created a game board based off of the board game "LIFE" that used the pie charts that I had created as the spinners as the decision points where different paths branch off. The game board took a lot of skills that I did not have before this class. For example, I had to learn what types of graphs to use to display the data I was dealing with. I also had to learn how to input data and make formulas in google sheets to be able to make the graphs. I also had to understand the economic concepts that fuel the disparities between different economic groups of people. I had to understand the difference between rich and poor banking, the effects of compound interest on savings and debt. All of this knowledge culminated in the board game. It was a big success. People really liked playing the game and were more eager to listen to what I and my group members had to say.
I set three goals for myself at the beginning of the semester. I achieved my goals on the first two of my goals. My first goal was to get more comfortable with using several approaches to try and solve a difficult problem so I could solve it without getting discouraged and giving up. I have accomplished this goal. I have persisted in trying to solve all the problems I encounter while not getting discouraged. One of the hardest things for me to understand this semester were the compound interest formulas and annuities formulas. I was confused when to use which formula and where to put the information I had into that formula.
For example, when I was working on the “Paying for College” activity I had to calculate my monthly payment to pay off my college loans. At first, I was unsure whether I should use the compound interest formula or the annuities formula. I thought I should use the compound interest formula, because I was more comfortable with that formula at the time. I got an answer that seemed very improbable so I tried using the annuities formula. This was the right formula but unfortunately I calculated my present value (PV) which is completely different from the monthly payment (C). That answer seemed off so I asked several of my friends how they did it. I found out that I had been using the right formula but solving for the wrong variable. Finally, I knew which formula to use and which variable I was solving for.
Getting the correct answer was a difficult and time consuming process. I went in the wrong direction several times but I learned from each mistake instead of getting discouraged and giving up. Through my persistence, I was able to solve the problem and gain an understanding of which formula to use when.
Being more willing to experiment with several different approaches without getting discouraged helped me to accomplish my second goal, which was to know what to do when I encounter certain kinds of problems. At the beginning of the year, I planned to familiarize myself with formulas and rules that I had not memorized. I have succeeded in this task. I am most proud of memorizing many of the rules for exponents and logarithms. I studied the formula pages that I got at the beginning of class and also used acronyms to help me memorize certain rules.
For example, the acronym BAE helps me remember how to change an exponent into a logarithm and vice versa. BAE stands for Base, Answer, Exponent. This means that if I have the equation 5x=7 I can rearrange to formula to become a logarithm by making 5 (the base) the base of the exponent, making 7 (the Answer) the big number in the logarithm and putting x (the exponent) on the other side of the equals sign. This means that 5x=7 is equivalent to log57=x. I can now solve for x because it is isolated.
Throughout this entire semester, I found two main concepts the most significant. The first concept was economics. Specifically, compound interest, annuities and their relationship to savings, debt and accomplishing my financial goals. The second concept was statistics. Specifically, using descriptive statistics to interpret data and display it through graphs.
Learning about economics helped me to create a personal financial plan that contained the cost of my desired college and how I would pay for it, the taxes that I would have to pay based on my estimated income after college, a short term, mid term and long term investment with the monthly payments I would have to make in order to achieve them and a monthly personal budget (based of of my estimated income).
All of the calculations were based off of estimates, but calculating the money that I could gain through savings and the money that I could lose through debt helped me to understand the importance of planning out my economic goals with my economic realities in mind. Setting hypothetical, yet realistic, financial goals for myself has equipped me with the tools that I will need to calculate the cost of the choices I make.
When I am accepted to college and receive my financial aid package, I can use the skills i learned in this class to see what my college debt and return on investment will most likely be. When I start my first professional job after college, I can use the skills that I learned in this class to make a monthly budget and calculate how much money I have to save each month to achieve my goals.
Learning about descriptive statistics helped me to understand that data can be used to help people visualize facts. I also learned how different ways of displaying the same data can send different messages to the viewer. For example, I had a data set from the Kaiser Family Foundation that gave the 2013 US poverty rates by race in each state. I decided to display the different poverty rates as a histogram on Google sheets. Google sheets generated histograms automatically but as I experimented with the advanced edit, I realized that I had a lot of power over how the data looked and, in turn, the message it conveyed.
By increasing or decreasing the bucket size of each histogram, I could make the poverty rate of different rates seem small or huge. A bigger bucket size made the poverty rates look higher for some races because it grouped more poverty rates into one bar. Similarly, decreasing the bucket size made more bars, but each bar was lower because less percentages fit into the same bar. When my classmates saw a few really tall bars, they thought that the poverty rate was higher than when they saw many short bars. I had showed them the same exact data, but by showing it in different ways I sent different messages.
Throughout this semester, I have gained so much mathematical knowledge and experience. I believe that I have not only taken but also contributed to the class environment by being an engaged and active student. I have asked questions whenever I need clarification. Sometimes, I also ask a question when someone at my group has a question but does not want to ask it. I also always collaborate with my peers at my table on the warm up problems at the beginning of class and during class activities. I propose my ideas and give my peers feedback on their ideas as much as possible. Finally, I seek help from my peers around the class and give help to those who ask.
Next semester, I want to be prepared for the tests that I am going to take such as the SAT, ACT and Math 2 Subject Test. I have studied several of the concepts in the Math 2 Subject Test book, but there are still some that I have study. I want to be prepared to the best of my ability for all of the different topics that the math tests cover. I would also like to learn more about inferential statistics and the equations behind probability. I am very interested in the math behind reasoning and judgment. I also plan on continuing to be an engaged and active student. I will continue to ask questions whenever I need clarification. I would like to plan out the assignments more ahead of time. I need to look at the syllabus for next semester and fill out the due dates on my calendar so that I turn all of my assignments in on time and organize my work so that it is easy to find when I need it.
Thanks to you, I have learned how to use mathematical concepts that I never even knew about before such as economics, statistics and probability. I have really enjoyed the learning environment that you create in your class. I feel comfortable not getting a mathematical concept immediately because both you and my peers are supportive and willing to explain the concepts to me. I look forward to being in your class next semester.
Happy Holidays!
Sincerely,
Sol Manuel
I really appreciate all that you have done to make this a great math class. This has been the best semester of math that I have ever had. In your class I have made made work that I am proud of.
For example, I am most proud of the board game, an interactive infographic, that I made and presented during the Mind the Gap symposium. I had to collect data and display that data in a way that would be interactive. I created a game board based off of the board game "LIFE" that used the pie charts that I had created as the spinners as the decision points where different paths branch off. The game board took a lot of skills that I did not have before this class. For example, I had to learn what types of graphs to use to display the data I was dealing with. I also had to learn how to input data and make formulas in google sheets to be able to make the graphs. I also had to understand the economic concepts that fuel the disparities between different economic groups of people. I had to understand the difference between rich and poor banking, the effects of compound interest on savings and debt. All of this knowledge culminated in the board game. It was a big success. People really liked playing the game and were more eager to listen to what I and my group members had to say.
I set three goals for myself at the beginning of the semester. I achieved my goals on the first two of my goals. My first goal was to get more comfortable with using several approaches to try and solve a difficult problem so I could solve it without getting discouraged and giving up. I have accomplished this goal. I have persisted in trying to solve all the problems I encounter while not getting discouraged. One of the hardest things for me to understand this semester were the compound interest formulas and annuities formulas. I was confused when to use which formula and where to put the information I had into that formula.
For example, when I was working on the “Paying for College” activity I had to calculate my monthly payment to pay off my college loans. At first, I was unsure whether I should use the compound interest formula or the annuities formula. I thought I should use the compound interest formula, because I was more comfortable with that formula at the time. I got an answer that seemed very improbable so I tried using the annuities formula. This was the right formula but unfortunately I calculated my present value (PV) which is completely different from the monthly payment (C). That answer seemed off so I asked several of my friends how they did it. I found out that I had been using the right formula but solving for the wrong variable. Finally, I knew which formula to use and which variable I was solving for.
Getting the correct answer was a difficult and time consuming process. I went in the wrong direction several times but I learned from each mistake instead of getting discouraged and giving up. Through my persistence, I was able to solve the problem and gain an understanding of which formula to use when.
Being more willing to experiment with several different approaches without getting discouraged helped me to accomplish my second goal, which was to know what to do when I encounter certain kinds of problems. At the beginning of the year, I planned to familiarize myself with formulas and rules that I had not memorized. I have succeeded in this task. I am most proud of memorizing many of the rules for exponents and logarithms. I studied the formula pages that I got at the beginning of class and also used acronyms to help me memorize certain rules.
For example, the acronym BAE helps me remember how to change an exponent into a logarithm and vice versa. BAE stands for Base, Answer, Exponent. This means that if I have the equation 5x=7 I can rearrange to formula to become a logarithm by making 5 (the base) the base of the exponent, making 7 (the Answer) the big number in the logarithm and putting x (the exponent) on the other side of the equals sign. This means that 5x=7 is equivalent to log57=x. I can now solve for x because it is isolated.
Throughout this entire semester, I found two main concepts the most significant. The first concept was economics. Specifically, compound interest, annuities and their relationship to savings, debt and accomplishing my financial goals. The second concept was statistics. Specifically, using descriptive statistics to interpret data and display it through graphs.
Learning about economics helped me to create a personal financial plan that contained the cost of my desired college and how I would pay for it, the taxes that I would have to pay based on my estimated income after college, a short term, mid term and long term investment with the monthly payments I would have to make in order to achieve them and a monthly personal budget (based of of my estimated income).
All of the calculations were based off of estimates, but calculating the money that I could gain through savings and the money that I could lose through debt helped me to understand the importance of planning out my economic goals with my economic realities in mind. Setting hypothetical, yet realistic, financial goals for myself has equipped me with the tools that I will need to calculate the cost of the choices I make.
When I am accepted to college and receive my financial aid package, I can use the skills i learned in this class to see what my college debt and return on investment will most likely be. When I start my first professional job after college, I can use the skills that I learned in this class to make a monthly budget and calculate how much money I have to save each month to achieve my goals.
Learning about descriptive statistics helped me to understand that data can be used to help people visualize facts. I also learned how different ways of displaying the same data can send different messages to the viewer. For example, I had a data set from the Kaiser Family Foundation that gave the 2013 US poverty rates by race in each state. I decided to display the different poverty rates as a histogram on Google sheets. Google sheets generated histograms automatically but as I experimented with the advanced edit, I realized that I had a lot of power over how the data looked and, in turn, the message it conveyed.
By increasing or decreasing the bucket size of each histogram, I could make the poverty rate of different rates seem small or huge. A bigger bucket size made the poverty rates look higher for some races because it grouped more poverty rates into one bar. Similarly, decreasing the bucket size made more bars, but each bar was lower because less percentages fit into the same bar. When my classmates saw a few really tall bars, they thought that the poverty rate was higher than when they saw many short bars. I had showed them the same exact data, but by showing it in different ways I sent different messages.
Throughout this semester, I have gained so much mathematical knowledge and experience. I believe that I have not only taken but also contributed to the class environment by being an engaged and active student. I have asked questions whenever I need clarification. Sometimes, I also ask a question when someone at my group has a question but does not want to ask it. I also always collaborate with my peers at my table on the warm up problems at the beginning of class and during class activities. I propose my ideas and give my peers feedback on their ideas as much as possible. Finally, I seek help from my peers around the class and give help to those who ask.
Next semester, I want to be prepared for the tests that I am going to take such as the SAT, ACT and Math 2 Subject Test. I have studied several of the concepts in the Math 2 Subject Test book, but there are still some that I have study. I want to be prepared to the best of my ability for all of the different topics that the math tests cover. I would also like to learn more about inferential statistics and the equations behind probability. I am very interested in the math behind reasoning and judgment. I also plan on continuing to be an engaged and active student. I will continue to ask questions whenever I need clarification. I would like to plan out the assignments more ahead of time. I need to look at the syllabus for next semester and fill out the due dates on my calendar so that I turn all of my assignments in on time and organize my work so that it is easy to find when I need it.
Thanks to you, I have learned how to use mathematical concepts that I never even knew about before such as economics, statistics and probability. I have really enjoyed the learning environment that you create in your class. I feel comfortable not getting a mathematical concept immediately because both you and my peers are supportive and willing to explain the concepts to me. I look forward to being in your class next semester.
Happy Holidays!
Sincerely,
Sol Manuel