Final Update: Habits of Mathematician
Generating Ideas:
For the final project I was expected to create a project that I could clearly represent to an audience that had little math knowledge. Now this may seem like a difficult task because Algebra 2 is not your easiest math class and neither is exponential growth and Decay. For this project I decided to create and Exploration that outlined the key components of solving exponential equations. My biggest weakness when I was creating this project was my ability to make it friendly and approachable to all parents. It was difficult to find the perfect balance of hard problems and approachable problems, but I was able to overcome this by creating a cheat sheet that allowed for the parents to break down the problem step by step. I would have to say that the biggest strength I had through this project was making the problems on the exploration relevant and funny. It was a great way to hook the audience. For example, I used a problem that Involved the exponential growth of Durango by a certain time and if this growth would be big enough to hold an olympics.
Communicating thinking in a clear and accessible way:
For the exploration project I thought that my ability to communicate concepts in a variety of different ways was fantastic. I was able to continue the same problem in three different ways that expanded on the understanding of it. For example I asked how population might change after x amount of years, or interest compounded quarterly and yearly and the effects that it had on the overall outcome of exponential growth. I was able to communicate my thinking in clear and accessible way by continuing the problem in a variety of different ways. I created a problem that involved investments that TJ made, and this is how I continued it;
Tj invests $2,400 of his hard earned money at machos into a bank that offers 5% compounded annually. What is the growth factor of his investment?
a. How many years will it take for him to double his investment?
b. If the bank Tj invested with decided to offer 5% compound interest quarterly how big would his investment be after 3 years using this equation.
Making these problems continue made it easier for the audience to have a better understanding of the concept as a whole and also how to approach it from different ways.
Recognizing and resolving errors:
I was able to recognize and resolve errors in my exploration project by paying close attention to detail and after reviewing my exploration more than once, I was certain that it was the best that I could do. In fact, I did not stop there and had multiple different peers check my work to look for logical flaws or flaws in my work that required attention to detail. For example I could have left out a negative sign that could possibly affect the entire answer to my problem or I could have calculated the wrong growth factor, all of which could be critical to the flow of my problems. When I first was solving my own problem I did not remember to account for the one year in my growth factor and represented it at .029 which would be wrong and after I had it peer critiqued, Brenden noticed that I forgot to put the 1 in front of the calculated value. This left me with growth factor of 1.029. See my steps below:
After one year the population would be
17,577 + 0.029(17577)
17,57(1.029).
Growth Factor = 1.029
Reflecting and synthesizing:
Overall, I felt like I made great connections to real world examples through my exploration project and made it easy and approachable to all audiences. I developed general rules for my problems that could have been applied in different ways though the course of the exploration. I also extended my problems in a way that required critical thinking and for people to be aware of the situation. I was able to make problems that allowed for people to realize the capacity of the equations and how they could plug values into model future growth by month, week, year and so on. It was a great way to hook the audience and set the bar for future explorations in Dans Class. I hope that he is able to use some of my ideas to bring success to his future students as well as providing them with a fun and thought provoking problem. My equation to model future growth for the town of Durango is listed below.
Y = ab^x = a(1.029)^x = 17,577(1.029)^x
For the final project I was expected to create a project that I could clearly represent to an audience that had little math knowledge. Now this may seem like a difficult task because Algebra 2 is not your easiest math class and neither is exponential growth and Decay. For this project I decided to create and Exploration that outlined the key components of solving exponential equations. My biggest weakness when I was creating this project was my ability to make it friendly and approachable to all parents. It was difficult to find the perfect balance of hard problems and approachable problems, but I was able to overcome this by creating a cheat sheet that allowed for the parents to break down the problem step by step. I would have to say that the biggest strength I had through this project was making the problems on the exploration relevant and funny. It was a great way to hook the audience. For example, I used a problem that Involved the exponential growth of Durango by a certain time and if this growth would be big enough to hold an olympics.
Communicating thinking in a clear and accessible way:
For the exploration project I thought that my ability to communicate concepts in a variety of different ways was fantastic. I was able to continue the same problem in three different ways that expanded on the understanding of it. For example I asked how population might change after x amount of years, or interest compounded quarterly and yearly and the effects that it had on the overall outcome of exponential growth. I was able to communicate my thinking in clear and accessible way by continuing the problem in a variety of different ways. I created a problem that involved investments that TJ made, and this is how I continued it;
Tj invests $2,400 of his hard earned money at machos into a bank that offers 5% compounded annually. What is the growth factor of his investment?
a. How many years will it take for him to double his investment?
b. If the bank Tj invested with decided to offer 5% compound interest quarterly how big would his investment be after 3 years using this equation.
Making these problems continue made it easier for the audience to have a better understanding of the concept as a whole and also how to approach it from different ways.
Recognizing and resolving errors:
I was able to recognize and resolve errors in my exploration project by paying close attention to detail and after reviewing my exploration more than once, I was certain that it was the best that I could do. In fact, I did not stop there and had multiple different peers check my work to look for logical flaws or flaws in my work that required attention to detail. For example I could have left out a negative sign that could possibly affect the entire answer to my problem or I could have calculated the wrong growth factor, all of which could be critical to the flow of my problems. When I first was solving my own problem I did not remember to account for the one year in my growth factor and represented it at .029 which would be wrong and after I had it peer critiqued, Brenden noticed that I forgot to put the 1 in front of the calculated value. This left me with growth factor of 1.029. See my steps below:
After one year the population would be
17,577 + 0.029(17577)
17,57(1.029).
Growth Factor = 1.029
Reflecting and synthesizing:
Overall, I felt like I made great connections to real world examples through my exploration project and made it easy and approachable to all audiences. I developed general rules for my problems that could have been applied in different ways though the course of the exploration. I also extended my problems in a way that required critical thinking and for people to be aware of the situation. I was able to make problems that allowed for people to realize the capacity of the equations and how they could plug values into model future growth by month, week, year and so on. It was a great way to hook the audience and set the bar for future explorations in Dans Class. I hope that he is able to use some of my ideas to bring success to his future students as well as providing them with a fun and thought provoking problem. My equation to model future growth for the town of Durango is listed below.
Y = ab^x = a(1.029)^x = 17,577(1.029)^x