Free Think Fridays
January 16, 2015 -
Why Calculus?
Reflection of my peer's paper: Here
The main point of this article was to emphasize the fact that math was developed in order to help us understand complicated problems in a simpler way. Understanding basic math is crucial for most industries, and our reliance on math is only getting stronger with technological advancements. The paper argued that people who challenge themselves to study more difficult math will have an easier time adapting to the changing circumstances around them. The author also argues that learning advanced mathematics as a young person is easier than trying to learn it later in life. This paper got me thinking about all of the implications of math on our society, and how math is intertwined around all fields of study and daily life. This paper helped me formulate my thoughts into more concrete ideas about who should study challenging mathematics. I used to think that students in late high school or college should be self motivated to learn challenging math, but now I believe that it is very important to incorporate into the curriculum of younger students, even if they do not yet understand its importance. I agree with the majority of the points discussed in this paper, with the exception of the suggestion for how to teach math. The author reports that teaching math with more of a 'coaching style' instead of traditional techniques. I believe that, while allowing students to be creative in the way they discover answers, practice is very valuable for the field of math. Sometimes, especially for young children, repetition is very helpful in teaching. From my own experiences as a student, I sometimes feel very frustrated when teachers give me a problem without any guidelines at all about how to find the answer. I believe that 'open ended problems' should be used after a student has a basic understanding of the content required to find the solution. I think this paper will relate to my work in this semester because it will keep me motivated to study mathematics not just for the grade, but for the long term benefits it will provide for my life.
Reflection of my peer's paper: Here
The main point of this article was to emphasize the fact that math was developed in order to help us understand complicated problems in a simpler way. Understanding basic math is crucial for most industries, and our reliance on math is only getting stronger with technological advancements. The paper argued that people who challenge themselves to study more difficult math will have an easier time adapting to the changing circumstances around them. The author also argues that learning advanced mathematics as a young person is easier than trying to learn it later in life. This paper got me thinking about all of the implications of math on our society, and how math is intertwined around all fields of study and daily life. This paper helped me formulate my thoughts into more concrete ideas about who should study challenging mathematics. I used to think that students in late high school or college should be self motivated to learn challenging math, but now I believe that it is very important to incorporate into the curriculum of younger students, even if they do not yet understand its importance. I agree with the majority of the points discussed in this paper, with the exception of the suggestion for how to teach math. The author reports that teaching math with more of a 'coaching style' instead of traditional techniques. I believe that, while allowing students to be creative in the way they discover answers, practice is very valuable for the field of math. Sometimes, especially for young children, repetition is very helpful in teaching. From my own experiences as a student, I sometimes feel very frustrated when teachers give me a problem without any guidelines at all about how to find the answer. I believe that 'open ended problems' should be used after a student has a basic understanding of the content required to find the solution. I think this paper will relate to my work in this semester because it will keep me motivated to study mathematics not just for the grade, but for the long term benefits it will provide for my life.
January 23, 2015 -
Problem Statement
For Free Think Friday this week, my table group was given a problem with a very simple question. The question was 'who owns the fish?'. The challenging part of this problem is that certain facts are given that are seemingly random, but all are needed to figure out the answer. The paper we were given included 15 clues to help us find the answer. We figured out that there were five different categories that all of the people in the problem were organized into, theses where their country of origin, the type of beverage they drank, the type of pet they kept, what brand of cigarettes they smoke, and the color of their house.
Process Description
To solve this problem, we first started by making a graph. We hoped that we would be able to fill in the missing information and eventually figure out who owned the fish. Then, after making our graph, we realized that the order of the house mattered, not only the color. So, we created a new graph that was organized by houses instead of the person. This helped us figure out the order of the houses, which helped us figure out clues such as 'the person who owns a dog lives next to the person who drinks tea.' After we figured out the order of the houses by their color, the rest was relatively easy. After we figured out the order, we started putting everything back on our original graph just because it was easier to visualize. One thing that we did that was very helpful was that we all made our own graphs in different ways. This helped us visualize the information in many different ways, and some people were able to find out answers that others couldn't find out just because their graph was organized differently. My group worked very well together, because we all communicated and shared what we found with everyone in the group. Even if some of the group members were quieter and found solutions on their own, we all still worked together by sharing our solutions to each step and double checking our work with each other. Checking our work with each other helped us catch any mistakes before it messed up the whole problem.
Solution
We concluded that the German owned the fish (see middle graph above). We know that the German owned the fish by process of elimination. We used the given clues to figure out who owned all of the other animals, then concluded that the German must own the fish because it would be the only way that all of the other clues would fit.
Self Assessment and Reflection
From this problem, I learned the importance of different views. It was challenging to figure out the answer at first until some group members decided to write the information we already had in a different way, which allowed us to find out more clues. We started by organizing the information by person, but it was only after we organized the information by the order of the house. I feel that I deserve to get a grade of 9.5 out of 10 because I feel that I worked effectively with my peers and listened to everyones voice. I think our group dynamics allowed us to solve the problem in the time we were given, because we could communicate effectively. While solving the problem I tried my best to keep an open mind and listen to everyones ideas, in addition to sharing my own. I think that my group and I used the 'mathematical practice' of "use appropriate tools strategically" because we were able to use the clues we were given to find our solution. We were given only a few hints and the suggestion to use a chart, which we did. Using a chart was very helpful to finding out an answer, because it allowed us to organize the tools we were given.
For Free Think Friday this week, my table group was given a problem with a very simple question. The question was 'who owns the fish?'. The challenging part of this problem is that certain facts are given that are seemingly random, but all are needed to figure out the answer. The paper we were given included 15 clues to help us find the answer. We figured out that there were five different categories that all of the people in the problem were organized into, theses where their country of origin, the type of beverage they drank, the type of pet they kept, what brand of cigarettes they smoke, and the color of their house.
Process Description
To solve this problem, we first started by making a graph. We hoped that we would be able to fill in the missing information and eventually figure out who owned the fish. Then, after making our graph, we realized that the order of the house mattered, not only the color. So, we created a new graph that was organized by houses instead of the person. This helped us figure out the order of the houses, which helped us figure out clues such as 'the person who owns a dog lives next to the person who drinks tea.' After we figured out the order of the houses by their color, the rest was relatively easy. After we figured out the order, we started putting everything back on our original graph just because it was easier to visualize. One thing that we did that was very helpful was that we all made our own graphs in different ways. This helped us visualize the information in many different ways, and some people were able to find out answers that others couldn't find out just because their graph was organized differently. My group worked very well together, because we all communicated and shared what we found with everyone in the group. Even if some of the group members were quieter and found solutions on their own, we all still worked together by sharing our solutions to each step and double checking our work with each other. Checking our work with each other helped us catch any mistakes before it messed up the whole problem.
Solution
We concluded that the German owned the fish (see middle graph above). We know that the German owned the fish by process of elimination. We used the given clues to figure out who owned all of the other animals, then concluded that the German must own the fish because it would be the only way that all of the other clues would fit.
Self Assessment and Reflection
From this problem, I learned the importance of different views. It was challenging to figure out the answer at first until some group members decided to write the information we already had in a different way, which allowed us to find out more clues. We started by organizing the information by person, but it was only after we organized the information by the order of the house. I feel that I deserve to get a grade of 9.5 out of 10 because I feel that I worked effectively with my peers and listened to everyones voice. I think our group dynamics allowed us to solve the problem in the time we were given, because we could communicate effectively. While solving the problem I tried my best to keep an open mind and listen to everyones ideas, in addition to sharing my own. I think that my group and I used the 'mathematical practice' of "use appropriate tools strategically" because we were able to use the clues we were given to find our solution. We were given only a few hints and the suggestion to use a chart, which we did. Using a chart was very helpful to finding out an answer, because it allowed us to organize the tools we were given.
January 30, 2015 -
Solution
We concluded that the German owned the fish. We figured out this answer by looking closely at all of the clues we were given and organizing the data in multiple ways. We figured out our answer on the first week, and double checked our work on the second week. On the second week, we decided to make our problem more difficult, so we added another house to the problem. By adding a sixth house, we also had to add more clues. We added a clue for each of the pets, drinks, cigarettes, house color, and house placement. The main focus of this week for our group was to create a poster displaying our solution.
Personal Pride
This problem pushed me to be a problem solver because it forced me to try new methods for finding the solutions when the first attempt did not work. This problem was really fun because it was kind of like sudoku, each step gives you another clue to find out which thing goes in which box. Because we found the solution last week, this week pushed me in other ways. This week I focused more on finding creative ways to display our solution, and I think we will be proud of our final poster. I feel that we all came together, building off of each other's ideas, to come up with a creative poster idea. Because I had a relatively quiet weekend, I decided to get started on building our poster at home. So far I have built the houses and the 'shelf' thing that is light enough to hang with the other posters (see pictures above).
I feel that the Mathematical Practice I used the most this week was 'attend to precision'. When I was building our poster, I was very careful when cutting the cardboard for the shelf. I used a long ruler to measure and make sure everything would fit perfectly together when I glued it. When I built the small houses, I had to measure each piece carefully or else the corners wouldn't match up properly and that would look really bad. I measured each house to have a 2 2.5 inch walls, and the front and back were 2.5 inch squares with a triangle that had a base of 2.5 inches and a 1 inch height. I used precision when cutting out each piece for the house, because when something is that small even a slight mistake could make the entire house not fit together.
Group Collaboration
This friday, we all worked together to check our work, then see if we could add to our problem to make it more difficult. After we were done with that, we started brainstorming what we could do for our poster. We decided to challenge ourselves with this poster by making a three dimensional poster. We all worked together to create the plans for the poster. Over the weekend I built the houses and the 'shelf' out of cardboard (see picture above). Before next Friday, I will talk with my group and we will split up the rest of the work for the poster. To finish our poster we will need to paint the houses, create tiny flags out of toothpicks to show the country of origin of the residents, figure out how to put pets in the houses, figure out how to put cigarette brands somewhere in the house, and make tiny drinks. The biggest strength my group has is our tendency to push each other to create our best work. We could improve by communicating our goals better with each other, to make sure everyone is on the same page.
We concluded that the German owned the fish. We figured out this answer by looking closely at all of the clues we were given and organizing the data in multiple ways. We figured out our answer on the first week, and double checked our work on the second week. On the second week, we decided to make our problem more difficult, so we added another house to the problem. By adding a sixth house, we also had to add more clues. We added a clue for each of the pets, drinks, cigarettes, house color, and house placement. The main focus of this week for our group was to create a poster displaying our solution.
Personal Pride
This problem pushed me to be a problem solver because it forced me to try new methods for finding the solutions when the first attempt did not work. This problem was really fun because it was kind of like sudoku, each step gives you another clue to find out which thing goes in which box. Because we found the solution last week, this week pushed me in other ways. This week I focused more on finding creative ways to display our solution, and I think we will be proud of our final poster. I feel that we all came together, building off of each other's ideas, to come up with a creative poster idea. Because I had a relatively quiet weekend, I decided to get started on building our poster at home. So far I have built the houses and the 'shelf' thing that is light enough to hang with the other posters (see pictures above).
I feel that the Mathematical Practice I used the most this week was 'attend to precision'. When I was building our poster, I was very careful when cutting the cardboard for the shelf. I used a long ruler to measure and make sure everything would fit perfectly together when I glued it. When I built the small houses, I had to measure each piece carefully or else the corners wouldn't match up properly and that would look really bad. I measured each house to have a 2 2.5 inch walls, and the front and back were 2.5 inch squares with a triangle that had a base of 2.5 inches and a 1 inch height. I used precision when cutting out each piece for the house, because when something is that small even a slight mistake could make the entire house not fit together.
Group Collaboration
This friday, we all worked together to check our work, then see if we could add to our problem to make it more difficult. After we were done with that, we started brainstorming what we could do for our poster. We decided to challenge ourselves with this poster by making a three dimensional poster. We all worked together to create the plans for the poster. Over the weekend I built the houses and the 'shelf' out of cardboard (see picture above). Before next Friday, I will talk with my group and we will split up the rest of the work for the poster. To finish our poster we will need to paint the houses, create tiny flags out of toothpicks to show the country of origin of the residents, figure out how to put pets in the houses, figure out how to put cigarette brands somewhere in the house, and make tiny drinks. The biggest strength my group has is our tendency to push each other to create our best work. We could improve by communicating our goals better with each other, to make sure everyone is on the same page.