Habits of a Mathematician
Generating ideas
My strength for generating ideas is being able to think on my feet when it comes to identifying and applying the correct mathematical tool. One example of this was when I did pow #4. In this pow you had to find the right equation or create your own to solve it.
My weakness in generating ideas is being very limited to multiple ways to approach a problem. This can be seen in many explorations. There is not a specific exploration that can show this but on most of the explorations if I become stuck I would give up instead of looking for a new way out.
Communicating thinking in a clear and accessible way
My strength for communicating thinking in a clear way would have to be in class. Every time we would turn in homework we would write the answers and how we got it up on the white boards around the room. If a student didnt understand the problem I would help them understand more before we move to the next problem.
My weakness for communication of thinking is not being able to translate my math into words. I can explain the math with numbers on a white board for example POWs. As soon as I would get to writing out the problem the words wouldn't explain actually what was happening.
Recognizing and resolving errors
My strength for recognizing and resolving errors would have to be taking my errors and then building a new answer. You can see this in my final project of building a table for my car. I would find an error like the string was too lose so the table would fall over. I would then change the string into a different less stretchy material (chains).
My weakness for this is being stubborn with my answer. I would show my answer on an exploration in class and proving it with little evidence and then it was still wrong. I had to overcome this by finding ways to prove my work every time and make sure it was right.
Reflecting and synthesizing
My strength for reflection is making the connections to the real world. We did a POW about how much force it would take to break a 2x4 and then what would the optimal log size be to sop it from breaking. Bringing this work into the real world with my construction background was very easy and helped me learn a lot about how to build structures.
My weakness for reflecting is once again not excepting the fact that I am wrong. Naturally I am a very stubborn person with my math. It takes a lot to prove me wrong to the point I second guess myself. This habit is one that needs to be broken and I need to be more accepting in general.
My strength for generating ideas is being able to think on my feet when it comes to identifying and applying the correct mathematical tool. One example of this was when I did pow #4. In this pow you had to find the right equation or create your own to solve it.
My weakness in generating ideas is being very limited to multiple ways to approach a problem. This can be seen in many explorations. There is not a specific exploration that can show this but on most of the explorations if I become stuck I would give up instead of looking for a new way out.
Communicating thinking in a clear and accessible way
My strength for communicating thinking in a clear way would have to be in class. Every time we would turn in homework we would write the answers and how we got it up on the white boards around the room. If a student didnt understand the problem I would help them understand more before we move to the next problem.
My weakness for communication of thinking is not being able to translate my math into words. I can explain the math with numbers on a white board for example POWs. As soon as I would get to writing out the problem the words wouldn't explain actually what was happening.
Recognizing and resolving errors
My strength for recognizing and resolving errors would have to be taking my errors and then building a new answer. You can see this in my final project of building a table for my car. I would find an error like the string was too lose so the table would fall over. I would then change the string into a different less stretchy material (chains).
My weakness for this is being stubborn with my answer. I would show my answer on an exploration in class and proving it with little evidence and then it was still wrong. I had to overcome this by finding ways to prove my work every time and make sure it was right.
Reflecting and synthesizing
My strength for reflection is making the connections to the real world. We did a POW about how much force it would take to break a 2x4 and then what would the optimal log size be to sop it from breaking. Bringing this work into the real world with my construction background was very easy and helped me learn a lot about how to build structures.
My weakness for reflecting is once again not excepting the fact that I am wrong. Naturally I am a very stubborn person with my math. It takes a lot to prove me wrong to the point I second guess myself. This habit is one that needs to be broken and I need to be more accepting in general.
Semester 2 Wrap-up
Content Skill
The topic that I feel I have mastered this semester is converting e problems to exponential form and Log equations. The activities that show this are my exploration 15 and exploration 16 on a few problems. These are just some of my pieces of work that helped me master this skill. It is a very important skill to have to be able to solve for x when you only have either one of the equations. The Exponent and Logarithm Exam for math and Practice 16 shows how I really learned the topic. They can prove that I feel I have mastered the equations.
Master Content Examples
Problem Solving Skill
One Problem solving skill that I have improved would be to generate multiple means of approaching a problem. This is a very helpful tool to grow for everyday life. It applies to almost anything so I can practice it everywhere. My example of this in math is Pow #6 The Collectors Dilemma. In the Pow I formed a great brainstorm that would help me later with the whole pow.
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The other skill that has improved a lot and that I can show is to translate ideas using other forms or representations. In Pow #7 I explained my math equations in words very well so you can understand them. It helps out a lot if you don't understand a math equation you may understand it in words that explain what is happening.
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