**Habits of a Mathematician **

**Generating Ideas: **

**Strengths:**

A strength for me when it comes to generation ideas is formulation a plan. Going into our final project I had previous knowledge of what taxes were due to our last project but I knew I needed to put a plan in place in order to have a refined project. I came up with steps that I would take, starting with compiling research in an organized document. From there I knew I could use my knowledge of the research to brainstorm the best way to display the information. I ultimately came up with a pasteboard that displayed each candidates tax plan by filling out a W2 and a 1040. With this brainstorm I also showed the strength of identifying appropriate mathematical tools to use. I knew I would need to create a spreadsheet with the appropriate equations so that I could plug in a dollar amount and see the amount taxed based off their tax plan.

**Weaknesses: **

A weakness I show under generation ideas is generating multiple means of approaching a problem. I often approach problems in the way I feel comfortable. For example when identifying asymptotes I initially approach the problem just by looking at the equation, where I knew you can identify them graphing too. This shows that I just go the path I feel most familiar with rather then identifying multiple approaches.

**Communicating thinking in a clear and accessible way:**

**Strengths:**

A strength I find I have under this category is restating the problem in a different way that adds to the understanding. I gained this skill during exploration seminars. We often dealt with word problems that could be tricky to break apart and understand what exactly it is asking. I often found myself being able to reword the question in a simpler manner that could be understood by my peers left puzzled by the question. I often did this by translating the ideas into visuals or by using different word choice. I also found myself in the other shoe where I was the one left puzzled by the question and those situations help me build the strength of responding to others ideas. I often have to draw or say allowed my ideas to fully express and understand my thought process so when a peer lead me to the right path of a problem I was often able to build off of it.

**Weaknesses:**

A weakness I find I have when it comes to communicating thinking in a clear and accessible way is soliciting contribution from quieter peers. When we would seminar on explorations I found myself more frustrated with the people not participation rather then encouraging. More often then not these people had ideas they were probably too hesitant to share. If I had been more encouraging I would probably gain a different insight and so might my quite peer. This was shown when in feedback circles I expressed my frustration with non-participating peers instead of contributing solutions to that problem.

**Recognizing and resolving errors:**

**Strengths:**

A strength I have in recognizing and resolving errors is once I find the error I can disprove it by using what I found to be a correct method or solution. This ofter occurred during explorations. When I found a different answer then my peers instead of just saying they are wrong and moving on I would exhibit how I got to my answer by displaying my step by step process. I also have the strength of attending to precision and detail. I could correct my mistakes by being so attentive to detail because often times it was one step I messed up and not the whole people. This came in handy mostly with test and exploration because by writhing out and showing my work I would see and analyze each step and detail of the problem. Making it easy to identify where the error was. You can see this strength in a photo attached below.

**Weaknesses:**

A weakness I have when it comes to recognizing and resolving errors is generating new ideas from the errors found. This correlates back to my weakness in generating ideas, where I find myself only a approaching a problem one way. Once I find the error i'm often lost on where to go after that. I find this weakness playing out in exploration seminars when my answer is wrong I rely on a peer to tell me what approach I can take next. This also shows my weakness in finding and correcting errors I make. As mentioned previously I will sometimes rely on my peers to correct my problems for me, especially during seminar explorations. I would saying finding an error is half a strength for me and half a weakness. I can find my errors in step by step problems however when it comes to graphing or more direct problems I often find myself looking right past the error.

**Reflecting and synthesizing:**

**Strengths:**

A strength I find I have is connecting mathematical ideas to real world examples. I exhibited this skill through my final project of creating a W2 and 1040 based on our presidential candidates proposed tax plans. In this project I took our unit on taxes and spreadsheets and applied it to something extremely relevant in all of our lives right now, the upcoming presidential election! I also have a strength of justifying how I came to the conclusion that I did. As mentioned before when completing exploration I wright out my step by step process. This helps me think through the problem i'm completing as well as being able to refer to it later, such as discussing problems in exploration seminars.

**Weaknesses:**

A weakness I come across when reflecting and synthesizing is developing general rules based on specific problems. I am not good at reflecting on a problem and finding general rules based off of the answer I got to. One I am told however, such as in not taking, I fulling understand and an=m able to make the connection. I feel this correlates with my weakness of contextualizing my answer. I am not able to directly identify why I came up with the answer I did, only the step by step on how I came up with the answer I did. This weakness is shown in practices when I cant find the common denominator of the problems at hand and therefore have to spend extra time diving into each problem.

**Semester 1 Portfolio **

**Content Skill:**

A skill that I feel I've mastered throughout the course of the semester is working in spreadsheets. I feel these four pieces of evidence best exemplify my knowledge in spreadsheets. This has not only been a helpful tool but a tool I enjoyed learning about. I can use this tool to text functions, estimate prices, and essentially a whole world of options. The most helpful exercise in learning to use spreadsheets was the spreadsheet workshop. Throughout this project We explored many elements to spreadsheet including, how to add text, how to create a formula, how to carry formulas throughout the spreadsheet, graphing, how to add multiple tabs in one sheet, and so much more. Another exercise that helped me better understand spreadsheets was applying the skills I learned in spreadsheets to my spreadsheet project. Spreadsheets is a very valuable skill to have and I am happy to obtain, and continue to grow on this skill.

Spreadsheet workshop:This is where I first explored spreadsheets and developed skills. We were presented with different tasks to complete within this workshop and each task taught a new skill. |

Spreadsheet Project:This project I got to strengthen my skills in spreadsheets by applying all the skills I learned in the spreadsheet workshop. Doing this helped all the methods I already know stick in my mind and also helped me explore new concepts in spread sheets. |

**Problem-Solving Skill:**

A problem solving skill Ive developed throughout this year is developing general rules. This has helped me grasp concepts faster and overcome challenging problems. This skill I found to be useful tool in over coming projects that stumped me. It helps you get a better general understanding of the problem because it establishes a basis for you to work off of. Allowing yourself to take a step back and use this approach is a much more effective way of solving then blindly tackling a problem. I will continue to use this skill throughout the rest of my academic, and even post academic career.

**Spreadsheet Workshop **

**Spreadsheet Workshop**