## First Semester Reflection

**Content Skill: Logarithms**

Our first exposure to the true nature of Logarithms was in Exploration 14. We learned to discover for ourselves the relationship between Logarithms to define their function in the world of math. Such as through noticing that Log (10^4) and Log (10,000) have the same output value of 4. Our Exponents and Logarithms Exam summed up our overall understanding of Logarithms. Such as through Log base 7 (343) equaling 3. I first encountered Logarithms on an Exploration problem in which I found myself trying to find the unknown value of an exponent; I had no understanding of the function of Logarithm that I was using to find that value and after we were properly introduced to them as a class, my previous confusion with the subject had become answered.

Habits of a Mathematician: Translate Ideas Using other FormsAs a mathematician, I need to understand the relationships between different forms of the same content. Most often these forms are transitions between an equation, a graph, a table, and written text. To be able to comprehend how an equation can be represented as itself in words, a table, or a graph is essential to communicating ideas. In Exploration 20, we translated newly found knowledge of a parabola onto a graph which was also represented through the equation f(x)=x^2-3x as well as in many of our POW's when we need to translate written ideas into other mathematical forms such as equations, graph, tables, and lone values. |
Habits of a Mathematician: Ask Clarifying QuestionsAs a mathematician, I need to be able to understand mathematical concepts. In order to be successful as a mathematician, I need to be able comprehend the logic behind the math as well as the math itself. When unable to comprehend in math, asking clarifying questions will allow you to move forward in your mathematical career. In Exploration 18, I was unable to understand how to distribute compounded values within parentheses with other compounded values that were also within parenthesis. Now that I had asked Clarifying questions, I understand and can perform this concept. |