Pre-calculus: Unit 7

 

In this unit in math we learned about trigonometric function properties, identities, and parametric functions. The goal of this unit was to delve deeper in to understanding different trigonometric functions, specifically different line graphs and circle graphs. In this unit I struggled a lot to understand the content in class. Before this unit I struggled a lot to learn on my own, but because of this experience, I grew in my ability to find other ways to learn when I’m not learning the material in class. This growth can be seen in a worksheet that I worked through with my tutor and the partner quiz of this unit.

 

The first step in learning this unit was working with our groups to complete and understand worksheets that taught new concepts. These worksheets, called explorations, typically contained six to eight problems that helped us understand different aspects of the new concept we were focused on. Our teacher normally handed these out and had us work through them with the classmates at our table. When we didn’t understand something we worked with the rest of our class and our teacher to complete the worksheets. One or two times a week our teacher would hand out a Key Problem for us to complete, which tested important concepts covered in class. These were then collected for a grade.  Every week or two we would have a quiz to check up on our progress to ensure that we were learning what we were supposed to be learning. Once we completed all of the lessons in the unit, we reviewed concepts in the lesson. We then completed a partner quiz with our group covering the unit and then took a test covering the entire lesson.

 

This is the process our teacher has used all year, but it doesn’t work very well for me. This unit I was completely lost during class and didn’t receive much guidance from my teacher. Instead of giving up, like I wanted to, I asked my peers and parents for help which cleared up a little bit of the confusion. It was at this point my mom suggested going to a tutor. After getting more and more lost, I decided to go. The tutor was able to offer guidance and help me actually understand parts of this unit, specifically in how to solve functions involving arcsine and arccosine. I understood algebraically how to solve equations down to where I needed to take the arcsine or arccosine of one side to get the answer, but didn’t understand how to go on from there. My tutor explained arccosine (inverse cosine of x plus or minus 360n) and arcsine are (inverse sine of x or 180-x) respectively. She then led me to find out how to solve the problems using the arcsine and arccosine functions.

 

The first artifact that shows my growth in my ability to find other ways to learn when I’m not learning the material in class is the worksheet and notes I completed with the tutor. One of the pieces of classroom content evident in this worksheet is the Unit Circle. The unit circle is a graph of a circle with a radius of 1. It can be used to solve equations. Another piece of classroom content evident in this worksheet is the process for solving trigonometric equations using the Unit Circle. My tutor showed me how to use the unit circle to identify which trigonometric functions were positive in which quadrant. This artifact indicates my growth in my ability to find other ways to learn when I’m not learning the material in class.

 

The second artifact that shows my growth in my ability to find other ways to learn when I’m not learning the material in class is the partner quiz I completed at the end of the unit. One of the pieces of classroom content evident in this quiz is the property that sin^2+cos^2=1. This property is useful to manipulate and solve equations. One of the main ways that we can solve equations algebraically is by using equations that are properties in order to change the equation into a solvable form. Because I got a good grade on this quiz in spite of the lack of guidance, this proves I grew in my ability to find other ways to learn when I’m not learning the material in class.

 

I know that in life I will not always have teachers that guide their students and make things clear, and so I know I will use these skills I have developed later on in life. In college I know I will have to learn on my own for some classes. I now understand the value of tutors in learning and am much more open to working with them for any class, not just math. I have learned to take advantage of the resources available to me, whatever those may be. It is important to always address difficulties and meet them head on. This is the most efficient method to find solutions to problems. Although I learned some math concepts through this unit, the biggest way I grew through this unit was in my ability to find other ways to learn when I’m not learning the material in class.