Classroom Environment

Since we began learning about trigonometry, class has been structured differently. We have been working with partners or groups daily, and instruction time has been in short spurts throughout class time. We have also had background music ranging from Coldplay to Bach.

Reflect on your “new” classroom experience. Do you like it? Do you dislike it? Do you find it more or less engaging? Has it helped you to learn?

I have tremendously enjoyed working with partners and small groups of three. It helps me get a better feel of the concepts. For example when someone in the group has a problem or a question, I have the opportunity to answer the question, which helps reinforce the concepts. I also learn different ways of doing different problems and get a chance to see what works for others and what works for me. I get a chance to try different things and helps everyone feel like they apart of the group discussion. I also think that the labs are helpful because a lot of the questions help me understand why certain things are certain ways instead of just memorizing the concepts. I think the background music is sometimes a big distraction, especially during homework quizzes and tests. Sometimes they are calming but a lot of times it can be loud and a  lot of the instruments used can get in the way of thinking and talking.

Some people say trigonometry is all about memorization, especially when they are talking about the unit circle. We have done some activities and labs that illustrate ways in which we can learn the unit circle without doing a bunch of memorization. Explain how you can use skills you already learned in algebra and geometry to help you understand and remember the unit circle.

The unit circle consists of right triangles using those right triangles we can find the ordered pairs. The radius of a unit circle is 1 which is also the hypotenuse. So using the radius we can use the 30-60-90 special right triangle and 45-45-90 special right triangle. We can also use sine, cosine, and tangent. Sine is opposite over hypotenuse, which means that its going to opposite over 1. We can find the opposite using the right triangle and since we know the hypotenuse we can find the other using x-x(root3)-2x. We know that the radius is 1 which means the hypotenus is 1 and from that we can find x by equating the 1 to 2x (2x=1) and then solve for 1 which gives us 1/2. 1/2 is the is the side opposite to 30 degrees because the side opposite to 30 degrees is x. Now that we now what x is we can find  the side opposite to 60 degrees, which would be x(root3). Now that we know x is 1/2, we can put that in for x so that it looks like (1/2 * root3) now we have to multiply those together so it is root3/2. This is the side opposite of 60 degrees. The same thing can go for 45-45-90 special right triangles except the sides are x and the hypotenuse is x(root2). These can be used for the quadrant one of the unit circle, the rest can be found using the reference angle which would either be 30, 60, or 45.

Technology in Math

How do you think technology works best in the classroom setting? Does it engage you or distract you? If it does both, when is it engaging and when is it distracting? Do you like using the smart boards or do you prefer the regular white board? Why?

I like using the white board in math rather than smart boards. I feel like when we do examples in class the smart board is helpful, but when we are taking notes I would rather see it on the white board because I like being able to see all the work step by step. For me personally, I think the smart boards are a bit distracting especially when we have technical difficulties. On the other hand, using the smart board is a good thing for when a person is absent. They can just take the notes from the class conference and when they come back to class they do not have to catch up because they are already caught up.

Techniques in Math

Here is your first question: Reflect on your math class this year and your math classes in the past. What works well? What doesn’t work well? How would you rate your level of engagement? Feel free to include specific examples.

I think that in math class I like to see things visually. I like to take notes and have many examples to look back too. I also like having homework that would be somewhat like the tests. I also like having homework quizzes because not only does that help me keep track of my homework but also forces me to understand all the materials. I don’t like having too much technology involved in math such as the promethean board because I like being able to see all the work step by step for example when we are graphing functions. Its much easier to see it drawn out on the board. On the contrary, I like the activeness we have when we use the board for example when we go and work out different examples. I also like working out the homework problems and looking at how different people have different approach to different problems.

“Pure Mathematics”

1. Respond to the quote: “Pure mathematics is, in its way, the poetry of logical ideas.” ~Albert Einstein

I agree with this quote by Albert Einstein because math explains everything in the world. Take physics for example, if we didn’t have math how would we be able to solve equations and find out the density or the volume of a cube or the displacement of an object. The world is full of logic from the way the roads and highways are constructed to the ways the buildings are constructed. Another example would be E=MC^2. This is also explained in mathematical terms because of the fact that we have to find energy using the mass of the object and using the SI units for joules, without knowing how to solve equations and adding and subtracting there would no way for us to understand how to use that equation or how to come up with that equation.

Methods

Factoring, Using the Quadratic Formula, Completing the Square, Extracting Square Roots, or Graphing.

2. If you needed to teach an algebra II student how to solve quadratic equations and you only had time to show her one method, which one would you use and why? Why would you omit the other methods? Please comment on each method listed in question #1.

If I had to teach an algebra II student how to solve quadratic equations I would tell her to use the quadratic formula because they quadratic formula works every time for every problem. If you have the ax+bx+c sometimes factoring doesnt work if it has imaginary numbers, but quadratic formula always works with imaginary numbers. Extracting the square root would also not work every time because not every problem has a square root in it. Graphing also doesnt show the imaginary numbers just like factoring doesnt.

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