ashleymth229-blog

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The last one

My final Blog post will talk about statistics specifically the correlation coefficient.  During my math 229 Class we have been discussing statistics a class that I have personally never taken. I was lost at the beginning of class on Monday however, through a couple of activities I was able to make sense of what the correlation coefficient is. The correlation coefficient helps show how correlated your data is, which means how close or how different they are from each other. 

We used a desmos activity to test different properties of the correlation coefficient, which was confusing at first. I think that if you are to use that type of activity there should be some basic definitions and instruction given. I believe that reasoning through problems yourself is a very big part of learning however, I also think that you need to understand the material or else reasoning through won’t help you. I think the second activity we did was more beneficial for me because it showed what an almost perfect correlation was compared to a problem that had almost no correlation. This game of guessing the correlation helped me realize that the closer the data points are on a scatter plot to a straight line the more they are likely to have a high correlation rather than a low correlation. I wish I would have competed in the “to the death” correlation battle because I had a high score of 32 on the game because I was guessing the correlation that closely. This helped us when we moved onto our next activity which was finding the correlation coefficient for an experiment of our own choice. 

The next activity was creating our own experiment, collecting data and then finding the correlation coefficient. We decided that we wanted to see how many times someone could sign their name in 15 seconds, and we did 5 trials of this and then found the data. Most people were able to sign their names about 3 times but as the trials went on we either say a correlation with people getting more competitive and a correlation with people fatiguing. I compared my experiment with another classmates where they did the same experiment but they used times of 5, 10, 15, 20, and 25 seconds. It was also evident in their data that they had the same correlation with either getting more competitive you say an increase in times signed or tired you saw a decrease in times signed. Overall, I found this experiment to really help model the actual math behind the experiment. I think that this helped solidify my thinking when it came to correlation coefficient and put them into perspective of what they are supposed to be. This experiment help demonstrate exactly what they look like. 

My major take away from this unit is that there should be some background presented if people don’t understand. But also that by using games and experiments you can learn a lot about a certain topic. 

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The Big, The bad, The Scary: Trigonometry

For this blog post I will be discussing Trigonometry and the way it is approached in my math 229 class along with its real life applications.

           Trigonometry has been considered one of the worst subjects in math by most math students because they can’t understand the identities. However, I personally love trigonometry because I understand sine, cosine, and tangent and how they work together. In my math 229 Class, I feel that we have been discussing the very bare minimum when it comes to actually trigonometry. During our Algebra unit, we went in depth about different ways you could explain each function. We talked about different activities we could use in order to engage our classroom while reviewing how to do these problems. Whereas when it comes to trig, we have just brushed the surface. We have discussed basic trig functions when it comes to sine cosine and tangent in circles and triangles, however we haven’t gone in depth on how to teach these to our future students. I know that when I was first learning trig, I had to memorize the unit circle, and that really helped me because I was able to use that to build on the rest of trig. I still remember the unit circle to this day because it was so helpful. One activity that we did in class that I found extremely helpful was the equilateral triangle day activity. We all drew triangles and had to come up with rules in order to determine whose triangle was the best.  My table created the rule that for each degree that you were off of 60 you got a point and then for each length you were given a point if it was correct, you wanted the lowest amount of points. My triangle that I drew had three 60 degree angles but somehow one of the sides was .1 cms off. Later we shared our rules with the class and voted on which rule we thought was best as a class. Then we had to all draw triangles and use that rule in order to see whose triangle was the best in the class. I loved this activity because I feel like it showed the definition of what an equilateral triangle was, and that it didn’t have to look a certain way. I think this activity would be really beneficial for a class in the beginning stages of trig because it could help define some things along with beginning a great activity without feeling like a lesson. My hope for Math 229 is that we start going more in depth about the trig identities and how to explain them to students because I feel we are falling short in this unit.

           I also think that it’s important to explain how trig can be related to things in the real world. I believe that in order for student’s to really understand real life examples you have to make them meaningful. We recently read a blog post that talked about building a dock for a pier and they approached it by having students look at the problem logically first before going into the actual trig identities. I think this answers the age old question “when will we ever use this in real life?” I believe that when we use examples like this rather than we are walking this amount of distance to get to this place type of problems. When you put real life places and meaning to the problems then students will learn much easier. I think that’s a problem teacher’s are facing right now is making the content mean something. I am very interested in learning how to create application problems for my students because I know that they tend to learn better.

           Overall, Trigonometry has its ups and downs in the classroom, but I feel that if we start going more in depth we can learn better strategies to teach trig. I also think it would be beneficial to learn how to teach problems with more meaning in their content. I believe that it’s really important, to go in depth with every unit or else how are we going to learn activities that we can apply in our own classrooms.

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Types of problems used in the classroom

For my third blog post I am going to discuss the importance of group activities, application problems, and practice problems in the classroom.  I am going to first discuss application problems in the classroom. Recently in my Math 229 class we were able to choose from a list of activities in order to explore our knowledge and understanding about logs. My group chose to work on Sprikinski maps, which are designs that can be made to fit logarithmic functions on a graph. It was a very cool activity because you spent part of the time coloring your design and the other time was spent finding an equation to fit our data. I didn’t realize that it would be as simple as plotting points based off of how many empty squares I had and finding an equation to fit. I think this would be an excellent activity to do in my classroom with my future students because they would have no idea that they are doing logs until I had them fit an equation to the data from their picture. Another group in class was working on finding a log function to fit data that had to do with blood glucose level and medications. This type of activity would answer the over arching question high school students face of “when will I ever use this again?” This would show them that logs are applicable in different fields of study and that it could affect everyday life.  The last application problem we discussed was the gros rate of movies at the theaters. It was really cool to see how each weekend the movies would decrease in the amount of money they would bring in. I was shocked at the exponential decay rate of the money they brought in, and it was interesting to see how normal movies fit this pattern but how some films don’t fit this pattern. I believe this would be an amazing tool to use in my classroom to keep students interested in the topic.

           My Second topic of discussion is group activities in the classroom. I think they are a very important tool, when trying to help students understand what they are learning.  One activity that I thought was very beneficial to do in a group was explaining why the log rules work, and how they are connected. My group discussed why log(x^2) and 2logx are the same. We discussed how x^2 is the same as x times x which means that it could be written as log(xx). You would need to grasp the rules of logs such that you would know you could split log(xx) into log(x)+log(x) which would  be the same as 2log(x). At first when someone at my table brought up this concept I had no idea how they came to this conclusion. They wrote out their explanation and I was better able to understand their thinking which helped me learn how this concept worked. I think that being able to discuss this problem with my group was helpful because I was able to ask questions without having the fear of seeming stupid in front of the class. I think a lot of students get confused in activities but are too afraid to say anything in fear that they will be the only one. So I believe that using group activities help students to have a safe space to ask questions because its less embarrassing to ask a peer than it is to ask the teacher in front of the class.

           The last type of activity that I would like to discuss in the classroom is the idea of practice problems and worksheets. I think that these are beneficial when the student already has a good basis of understanding, but overall are just drill methods. These help students practice so that they know the material but rarely challenge them to go further than just computations. I think that students get tried of these activities more than others but are necessary in order to test their basic understanding.

           To conclude, I believe that group activities, application problems, and practice problems are all beneficial in the classroom. I would like to do a lot of group work and application problems in my future classroom because I think that they help create a deeper understanding of the content. I think they also promote a safe space to ask questions if they are confused. I also think that practice problems are necessary to assess understanding and to help further growth and practice, however I would like to limit them in my classroom and have them used as more of a homework activity rather than an everyday in class activity.

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Hello All, I will be discussing a couple of topics for this blog post.

My first topic I want to discuss is what happens when a major event takes place, how to approach it in your classroom. For example, we talked about the taking a knee controversy in our math 229 class. We discussed how we feel that we need to create a safe environment where students can express their feelings about the issue at hand. Along with that we also said that we could try to connect the issue to a lesson in class so that it could be considered curricular based while discussing the issue. For example we could talk about the percentage of money that Colin Kapernic is losing when he takes a knee in an NFL game. I personally feel like if the issue is going to take time away from class anyways because the students are focused on it, we should address it so we can move on and have a successful class period.  I would rather my students talk about it in a safe environment where the debate can be controlled then somewhere, where they could be ostracized for their opinions.

The next topic I want to discuss in my blog is the different ways you can teach division of polynomials. I loved what we did in class where we used the white boards to problem solve with our table groups. I feel like the white boards are a really good way to collaboratively work together on solving a problem. I also liked the fact that if you got confused it was more of an open space to be able to talk through your thinking, rather than being alone and having to struggle through the problem. My group started the problem using the reverse long division method, where you multiple the polynomial by a factor to get to the next. This method was actually really cool, and easier than I expected. However, I am still a huge fan of long division so I decided to show my group my thinking through long division. I like long division because as a middle school student, I was forced to practice over and over. My least favorite method I found out was synthetic division because it is very complex when you have a coefficient greater than one. My group was able to solve the problem but was having trouble understanding why we had to do certain steps to get the correct answer. Which brings the question up, what would we do if this were the first and only method we were using? Would we have divided the entire problem by 2 like we were supposed to or would we have left it? It’s a good idea to help your students move through each step of the problem and talk through why each step is important or else they could get stuck like we did. Overall, I found this activity to be extremely helpful and I think it would be a really cool thing to use in the classroom for group learning.

           My next topic for discussion is the marble sliders function game that we play in class. I think this is an extremely creative way to keep your students engaged in what they are learning along with teaching them what the functions mean. For instance a lot of the time, we are frowned upon using the guess and check method in math however, in this game it helps learn what each coefficient does in the polynomial. This is an awesome way to teach students how polynomials shift and transform. I wish that we would have, had an activity like this in my algebra 2 class because it would have been so helpful when learning quadratic transformations. I also believe that the marble sliders could help you learn the different degree functions, because when you have to hit all the stars you need to use different polynomial functions in order to complete that.  I really liked using these sliders because its very different way of learning than I am used to. I think it would be cool to incorporate in my classroom when we are in the middle of a lesson as a fun way to break up the chunks of learning but to also test what they know. They would have to be able to understand the concepts of polynomials at least slightly in order to do this activity and it would help them solidify what they don’t know as well.

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My first blog post

Through out my learning career, I have had a love hate relationship-involving math.  When I was in elementary school, I was terrible at math. I remember that in my classroom we were divided up into groups based on which times table we were able to complete. Once you were able to complete the table you moved up to the next number set. I remember that I was stuck at the 6 times table group for over two weeks, and while all my classmates were moving forward, I was stuck. Eventually, I began studying even harder at home and forcing myself to learn the tables so I could move forward. I wish my teacher had encouraged me more while in class, instead of dwelling on the fact that I wasn’t learning as quickly as the other students. From this experienced I learned that I needed to rely more on myself than others for the motivation to get better.

           The transition from middle school to high school in math was almost life changing. When I was in my eight-grade math class, everything began to click in my head. I was able to solve equations, and graph things way quicker than my classmates. My 8th grade teacher suggested that I move into advanced math for freshman year. I began to understand the concepts in math much easier. I was determined to be good at math no matter what new concept we began in class. When I finally started taking upper level math classes such as calculus and trig, I was able to visualize the concepts as they were being taught. I ended up seeing my elementary school teacher my senior year of high school, and when he asked me what my favorite subject was I said “math”. He looked at me and said “math really? I always remembered you being better at writing than math.” This conversation stuck with me because it made me realize that once a teacher labels you, that is all they will see you as. This teacher had labeled me as a poor student in math, and years later still expected me to be no better than I was then. I hope when I become a teacher that I will have higher expectations, and try to inspire my students to better themselves rather than just pass judgment based on their current skill level.

           One interesting thing we did in my mathematics for secondary teachers activities class was we planned an outdoor lesson. When our professor came to class, he asked us if we wanted to go outside since it was a really nice day, to which we all responded with yes. However, instead of just taking us outside and teaching us a lesson, he has us come up with a lesson as a class that we could use with our future students. We spent a little under an hour going over the different concepts and learning targets we wanted to accomplish when we went outside. What I thought was interesting was the idea that we needed to come up with the reasons of how the outdoors could benefit our students and their learning. We ended up doing a projectile function outside. However when we actually went outside we were all confused on what we were actually supposed to be doing. What I think would have been helpful in this situation is to explain the expectations to the class, and possible show an example of what our lesson is supposed to look like outside. We all figured out what we needed to accomplish, however everyone’s ideas looked very different so we all got a lot of different results. Then we went back to the classroom and talked about the results of our experiment. I think one thing we could have done better about this class period, was create more structure in the activity. A lot of us were really confused about the direction of the activity and so having more structure could have added to the conversation. I do believe that this activity was very beneficial in showing us how difficult it is for teachers to plan activities outside the classroom. However, I do think that it helps students get out of their comfort zone, and helps them expand their thinking.

           One thing that I am excited to do is the observation hours within a math classroom. Last semester I had a volunteer opportunity in an urban school in Grand Rapids. It was very stressful because the students were very under developed skill wise. It was almost unimaginable that this school had fallen so far below the curve on where they were supposed to be, and how they just kept passing students regardless if they knew how to do the problems. I had one 8th grade student in my group who didn’t know how to do simple multiplication.  I learned how to do multiplication in elementary school, and this student hadn’t learned and he was about to be a student in high school. This makes me hopeful that my observations in a classroom can only get better. However, this also has me worried that more students are like this in a class but don’t get the proper help they need.  I also want to compare these observations to my pervious math classes, and see the difference in teaching styles from my teachers to these teachers. I always like to see if students benefit from the same learning styles or different and I like to see how the teacher caters to each students individual needs.