What makes a mathematician?

Over the semester of taking this capstone class we have learned about quite a few mathematicians. We learned about Omar Jhayyam, Li Zhi, Descartes, Fermat, and so many more. There are so many famous mathematicians that have made a great impact over the years. It is hard to pick one to write about in a blog. This got me thinking, what makes a person a mathematician? According to dictionary.com, a mathematician is an expert or specialist in mathematics. There are a few people I know that I think are mathematicians.

In my opinion, a mathematician is a person who is passionate about mathematics and invests time into solving problems. Having the chance to work with students this semester, I consider some of them to be mathematicians. Even though I hear a lot of my students complain about math and how it is so hard, there are a few of them that enjoy it and well not stop until they solve a problem they are given. Even the activities we give them that are supposed to be fun and relaxing, students got frustrated when they couldn't figure it out and wanted more time. We had an activity called 31 where students had a deck of cards and had to make put cards in a 5 by 5 grid. Each row and column had to add up to 31. Students got to the end of the hour and wanted to take cards home so they could figure it out. Some of them even drew it out on a piece paper because they didn't have any cards. They were not getting a grade or any prize. They wanted to figure out the problem and started to find the patterns. That is when students start to become mathematician in my opinion. 

Some on my teachers are mathematicians. My professor John Golden is a mathematician. His passion and dedication to exploring and teaching students mathematics is something I admire. I hope that I can be a great math teacher one day and get my students excited about math just like he does for his college students. He always comes to class with different activities and topics to explore. I am always interested to see what we are going to do next.

Now to the question of am I a mathematician? I will admit that I did not always love math (surprising yes). However, I did grow to admire math and began to love it when I had teachers who showed my how I could learn it. There are some topics in math that I get fascinated by and could spend hours exploring it. Do I ever see myself spending time researching and making a knew discovery in math… no. I do see myself inspiring other kids to explore math and teach them that it is possible to learn math. I want to help my students who think math is hard find a way that it makes sense to them. I want to be able to show enthusiasm while I teach so that my students get excited to learn. So I guess yes, I am a mathematician because I am passionate about teaching math and want to help my students learn.

Mathematicians are not just those people so create a formula or make the next big discovery and publish a book. Mathematicians are everywhere and most do not become famous at all. I think every person might have a little mathematician inside of them but not every person is a mathematician. So who do you consider to be a mathematician?

Shark Tank

This semester I have been in an algebra 2 class and we just finished one of two projects they do during the school year. I'm sure by the title of the blog you can guess what the project was. The project was Shark Tank. Students were split up into groups of 3 or 4. Each group had to assign roles to each student which would tell them what part of the project they were responsible for. There was the Director of Marketing who is in charge of the groups advertisements, Director of Finance who is in charge of the graph for the group, and Director of Sales who is in charge of the PowerPoint used to present to the sharks. Once they were in their groups they needed to come up with a product that they wanted to sell. The product needed to be something that could actually be invented or that the technology needed to make it had already been invented. They would work on this project in steps for two weeks and present to the sharks after that. 

Some of the math they had to do was to first figure out their costs. They had to decide on how much space they needed and the cost of rent ($12 per square feet), the number of workers ($10 x number of workers x 40 hours x 4 weeks), and the type of advertisement they wanted. These had a cost already set for them, but they needed to decide which one based on the cost. For example, for advertising, they could choose a Radio advertisement ($200), Billboard advertisement ($1000), or a TV advertisement ($2000). All of these costs would give them their fixed cost per month. Students also needed to figure out how much money it would cost to make one of their product. They had to research each item and come up with a cost to make their product (variable cost). These two prices would give them their cost equation which is the variable cost times x plus their fixed cost. Once they had their cost equation they needed to make a revenue equation as well. They had to decide how much they were going to sell their product for to make a profit. They could change any of the fixed costs along the way if they thought their costs would be to high. Once they had both of these equations they had to graph them to see how long it would take for them to make a profit and their break even point. 

Students really got into this project. Students were talking about this project as if they were actually going to make these items. This was great to see because it showed their passion for their product. Students had to make calculations and equations but were focused on how they could make their product better. Some groups complained about all the math but I think that most groups did not even realize how much math they were actually doing. Students came up with numbers that made their profits reasonable and were quite high. I think students realized that opening a business was hard but it was possible.

At the end of the two weeks I had the opportunity to be a shark and listen to a few presentations. Some groups struggled a little with the numbers and presentation but I was surprised with some of the products students came up with. Most groups came up with a product that either had something to do with their phone or with food. This honestly didn't surprise me but I did think that most of the products would be quite useful if they were actual products. I ended up "investing" in 4 out of the 5 products that I saw. The sharks were great as well. Not only did the students get into the project I think the sharks did as well. After getting to participate in the project I would definitely love to incorporate it into my class one day. Students loved it and I think it was a nice break from the "normal" class day. 

Semester reflection

            This semester has been one of the hardest semesters I have ever had. Teacher assisting has taught me so much but has been even more stressful than the semester when I took four math classes at the same time. Even though it is not quite over yet, I want to take a moment to reflect and share my experience with whoever is reading my blog. So here it goes.

My summer was not much of a summer. After my college classes were finished I spent the next month and a half subbing and volunteering at a high school. I was not yet in the College of Education and was getting even more nervous I might not make it in. I had to take the ACT again and I had to retake a chemistry class so I could get my GPA up enough to get in. Fast forward to the end of the summer. A week after getting a solid B in my summer course I was quickly accepted into the College of Education. The next day I was given my placement for teacher assisting at a High School. That night I contacted my CT and signed up for all my classes. I went to Professional Development the next day and got to meet my CT and the following Monday was the first day of school. Very fast pace and all of this happen within two weeks. 

Looking at the semester to come I was quite nervous. Talking to other people, I was warned that I might see a lot of fights at the school and to be careful. Starting at a new school is always scary even for teachers but I knew I had support from friends and family. After getting to know these kids, I couldn’t believe I was ever nervous to be there. They are some of the nicest kids I have ever met and they welcomed me into their school. They were open to me teaching them and kept encouraging me to teach. I was quickly able to get to know my students and gain their trust. 

As the semester continued my classes did not get any easier. Taking 17 credits worth of classes while teacher assisting was not the best idea I have ever had. But these kids I have been working with stared to really have an impact on my life. These students struggle so much with confidence in themselves and their ability in school. So often students would raise their hand to ask a question and would do the problem without me saying a word. They are so smart and have bright future ahead of them. As them semester continued, students found out that we would not be staying the entire year. This came as a shock to them and a few of my students refused to believe I would be leaving. I had students tell me that I was their favorite teacher. I had another student say that they would switch schools, so they could have me as a teacher. Another said they would protest me leaving. Others said that I had to get a job there and that they would write recommendation letters for me to get a job at their school. With only a few weeks left I am so sad to have to be leaving. These kids have stolen a piece of my heart and I don’t know how I will ever leave.

Looking back, I have learned a lot about myself and about teaching that I will use in the future. I have learned that there is so much that goes into making a lesson that maybe I had not thought too much about. One thing I have really been working on this semester is getting all my students engaged in the lesson and in the activities. I am good at making creative activities but now I need to make sure that all my students are engaged and working. One example was the Jeopardy game we played for review. I had the majority of the class engaged in the activity but not everyone was participating. Each group had whiteboards to write their answers on but there was usually one person in each group that was writing. Next time I want to use Jeopardy I will make it so the whiteboard moves hands each round. This way each person in the group must write and everyone must communicate with the person writing to get the answer right. Coming up with strategies, like the groups I choose or even the layout of the classroom, is something that I will take with me to the future.

The Teaching Gap Book Review

I read the book The Teaching Gap by James W. Stigler. I enjoyed reading this book, for the most part, and would recommend it to others to read. The Teaching Gap is a book that describes the similarities and differences between the United States, Japan, and Germany's school systems. Topics include the layout of the classroom, teaching strategies, and professional development that each have. The book starts by talking about a video study that was done to compare all three and uses the results from the study to describe the major differences between them.

Chapters in the book are as follows:

1.     The Teaching Gap

2.     Methods for Studying Teaching in Germany, Japan, and the United States

3.     Images of Teaching

4.     Refining the Images

5.     Teaching is a System

6.     Teaching is a Cultural Activity

7.     Beyond Reform: Japan’s Approach to the Improvement of Classroom Teaching

8.     Setting the Stage for Continuous Improvement

9.     The Steady Work of Improving Teaching

10.  The True Profession of Teaching

What I found so interesting about this book is that while I was reading it, I found that a lot of the drawbacks the United States schools show is what I have been learning how to improve on in my education classes. When we compare the United States and Japan in this book, it looks as if we are just spoon feeding our students the answers and hope they can repeat a process we teach them. In Japan, students “struggle” a little before being shown how to do something and can develop their own thinking behind the mathematics.

I did enjoy this book. The only reason I say most of the time is because there are clearly parts that are said to insult American teachers and I wanted to through my book across the room. However, the information is relevant and could be used today and I would recommend that others, especially teachers, should read this book.

Blog 1-What is infinity

In class we were asked the question what is infinity. My definition for infinity is an endless amount of possibilities. So I leave you with this blank blog as a symbol on the endless possibilities of mathematical history I could write about...


























____________________________________________________________________________

Just kidding. As a future math teacher, I need to think about how to answer difficult questions much like this one. I’m sure every teacher has a list of questions that they hope students will never ask. This is one that is on mine. What is infinity is a hard question to answer because there are multiple ways of answering it. Like I said above, my definition of infinity is endless amounts of possibilities. The best way I think I can describe infinity is to compare it to the future. The future is never ending in fact there is always a future. If you are talking about a specific day in the future, as soon as you get to that day, it is no longer future it is the present. But there is still a future.  Infinity is always there and is never ending.

So what do we do as teachers when asked these kinds of questions? Well first I think we need to take a deep breath and get ready to think on our feet. We can't take away time from class to address these kinds of questions. We can however start the conversation and leave to student with something else to think about. Maybe tell them a quick thought and ask them what they think the answer to their question is. Maybe have it as an extra project that students could do outside of class if they really want the answer. Have them research the question and come up with their own answer. In most cases my guess is that the student is just trying to waste time in class so students are not actually going to go research the answer.

Some of these questions could be used to our advantage to get students to form their own opinions. We don't always have to give them our thoughts on questions. We can allow them time to form their own conclusions and thought on a topic.

These are just some ideas of mine and are in no way the correct answer. I am still learning how to be a teacher and I am open to any suggestions other people have. So, I leave you with this question. What would you say if a student asked you what is infinity?

Blog #5 EDT 370-02

Using a blog is a great way to reflect on how your lesson went. It also allows other teachers a chance to read your experiences and use them in their own classroom. Having a blog can give other teachers a chance to also offer advise to each other to help improve lessons that may not have gone as planned. There is always room for improvement so sharing your own experiences with others can help you and other teachers grow as educators.

As a teacher, I'm not sure if I will make my students use a blog. I may use a blog to talk about my own personal experiences in the classroom. However, blogs are not private and I think students would prefer something a bit more private in regards to talking about their school experience. My personal reflections from class I think are great especially as a new teacher. I have used my blog before to reflect on my experience as a substitute teacher. I got a lot of supportive comments from other people and great suggestions on how to improve myself in the future.

Blog #4 EDT 370-02

http://profjonh.blogspot.com/
Jon Hasenbank is a professor at Grand Valley State University. His blogs are math education related and are often about topics we have discussed in our class.

http://mathhombre.blogspot.com/
John Golden is a math education professor at Grand Valley State University. His blogs talk about different math activities and will often quote some of his students responses. He also provides other resources for his readers to use.


http://mrbilkos.weebly.com/
Connor is a math education student and in a few of my classes. Although he is not a teacher yet, I think reading other students blogs are just as useful as reading current teachers blogs. Our blogs can help us to share our own experiences in the classroom.


https://teacherwiththepersonalityofamiddleschooler.wordpress.com/
Kim is also a math education student. Her blogs often talk about her experiences with teacher assisting. Her blogs also involve a middle school perspective which is different from my high school experience.

https://johnmadeblog.wordpress.com/
Madelyn is a math education student. Her blogs are more for classes but talk about her experiences in the classroom. She is teacher assisting at a middle school.


I chose to put two teacher and three student blogs because I think it is important to not only read teachers perspectives, but also other students perspectives that are in the same point in their education as I am. We can learn from each others experiences in the classroom as we move forward in our education and professional experiences.