I was unsure of what to expect while attending the Fire Up Conference, but was pleasantly surprised. It was an extremely valuable experience where faculty from around the area presented on different topics regarding education. I attended quite a few sessions of which were very valuable including two sessions on classroom management. Both of the speakers from these sessions were principals from nearby high schools. Each had loads to say about classroom management, each with their own perspectives on how to handle certain situations and present yourself in your own classroom. While they both had quite a few differences in what they had to say in regards to classroom management, they both made one point very clear; the way in which you begin your year, meaning the way you build your classroom starting the very first day, will determine the rest of your year. You must be prepared the day you walk in and have a clear explanation for your students of how your classroom works. I thought the way they presented this material was excellent. They provided many examples of stories in which teachers failed at doing this and teachers who were extremely successful in doing this.When you consider the many personalities in the world, it is crazy to think that each classroom really has its’ own atmosphere and how you create yours is crucial. It is pressuring to think about, but with their helpful tips, I feel I really benefited and can go more confidently into my classroom.
I think I will always find this to be a difficult question to answer, but I definitely feel more equipped to take a stab at it now, considering all of the things I’ve learned or thought about this semester. It is especially challenging to answer such a question when you’re unaware of the gigantic umbrella that mathematics covers and the history behind it all.
When I first thought about this question months ago, I said that math is a way of thinking about patterns throughout the universe. Math is interpreting and studying these patterns to find more patterns. I think that this definitely still applies, but now I think I would broaden it a little more and put a little more meaning to it. This semester, I have realized so many things about mathematics that I never would have thought of or known about. It forced me to open my eyes to thinking of mathematics in different ways and looking through a different lens at many concepts. Many of these examples I am thinking of are art and math or the fibonacci sequence throughout nature.
I decided to ask my little sister (she is 14) what she thinks math is. Her first response was “ew”. While some may take this lightly, I did not. I realized that she was probably thinking of the math she is learning in school right now and how boring and rigorous it can be. So I asked her to be serious and tell me what she really thinks, and her response was something like “math is like things you do with numbers to get answers you need to find for a purpose”. Okay, not a terrible answer for a 14 year old I guess. But then I asked her what she thinks of when she thinks of math, and that’s where it got interesting. Her answers were so boring that I couldn’t help but understand why people don’t like math. When you can’t find the beauty in something, why would you like/enjoy it?
The majority of things we did in class this semester were things that made me love math even more. It can be so fun and eye-opening. It is so incredibly integrated into every aspect of our lives that it’s hard to ignore. It can be extremely complex such as abstract algebra or Euclidean geometry, but can also be simply defining the world around you and observing patterns.
I’ve never previously learned about the history of math or all of the many many concepts mathematics actually covers, and I think that’s really sad. I think it’s really important to know the history of concepts in order to fully appreciate them because some of them came from such crazy ideas, it’s so hard to believe that people discovered what they have. It has definitely made me look at mathematics in a new light made me more excited to become an educator in such a cool subject that has so much to offer!
When asked this question in class, it really made me consider not only my own personal views on the topic, but what else other people had to say about it. This war has been happening on and off again since the Pythagoreans. I’m pretty certain of my own opinion, but wanted to take a look into other’s and see if it would sway my decision at all.
There was one article in particular that gave a question to each side of the debate:
- For those who believe mathematics was discovered – where are you looking?
- For those who believe mathematics was invented – why can’t a mathematician announce to the world that he has invented 2+2 to equal 5?
Plato agreed with the side of mathematics being discovered, which is also known as the Platonic Theory. He described it as a “discoverable system that underlines the structure of the universe”. The more we understand numbers, the more we can understand nature and the world we live in. Math is here regardless if we are or not, it has and will always be a part of the universe. Another article suggested, “the structures of mathematics are intrinsic to nature”. We find things in nature that explain some mathematics and help us put meaning to it. These patterns in nature surround us and help us to create what we call mathematics.
The opposing view questions, well where are these ground of finding such mathematics? Math isn’t just sitting out there waiting to be discovered, we invent it and develop it over time. The only reason math describes the physical world is because we invented it do so and help us with purposes we needed it for. Many non-Platonic views argue that our mathematical models are simply approximations of reality. These models often fail us, or aren’t exact, and we invent new mathematics in order to improve this.
My personal opinion hasn’t really changed, but I can definitely see both sides of the argument. I definitely think mathematics is discovered. Mathematics describes our universe. I see it as almost embedded there and by exploration and connections, we discover patterns that lead to what our mathematics looks like today. Obviously we didn’t just pull the quadratic equation out of no where. It begins with small building blocks and when looking at those foundations, we notice more and more patterns that occur and we continue to break them down to discover new mathematical ideas. Looking at the opposing side, I can understand that it seems a little far-fetched that we could just discover some ideas. I also can see the argument for the idea that someone had to invent numbers at some point. They needed numbers in order to count things they needed, so they named 1, 2, 3, and so on. But, I also don’t think you can just invent something that works out so perfectly in our world and that everyone just agrees on. It’s like the question asked, how could you just invent something? You cannot invent that 2+2=5, it just doesn’t work. I think that when you think about all of the patterns in the world, that is really what it all boils down to.
When I think about this question it really helps me to try and understand what mathematics is all about and I think that as a future educator, it would be a cool idea to do some sort of activity with my students, asking them this same question. There’s obviously no right or wrong answer and I think it can be very valuable to hear other’s opinions and realize your own because it may change how your perceive mathematics.
Until recently I had never even heard the name of a woman who had influenced mathematics. I’m not sure if males have just made more significant strides, or if it’s that females are simply not recognized. Being a female, I find it curious that I have never known about all of the accomplishments many of these women have made, so I wanted to explore a few of them and take the time to learn about all they’ve done. I’m going to look at three in particular; Hypatia, Kovalevskaya, and Noether.
Hypatia of Alexandria (370-415)
Hypatia was one of the first women to make contributions to the development of mathematics. Her father, Theon of Alexandria, was a mathematician and philosopher and guided Hypatia in her mathematics studies. She began teaching mathematics and philosophy at Platonist school in Alexandria. Many of the people she taught were Christians, and she became a symbol of learning and science which was against their belief because they believed for it to be paganism. She was eventually murdered by them because they felt very threatened by her knowledge and learning. Although she didn’t necessarily make big strides herself in mathematical research, she assisted her father with creating a new version of Euclid’s Elements. All of her work is lost aside from titles and references, but it seems she was a great compiler, editor, and preserver of earlier mathematical works.
Sofia Kovalevskaya (1850-1891)
Kovalevskaya was from Russia, a middle child of two well-educated parents. She enjoyed math beginning when she was young when her uncle spoke very highly of the subject. At the age of 11, she had wallpaper of differential and integral analysis, introducing her to calculus, where she made connections between what her uncle had said and the content in the notes. She then had a tutor which gave her her first official study of mathematics. These lessons ended when Sofia’s father put a stop to them, but she then continued to study on her own. Professor Tyrtov brought her family a physics book and argued to her father that Sophia should be allowed to continue her studies, but it wasn’t until much later that her father agreed. She traveled to Heidelberg to study mathematics and natural sciences, but found out that women were not aloud to study there. She unofficially studied there by attending lectures as long as she had the permission. Sophia did this for three semesters before moving to Berlin where she was privately tutored by Weierstrass, Königsberger’s teacher. She wrote papers on partial differential equations, abelian integrals, and saturn’s rings. Sophia received her doctorate degree from Göttingen University after a long fight for her education. Her fight continued when she ran into many difficulties obtaining an education job. Six years later she ended up teaching at an elementary school. Much later, she held a chair at a European University, something only two other females had previously accomplished. She continued her studies and eventually won a prize from the Swedish Academy of Sciences.
Emmy Noether (1882-1935)
Noether was born in Germany and was the daughter of mathematician, Max Noether. Her goal was to become a language teacher in which she got her certification, but then realized she wanted to attend a university to unofficially study mathematics. This was clearly the difficult route until 1904 when she was aloud to officially study mathematics at a university. She recieved her doctorate degree while focusing on the theory of invariants for the forms of n variables. She worked on developing theories of rings, fields, and algebras. Emmy then continued her research as well as assisting her father in his. As she began to publish her work, her reputation grew and she was soon being elected into organizations and giving lectures. Emmy worked on a theorem in theoretical physics known as Noether’s theorem which proves a relationship between symmetries in physics and conservation principles. Hilbert fought for her to have a position on the Faculty, and meanwhile allowed her to lecture his classes while advertising her own courses under his name. She then continued her work on ideal theory while publishing her papers. Noether eventually moved to the United States where she accepted a position Bryn Mawr College. Upon her remarkable achievements, I thought it was very interesting to hear that a crater on the moon is named for her, a street in her hometown is named for her and the school she attended is now named the Emmy Noether School.
I think it’s very important for people to realize the strides that these women have made in mathematics. As a future teacher, I think it’s extremely important for my student to understand that mathematics doesn’t just appear, but people have worked hard to make the discoveries they’ve made, both men and women. I’m not particularly thrilled when learning about history, but it makes more sense to know that the mathematics we learned came from somewhere and I think students will be more apt to learning it when they know more about why it came about and where it came form.
For my second book, I read How to Bake Pi by Eugenia Cheng. This book was a giant metaphor between math and food (which really caught my interest). The book was super fun to read, not only because it included food, but because it shows a way of thinking about math in a completely different way than what we’re used to. There was a never a point while reading this book that I got bored or confused, which made it easy and enjoyable to read. I could always follow along because if she started discussing a concept in mathematics, she quickly related it back to something of familiarity.
This book is definitely catered to mathematicians and I wouldn’t necessarily recommend it to anyone outside of that which I guess may be a “low”. The terminology is definitely math-based and may not be appealing to someone outside of that. I think it is definitely a great book for mathematicians to read, especially because she is hilarious and does not make it boring at all!
My views on this have been changed slightly and I am now seeing more of a connection between math and science. I wanted to delve more into this topic so I started by simply looking up the definitions of mathematics and science, based on dictionary.com.
Mathematics: the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically
Science: a branch of knowledge or study dealing with a body of facts or truths systematically arranged and showing the operation of general laws
They both are systematic ways of expressing relationships and or laws/facts. I’ve begun to look at science as more of an applied mathematics, where you use math in order to prove or disprove a scientific observation. In science, we constantly interpret and analyze the data that some experience has created. In order to look at this numerical set and come up with some type of answer, we use math. This includes being able to look at any given pattern and conclude something from it. We are constantly using both charts and tables in order to interpret mathematical data or scientific research because this is the best way to analyze the data presented and build conjectures or observations. Using this data, we then prove our reasoning. We could not do this without using both the mathematical and scientific areas.
I could see where one would say that math is not science because there are times when you can work on a problem that may be pure math with no context behind it. This may be the case that math is not always science, but I would argue that science is almost completely math. Whenever you’re studying science, there is always some type of math behind it to give you the reasoning whether it be a table of data or an equation you had to solve.
This topic can be confusing and made me uneasy for a while because I can see both sides. I think the answer is pretty clear to me now that I’ve thought about it.
I’ve just finished reading the book “The Number Mysteries: A Mathematical Odyssey Through Everyday Life” by Marcus Du Sautoy, a mathematics professor at the University of Oxford. Marcus Du Sautoy discusses mathematics as the language of the universe in an easy to read context. He talks about the five greatest mysteries of mathematics and how they still have not been solved, regardless of the vast amounts of effort. He turns math into a fun subject to discuss for everyone, relating it to everything from sports to nature to games. It forces you to look at the world in a way that questions why everything is the way it is, making you realize math really is everywhere; the language of our universe.
The books begins its introduction by saying “Ever since we’ve been able to communicate, we’ve been asking questions, trying to make predictions about what the future holds, and negotiating the environment around us. The most powerful tool that humans have created to navigate the wild and complex world we live in is mathematics. From predicting the trajectory of a football to charting the population of lemmings, from cracking codes to winning at Monopoly, mathematics has provided the secret language to unlock nature’s mysteries.” I think this makes the book extremely relateable to everyone and really makes you want to read on. This book was so fun to read because every couple pages was a new exploration on a different topic. Du Sautoy breaks it into chapters that have an overarching theme such as prime numbers and shapes, and then has mini chapters within that discuss a certain area within that theme such as the exploration of why bubbles are always spherical. Almost all of these topics are something most people have seen or dealt with, which makes it so enjoyable and interesting to read.
I would definitely recommend reading this book, as it is nearly impossible to get bored with it. Every time I’d read it, I’d constantly be sharing some of these funny ideas with my boyfriend (who has no interest in math whatsoever) who thought they were pretty interesting as well! Marcus Du Sautoy does a great job of keeping the reader interested while thoroughly explaining his ideas in a way that anyone could understand.