Course Synthesis

I have learned a lot about literacy this semester, especially about how many different ways there are to be literate and how important it is to directly instruct students in the skills necessary to become literate. I am excited to integrate the things I have learned in my classroom as a teacher.

I plan on teaching my students how to correctly read graphs and spot misleading data in mathematical representations. This is how I am going to integrate critical literacy. I plan on explicitly teaching the language of math and what it means to my students. I also plan on teaching my students how to decode math problems to bits and pieces that they understand. This is how I plan on teaching comprehension and vocabulary to my students.

I am excited to integrate what I have learned from this class in regards to writing instruction. I have recently been learning through my classes with Jim Cangelosi, that writing is SO IMPORTANT in mathematics education. I knew it was important, but I was a little bit fuzzy on how to implement it. This was probably my favorite part of the course because now I have some very good ideas on how to get my students to write and make mathematical representations of their ideas.

This has been a great semester and I am glad I took it my last semester. It will be very nice to have this information fresh on my mind when I go into my student teaching and I hope I will be able to effectively implement the things I learned. I may not be able to implement them all, but I want to keep some of them and really practice them.

Affective Dimensions of Reading

I remember when I was first learning to read, I didn't like it very much. It was an assignment that I had to do and I did not look forward to that part of homework time. However, once I knew how to read, an interesting phenomenon occured.

When my Mom would give me an assignment to read for 30 minutes (I was homeschooled), I would hate reading and drag my feet when it came time to read. Yet during my free time, I would choose to read.

The funny thing is that my mom didn't even tell me what type of book I had to read, only that I had to read for 30 minutes. So, I would drag my feet to read a book in the morning during school time and then eagerly read that same book for several hours in the afternoon during free time. I guess I just didn't like being told what to do :).

Luckily, I grew out of this stage before I started going to public school. I think that my ability to read well really helped me be successful in school. In fact, I would have to attribute at least 80% of my success in school to my ability to read and comprehend texts. After I had outgrown my non-reading stage, I loved reading almost any type of fiction, historical fiction, and self-improvement books I could get my hands on. That love of reading has stuck with me although I don't tend to read as much fiction as I used to...mostly because I don't make the time in my busy schedule.

My parents and peers were always very supportive of my reading habits and I never got the impression that it was a negative, nerdy thing to be a reader. I do remember that my mom discouraged my excessive reading by not allowing me to read at the dinner table. But other than that I was never discouraged in my reading.

I think one of the best ways I can help my students enjoy reading and encourage them to read texts in math is to read math texts myself and enthusiastically tell them what I am learning from what I am reading. I have had several opportunities to teach math as my job to work through college and I have noticed that my students really appreciate and connect with me when I tell them (simplified) what I am learning in my classes. I believe that when a student knows his/her teacher is learning and growing as an individual, the student is inspired to learn and grow as well.

Discipline Specific Reading

In mathematics, most of the texts I have experienced have been textbooks and math worksheets. In my secondary mathematics classes, my teachers rarely deviated from those texts. However, I do remember one "text" that my AP Calculus teacher showed us.

After the AP test, we were required to do two or three little projects just so we didn't completely waste the last month of school. This text that she showed us was an example of one of the options we could choose from for our project. It was a three dimensional model of what an integral represented and that picture has stuck with me for a long time and helped me a ton once I got to multidimensional calculus. When it comes to math, a picture is worth more than a hundred symbols.

Another mathematical text I remember my mom using as she home-schooled me was a base 10 abacus and it really helped me understand why you "borrow" and "carry" when you subtract and add. She also had us create our own base 10 manipulatives with beads. I remember thinking that was really fun.

I think the most unique mathematical texts I have encountered have been introduced to me in college. I have discovered lots of amazing applets that could be used to teach mathematics more effectively and also a couple of cool videos and texts that I could use to supplement the textbook text.

One of my favorite things I have discovered is GeoGebra, an applet creation software. This software allows you to create your own applets and upload them to your website as an html page. I was so excited about it that I couldn't stop saying, "This is SO COOL!!!" when my teacher was explaining the features of the program.

I think I will use this software A LOT as a teacher because I really do think that a picture is often worth a hundred symbols in math and I can create applets that will help students visualize math. I know from my own experience that personally discovering a piece of mathematics makes it stick a lot better. I know I could design applets that would lead students to discover mathematics for themselves instead of just listening to me tell them the way it is.

You might be wondering exactly how an applet can be a text. Consider the fact that you can interact with it and draw conclusions from the interactions you have. I think in many ways, this makes it an even more powerful text than a textbook that doesn't give you feedback or allow you to explore your questions.

As a final note, I want to include an applet that I made using GeoGebra to introduce students to a unit on the transformation of the sine function. (Note: You need the most recent version of Java for it to work) Enjoy!

Sine Function This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com Jaylee Willis, 3 October 2013, Created with GeoGebra

Affective Dimensions of Writing

I have always been passably good at writing and I haven't hated it. I loved reading when I was little (and I still do) and I think that influenced me a lot as a writer. For one thing, I was able to pick up on the structure of writing very easily and it wasn't very hard for me to learn to write grammatically. I also understood very early that writing was a way to communicate and express yourself.

I think I am a pretty good writer and I occasionally enjoy writing just to write, but it isn't something I make time for very often. I think it is something I would like to do more when I have more time. I see writing as a way to make your thoughts permanent or at least long-lasting and I think would like to write a book some day because of this. I guess to do that I will need to make sure I have thoughts worth saving :).

Even though I don't do a lot of recreational writing right now, I do enjoy expressing my mathematical ideas in writing. I think one of the reasons I really like my upper division math classes is because we get to write math in sentences that flow into each other like sentences in an essay. I remember telling my friends that my favorite part of my Algebraic Structures was learning how to write mathematics in mathematical symbols because it made math so much easier to think about and discuss. I think that writing math has helped me to see math as much more than a bunch of steps to work through.

When I am a teacher I want to help my students learn how to WRITE math instead of just doing it. I never wrote math in any of my high school math classes and I don't think I started writing math until my third year of college and I think that is a shame. I don't know exactly how I will structure the writing of mathematics in my classroom, but I want to figure out a way.

I think I will need to be careful how I integrate writing in my math class because the students will not be used to it. I think I might help them get used to writing math by having them record themselves talking through a problem and then have them transcribe their recordings into writing. This will help them keep their train of thought as they work through a problem. I think it will also implicitly teach them how writing has many advantages over speaking because it is much more clear and concise.

I think that writing is an important component of mathematics education and I am excited to figure out ways to integrate it in my classroom.

Final Project - Math Website Page

For my final project, I decided to make a website page on how to multiply negative numbers. I included two videos where I modeled two ways of visualizing the multiplication of negative numbers. I also included an algebraic proof of why a negative number times a negative number equals a positive number. You can access the website here.

I really enjoyed making this website and I think many of my students would also enjoy making a website. However, I think it could be very frustrating for some of them, especially if it was a take-home project and their parents weren't very technology savvy. The most frustrating part of this project for me was getting the videos' volume to be loud enough and that problem was not math related at all.

If I were to require my students to make a website page, the purpose of the project would be for them to learn to express mathematics in a clear and interesting way. My main intent would not be for them to learn to make a website, although that is a fun side benefit. Because learning to create a website is not one of my main objectives and for some students the technology frustrations could subsume the math objectives, I wouldn't REQUIRE them to make a website. Rather, I would let the students choose between making a website and a couple of other options.

I do think that creating a video would be a great activity for students to participate in if my school had video cameras/webcams available for student use. Even if there were only a few available, it would not be difficult to schedule students to take turns going to a small study room and record their videos. I think it would be fun to assign each student (or maybe pairs of students) a math topic for the unit and have them create a 5 minute video on that topic. Then I would merge all the videos together and have a class period where they watched their own videos.

I think this would be good learning activity because the students would be verbalizing their math, which is very important. They would also be practicing how to present mathematical ideas in a clear and concise way. They would be actively thinking about how they could make math interesting and how they could apply it to the real world. And finally, they would be enjoying the expression of other mathematical ideas presented by their peers.

When I require my students to make a digital text, I think I will award 20% of the points based on how polished their project is, (appearance, clearness of speech, etc) and 80% of the points based on the presentation of the mathematical content (accuracy, clarity and conciseness of explanations, etc). This would put most of the focus on the mathematical content but also ensure that the projects were of good quality.

Introduction to Me

Hi! My name is Jaylee Willis and I am studying mathematics education at Utah State University with a minor in physics education.

I have enjoyed teaching as a special education aide, recitation leader and lab teacher as well teaching in many informal teaching settings.

I am the oldest of 11 children and I love it! I enjoy reading, public speaking, and teaching. My purpose in life is to spread happiness and joy by teaching truth, being beautifully honest, and laughing my delectable giggles :).

I decided to teach because, when I was teaching as special education aide, I realized that I really enjoyed inspiring students to realize that they are not stupid and that they are truly wonderful creations. There was one experience in particular where I was able to live in my purpose and teach that truth to one little boy and he got it! It brought me a lot of joy and I knew I wanted to have experiences like that over and over and over again.

I decided to teach mathematics because there are a lot of people who don't like math and I love a challenge. After all, what area needs more inspiration than an area that everyone has to take but most people don't like? Plus, I find mathematics very fascinating and challenging. I knew that if I was going to spend 4 years studying a topic to eventually teach, I wanted to learn something that was going to challenge my intellect.

In my studies, I have discovered that mathematics is a beautiful art of creative questioning, logical thinking, and fascinating exploration. I am excited to teach this view of mathematics to the students that will come into my classroom and I am excited to learn how literacy can aid me in doing that.