Synthesis
I have learned so much in this literacy class...I will admit, I was one of those who came into the class thinking that it was just one of those classes required for any education major...but it really wasn't going to apply to me all that much since I'll be teaching math. We use numbers rather than words, right?
How wrong I was. I have loved the changing that I have had to do about my ideas of teaching in math. I now feel quite passionate about the integral role literacy plays in mathematics. Math is not merely numbers, but math is ideas about how to solve problems. Math is about understanding the world around us.
If I were to sum this class up what this class has done for me into two main points, they would be that I have grown a passion for literacy and that I have learned scaffold (and the importance of doing so).
I had no idea how much of a difference scaffolding could make in teaching, but in teaching lessons during my clinicals, I tried to do this, and even though I didn't do it perfectly, I it still made a difference.
I think that making sure to never forget the importance of literacy in my class will help me to better teach my students to do "authentic math" rather than "schoolmath," as Jim Cangelosi calls it. In class we talked about product versus process. This is basically the difference between school and authentic mathematics. In schoolmath students are taught that the answer is the important thing. But really, mathematicians try and experimenting, and doing it some more, only sometimes succeeding at what they were going for. In their process of trying things they have learned and discovered so many things. This is like how in response to someone asking about his failing so many times in trying to make a light bulb, Thomas Edison said that he did not fail even once but rather found 1000 ways NOT to make a light bulb. ---This is the kind of thing we want to be teaching students. We want them to be willing to try and to not just make mistakes, but learn from those mistakes.
I have also quite loved learning about the different theories, such as behaviorism, constructivism, socioculturalism, critical theory, etc. I never would have really thought theories on education were that important, but in learning them it helps me to mentally organize where I think my teaching should. Because of my understanding of these I have clearer ideas on what I want my teaching to look like. Previously my experiences in math classes have been mostly lecture and then practicing problems and while I may need to do some of that, I hope that my classes will be much more focused on discovery, communication, application, and creativity.

Practicing Teaching Analysis
During my clinical observations at a couple of different schools, I had the opportunity to watch a couple of teachers really making an intentional effort to help their students with learning vocabulary.
In a middle school class I observed, I watched as the teacher and students worked through a problem of factoring a quadratic and then finding the zeros. After finding them, however, he told the class, that these were called the "zeros" or they can also be called "solutions" or "roots."
There are so many times that we toss around different words for things, without even realizing it, but without letting the students know that we may be using more than one word to mean the same thing, and thus we lead them to be confused. Simply doing as this teacher did and instructing them right up front that these words can be used interchangeably I am sure helped them avoid a lot of confusion. (And in fact, I'm sure my deduction is correct as I hear that his students consistently are the high scorers on the end of level tests they are required to take--and one thing that tends to be difficult on those tests is when differently terminology is used from the stuff you are familiar with, even if you understand the concept.)
I also sat in on a geometry class. I sat in on a lesson introducing tangent lines to circles and was VERY impressed by what I saw. The idea was not introduced by displaying an abstract picture of a circle with a line tangent to it, or with a lecture. Instead, the teacher had a real picture demonstrating circles with lines tangent to them (I think it was a picture of something with pipes, if I remember right). Then someone came up and pointed out what they thought the tangent was. Then there was a discussion, along with more real life pictures demonstrating circles and tangents to them. I was actually kind of blown away by how good this was! This of course made it so much more real to students. After discussing the idea in terms of real life pictures, some abstract ones were brought in, but still with real life pictures that showed the same idea as the abstract drawings. I was impressed by what I saw, and all the different ways that the teacher had found where circles and their tangent lines were found in real life things we encounter. It made the lesson he was teaching seem so much more relevant and important, even to me, so I'm sure to the students! I loved the way this was taught. There are many skills in math that students need to learn in order to be successful in higher math classes, but which they may not see any immediate use for at all. Getting students thinking about things they have encountered already in their lives, that demonstrate this idea, before abstracting the concept was so helpful to both making it seem important, and to making the idea easy to grasp.

Critical Literacy

I came into this class with the understanding that "critical literacy" meant being able to "read and write the world." Through this literacy class and others I am taking simultaneously, however, I have become more aware of how students become literate, different practices to help them, achievement gaps in schools, etc. With all of these, my idea of critical literacy and what good teaching looks like have become more refined.
Good teaching now looks more like this: specific and intentional questioning, scaffolding, lack of assumptions, not simply giving information but facilitating the discovery of that information, not merely teaching facts but teaching thinking.
I would say my definition of Critical Literacy has expanded from simple being able to "read and write the world" to being able to read, write, listen to and understand, and speak about the world. And more specific to my classroom, being able to critically think about and question, and then use the tools discovered my class to do so.

Text Set o' Joy!!

Novels:

• Lund, Gerald N. (1983). The alliance. Salt Lake, UT: Deseret Book Company
  
  This book has always been one of my very favorites. It is a fiction book that takes place in the future, about 18 years after "World War III" has happened. This book is a relatively simple read, so it is accessible to those not reading at high grade levels, yet the characters are incredibly well developed and the plot is so intriguing that  those of high reading levels will also love it. The underlying moral issue being fought about in this book is the ability to choose how to act. This book doesn't have anything to do with mathematics but it is a book that encourages critical thinking, so I would strongly recommend this book to any student or teacher.

Trade Books:

• Devlin, Keith (2000). The Language of Mathematics. New York, NY: Holt Paperbacks.
  
  This was my first experience with a math trade book. I was surprised at just how fascinating this was. In this book, Devlin explains in a way interesting to both mathematicians and non-mathematicians much of the history and development of math we use today. I would love to use this in a class, but depending on the grade level I am teaching. This would be something great to use in an advanced level class in a high school. There might be some words unfamiliar to them, but with a bit of vocabulary discussion, this would be very accessible to that group. I have been thinking that it might be a good idea to assign this book to be read during the school year or semester, but set mile markers to be hit along the way. I would require them to read to a certain point by a certain time, and there would be something, maybe a small writing response quiz for each mile marker, to keep them accountable for the reading. When first assigning this, I would probably read some aloud to them, before having them read it on their own so they can see just how interesting and accessible the book is. Then throughout the semester, here and there I would want to read some more out loud to them, or have their peers do so, during class. This would then be good material for in class, small group discussions every so often. (I would contemplate using this in a different high school class also, but I would want to be careful and use something else if I have students whose reading levels are significantly below where they should be.)

• Livio, M. (2002). The golden ratio: The story of phi, the world's most astonishing number. New York, NY: Broadway Books.
  
  This book is another that I have yet to read. From the reviews I have read, however, I am really interested in it. It is a book that discusses, of course, the Golden Ratio. It is supposed to be engaging for both mathematician and non-mathematician alike. It discusses not only math, but goes through art, architecture, botany, biology, physics, and mathematics, so it should be a good cross-curricular book.

• Seife, Charles (2000). Zero: The biography of a dangerous idea. New York, NY: Penguin Books.
  
  I have not yet read this book, but I have heard time and time again good reports of this book. From what I have heard, this is very accessible, informative, and interesting. This is a book I would probably like to keep on my shelf for students to be able read. I might possibly consider having students read a selection from the book as part of their homework.

Additional Textbook:

• Burton, D.M. (2007). The history of mathematics (6 ed.). New York: McGraw-Hill.
  
  This is a textbook that I had for the History of Mathematics and Number Theory class I took from Jim Cangelosi and Utah State University. This textbook has so much that is so intriguing in it. I have not read the whole thing, but I have enjoyed much of what I have read, and furthermore it was recommended to our class, by Jim, as a book we should definitely have on our shelves. This will be an excellent resource for history on the math I will be teaching in my classes, to make the class more interesting.

Websites:

• Gillespie, M. J. (2011). Aggiemail DUMMY https://sites.google.com/a/aggiemail.usu.edu/dummy/home website.
  
  This is my own website that I have been putting together. (I probably will want to figure out how to change the name from "Dummy" before using it in my classroom...) This website has a collection of explanations of a few interesting problems in Probability Theory, as well as a few links to further information/applets/videos on the subject. I would probably put a link of this to my class website or blog so students could go to it for something interesting. I could also forsee showing this to my students, and having them work together in groups to find an interesting problem in math/probability and then work together to come up with an explanation of the problem and solution, such that it could be an addition to the website. This could be fun and also help them learn how to explain math ideas in a way understandable to others.

• Isaacson, Michael (2012). USUMATH4500.weebly.com. Utah State University Math Department. Website.
  
  This is a website that was created for the Math 4500 class I am in. On this website we are able to upload lesson plans and such that we have done, for the rest of the class to be able to have. This text has many well written lesson plans that both I and future colleagues may find useful in our classrooms.

• Bogomolny, A. (2012). Interactive mathematics miscellany and puzzles.   http://cut-the-knot.org/ (accessed April 2012).
  
  This website is awesome! I have used it several times trying to find explanations of interesting math problems. It has explanations and applets and all kinds of good stuff. It has math games and puzzles, explanations of a large range of mathematical things from geometry to algebra to calculus, probability, and more. I would use this website probably both in finding intersting things to present to my students and also possibly as a resource for them to use should I assign them to present something.

Simulations/Applets: 

• Chang, K., Graham, S., Koen, V., Lindsay, M./The New York Times (8 April, 2008). Interactive feature: The Monty Hall problem. http://www.nytimes.com/2008/04/08/science/08monty.html (retrieved 10 April 2012).
  
  This simulation of the Monty-Hall Problem is really fun! I love this problem and will definitely present this problem in my class, and then hopefully have a class activity, where we do the game in class, and figure out the reason for the results. This online simulation would be good to give to them if we don't end up having time to do it in class, I could assign it as a way fun homework assignment, or as for those who might miss the in-class activity.

Children's Books:

• Ellis, Julie (2010). Pythagorus and the ratios: A math adventure. Watertown, MA: Charlesbridge Pub Inc.
  
  This is a book I have not yet read, but I have read another by this author and just loved it! This would be something fun to have to help explain ratios in a non-threatening way. Probably better for younger kids, but honestly, I think probably high school students could have fun with it too.

• Ellis, Julie (2004). What's your angle, Pythagorus? A math adventure. Watertown, MA: Charlesbridge Pub Inc.
  
  I love this book! I read it to one of my roommates as a bed time story! This just fascinated me because it teaches the Pythagorean Theorem in a very understandable way. Though it might be more difficult for them to read, I think it could be understood by even third graders. I think probably junior high school is where I would be able to get the most use out of this. I'd probably just have students sit down on the ground (how didn't love story time like that in the younger grades?!) and read it to them. Then we'd do the things in the book that the young Pythagoras did. 

• Neuschwander, C. (1999). Sir Cumference and the dragon of Pi (a math adventure). Watertown, MA: Charlesbridge Pub Inc.
  
  I have not yet read this one, but it was recommended with the books of Julie Ellis, which I was already very impressed with. This book I think would be great for teaching in a junior high school, which is where I would love to teach for at least some amount of time. Sometimes students find math in general to be an unapproachable concept. But kids can do knights and dragons!!
• Neuschwander, C. (1997). Sir Cumference and the first round table (a math adventure). Watertown, MA: Charlesbridge Pub Inc.
  
  Similar to what I have said about the other children's books, I would use these as a way of helping make math less scary and daunting, and make it seem more understandable and accessible to my students who will be at various levels of ability and understanding.

• Neuschwander, C. (2001). Sir Cumference and the great knight of Angleland (a math adventure). Watertown, MA: Charlesbridge Pub Inc.
  
  As said with the others, I would use this as a tool to help teach math to students who have a hard time grasping the abstract ideas thrown to them with math.

Articles:

• Stripp, A. (9 September 1999). How the enigma works http://www.pbs.org/wgbh/nova/military/how-enigma-works.html (retrieved April 2012). Article.
  
  This is an article describing how the Enigma (a ciphering/deciphering machine used by the Germans during WWII) works. I include this text because cryptography is done using prime numbers, and this is a real world example of how prime numbers are important in the "real world," a disputing a claim so many students make that the math they are learning bears no importance to their real lives. I also like this because the Enigma is something that can be discussed tying mathematics and history together. *I would love to use this in conjunction with the Nova video of cracking the Enigma, if I can find it.

Videos:

• Devlin, Keith (2008). Authors@Google: Keith Devlin retrieved from http://www.youtube.com/watch?v=3pRM4v0O29o.
  
  I love this video. It is just over an hour long and is really good. It discusses the origin of probability theory, discussing the problem of points. It is really interesting as he discusses how this is something that we now take for granted, but was a hard idea for people to accept at first. With probability we are able to essentially see into the future. This is a really interesting video and I would probably use this as something for my students to watch on a day when I am not there and have a substitute. There is a lot they can learn from this, so the time won't have to be wasted, but I also won't have to worry about the math ability of the substitute. 
• K50aker, (12 Aug 2007). "Abbott and Costello 13 X 7 = 28." Online Video Clip, http://www.youtube.com/watch?v=rLprXHbn19I (retrieved April 2012).
  
  This is a funny clip that would be great to use as a start to a discussion on mathematical reasoning, and what is sound and what is not. In the clip, one of the men explains in several ways that seem reasonable why 13 times 7 is 28. There is, of course, a definite flaw in each one, but it seems so reasonable, that it is really funny, and I think could be a great conversation starter.
• Mandlebrot, B., (February 2010). Benoit Mandelbrot: Fractals and the art of roughness http://www.ted.com/talks/lang/en/benoit_mandelbrot_fractals_the_art_of_roughness.html (retrieved 9 April, 2010).
  
  This is a Ted Talk where an elderly gentleman, Benoit Mandlebrot, discusses roughness, and fractals. He begins by showing a closeup picture of califlower, a vegetable we see all the time, and shows how this is a demonstration of a fractal. This is interesting as he uses every day things, and shows us mathematics in them. Then shows the marvelous and incredibly complicated and beautful shapes that can come out of simple simple formulas--"Bottomless wonders spring from simple rules...repeated without end." This is something I would probably not formally use in my class, but would have it as something extra that could be shown to students who might be curious.

• Myer, D., (March 2010). Dan Meyer: Math class needs a makeover. http://www.ted.com/talks/lang/en/dan_meyer_math_curriculum_makeover.html (retrieved 9 April 2012).
  
  This is a Ted Talk where a high school teacher is talking about how math classes here in the US really need  a "makeover." He discusses ways to teach students math such that "The math serves the conversation, the conversation doesn't serve the math." He also mentions a quote from Einstein, where Einstein says that the formulation of the problem may be more important than the solution. Yet despite thus we focus more on solution here. This text I would use as something to help myself and other teachers keep in mind how to teach effectively.

Pictures: 

• Demotivated Pictures (2 April 2011). "Division by zero: It just happened" http://www.demotivationalinc.com/photo/view/1030 (retrieved April 2012). Picture.
  
  This I would love to have a poster of in my classroom. This is just a funny reminder that trying to divide by zero is invalid. 

• Harris, S., (2012). Science cartoons plus - S. Harris math cartoons http://www.sciencecartoonsplus.com/gallery/math/index.php (retrieved April 2012).
  
  There are several very funny cartoons on this site. These could be fun to occasionally put at the bottom of assignments or agendas. When we give students things to laugh at, the math will be more enjoyable.

• Imgur, (2012). "Sin(b)/tan(b)=" http://imgur.com/gallery/30umX (retrieved April 2012). Picture.
  
  This is a really funny picture that would also be fun to hang in my classroom. It would be nice to help students learn about how tangent is sine over cosine. This poster is funny, and they will undoubtedly want to know why it works, or it won't be funny at all. When they understand, they won't forget.

• Imgur, (2012). "Beautiful dance moves" http://imgur.com/gallery/tEfBW (retrieved April 2012). Picture.
  
  This is a fun way to help students learn and remember what different graphs look like. I'd love to keep a poster of this hanging in my room, also.

Songs:

• Eddington, E., Gillespie, B., Muir, A., Olsen, A., (2011). That's how you know - Pythagorized. Roosevelt, UT: Union High School, Mr. Busenbark's class. Song.
  
  This is a funny video done by my little sister and her friends for their high school math class. This is a play off the song "That's How You Know" from the movie Enchanted. In this song they sing about Pythagoras and the Pythagorean Theorem. I would love to use this in my class as a fun tool to teach about the Pythagorean Theorem. It might be fun to have this be a demonstration, and have my students do a similar assignment to this, where they write a song about some mathematician and his contribution to mathematics. There is one minor error in this song that might also provide a start for a discussion of what the error was, and what it should have said, to make it correct.

• Fine, S. (producer) (2006). Twin prime conjecture. http://www.pbs.org/wgbh/nova/physics/twin-prime.html. PBS. Song.
  
  This is a song about the Twin Prime Conjecture. The clip is only about 3 minutes long, but I found it quite entertaining. The conjecture is that pairs of primes will appear into infinity. (Meaning that an infinite amount of twin primes (two primes right next to each other, separated by one even number inbetween) exist.) I could see myself using this to get a discussion started about the twin prime conjecture (or when wrapping up a discussion/discovery lesson, involving primes).
• WSHSmath (13 March 2012). "All I do is solve (WSHS math rap song)"  http://www.youtube.com/watch?v=1qHTmxlaZWQ&feature=relmfu  (retreived April 2012).
  
  This is a funny, yet instructional video created by high school teachers, and includes many students. This is a fun way to show that math is cool. The songs are also very catchy and could be used to help students learn and remember how to solve systems of equations.

• WSHSmath (13 May 2011). "Do the quad solve (WSHS math rap song)"  http://www.youtube.com/watch?v=jGJrH49Z2ZA (retreived April 2012).
  
  This is a funny, yet instructional video created by high school teachers, and includes many students. This is a fun way to show that math is cool. The songs are also very catchy and could be used to help students learn and remember how to solve quadratics.

• WSHSmath (31 January 2011). "Gettin' Triggy Wit It (WSHS math rap song)"   http://www.youtube.com/watch?v=t2uPYYLH4Zo&feature=relmfu  (retreived April 2012).
  
  This is a funny, yet instructional video created by high school teachers, and includes many students. This is a fun way to show that math is cool. The songs are also very catchy and could be used to help students learn and remember things in trig.
• WSHSmath (31 October 2011). "Super base (WSHS math rap song)"   http://www.youtube.com/watch?v=QIZTruxt2rQ  (retreived April 2012).
  
  This is a funny, yet instructional video created by high school teachers, and includes many students. This is a fun way to show that math is cool. The songs are also very catchy and could be used to help students learn and remember how to deal with exponents on numbers and variables, and when they can be added or multiplied or subtracted.

• WSHSmath (8 November 2010). "Teach me how to factor (WSHS math rap song)"  http://www.youtube.com/watch?v=OFSrINhfNsQ&feature=relmfu  (retreived April 2012).
  
  This is a funny, yet instructional video created by high school teachers, and includes many students. This is a fun way to show that math is cool. The songs are also very catchy and could be used to help students learn and remember how to factor.

Email... google... texting... writing papers... facebook... research...these are things I do on a regular basis and they all involve digital literacies.It is really surprising to take a step back an see how much time I spend on my computer or phone. Even just today, a day that I really haven't spend that much time on my computer, I have been on her thus far probably about two hours. This morning I got online to print off some notes for a test today...and while I was at it I checked Canvas for a message from one of my students, and also distracted myself looking at other emails. Then later today I got online to actually work on this blogpost...but got sidetracked into researching how to manage hair in places that are humid...and that lead to researching the best ways to take care of and style curly hair. Getting on here yet again still later today, I got distracted with facebook, looking up my best friend from my K-3 school years. Now I am writing this blogpost.
Then a suprising amount of time is spent texting people...even though I don't really consider myself to be a super big texter I have still sent 17 text messages just today.
I never would have thought, growing up, that I would ever spend this much time using my phone or my computer. My laptop was out of commission for a little while not too long ago, and boy did I learn how much I really rely on my computer!! Luckily there is a USU computer lab that I can get to within about five minutes of leaving my apartment.
In an age where students are growing up using, at least to some extent, phones and computers and other technological things almost as soon as they can talk, being familiar with technology and incorporating it into my classroom will be to use something right up their alley. They grow up playing computer games, so why not show them some computer games that involve math? They use computers to look things up and learn about them, so why not also use a computer to help them learn math? There are so many online tools that I am becoming aware of and learning how to use that will be so beneficial in terms of teaching. Some of these are GeoGebra, Geometer's Sketchpad, Wolfram Alpha, heck--I, myself, have even made a website dedicated to interesting problems in probabiliity! In all honesty, I don't know that I'll be able to incorporate as much technology into my teaching as other teachers might, just because I am less comfortable with it, but the more I am learning, the more I become comfortable with, and the broader the spectrum of technologies to use in my teaching.

Learning to Think
       I don't really consider myself to be a "writer" but I have always enjoyed putting my thoughts and ideas down on paper. Ever since I could write (no, before--I used to have my older brothers write for me before I could myself) I have loved writing letters. I used to write letters to my grandparents in California and to my very dear great-Aunt Mona. I still have a fondness for letters. When I am stressed or having a hard time, writing letters or writing in my journal is really soothing for me.
       This didn't ever really transfer over into writing in school, however, for quite some time. In school, writing consisted of following rules, but ideas never seemed to matter. Sadly, I can even think back to a specific time when I had to write a paper for a class and I thought to myself that it didn't even matter what I wrote in the paper, just as long as I didn't use any contractions or personal pronouns, that I punctuated correctly, and had clear formatting. ...And operating under this thinking, I did just fine, grade-wise, on everything I wrote. This is not the way it should be , if you ask me. I'm not saying it isn't important to have something that is grammatically correct, but it should be just that: something that is grammatically correct. In a lot of classes, however, it seems that we focus on the "grammatically correct" part but forget the "something." Punctuation, spelling, formatting, grammar, etc---these are great and can add credibility and readability to your message, but where are you without the message? Grammar, spelling, punctuation--easy.  Good thoughts and ideas, however, are so much harder to come up with.
       The initial turning point for me was the English 1010 class I took as a senior in high school. In this class I was given the assignment to write a personal narrative essay. Before this class, I was under the impression that it was NEVER okay to use personal pronouns in writing for school. I love to tell stories, but had no idea how to make anything interesting without using my own thoughts, and thus using the word "I." This narrative essay that I mentioned is the first time that I can remember actually enjoying a writing assignment. I just loved this assignment; I got to tell a story and practice "painting" with words as my professor had instructed. I was so pleased afterwards when the professor handed back our essays and asked that I read mine in front of the class. This writing assignment was really effective because it allowed me to express my personality and memories on paper in a way that would entertain others, something I have always loved to do.
       The next milestone in my development in writing was my English 2010 class up here at USU my freshman year. This class was unlike any English class I had ever had. I was surprised to learn that the instructor didn't care that much about our spelling and grammar. If it was clearly horrendous he would probably have taken some points off, but he cared about the ideas. "Master John" as we called him (he didn't have a PhD yet, so he told us we couldn't call him "professor") piqued my mind with his declaration that people misuse the word "think." He argued that many people believe they are "thinking" but in actuality they have not truly thought in who knows how long. He taught us that thinking was not just a passive thing--being in the audience of your mind, observing what is coming on stage--rather thinking is a active. Actual thinking is pushing your brain to work hard, to make connections, discoveries, come up with ideas, and to learn and grow. Before Master John, I thought research papers were about finding and telling what other people thought. Master John instead taught us to find what the experts thought, yes, but then spend most of the paper discussing that research, not just summarizing--we should be adding something to it, our understandings, new ways of looking at it, etc, so our papers were not merely abstracts of what we had read.
       Currently I am taking a class from Professor Jim Cangelosi. It is a math class--and our assessments are more writing than anything else. Before Jim's class, even though I enjoy math, I have never really just come out of a math class and talked excitedly about how fun the test was--yet that is exactly what I did upon coming out of the classroom after the very first assessment he gave us this semester. One of the questions on this assessment, or "Opportunity" as Jim calls his tests, was to "write a letter" to one of our younger siblings, explaining some particular thing. This test question made me think, as well as allowed me to put my personality into it--things that had really made a difference in those two English classes I mentioned. The rest of the test had other things that also included writing--one giving a funny situation where we had to decide what idea from the class would work best in that situation, and argue in defense of our decision, giving both pros and cons of that choice. I came out from completing this opportunity feeling so much mental energy because I had done so much thinking--it was like how clear your mind is after going for a run!
       I am really excited to be able to implement this type of thing in my classroom in the future. When we actual have to think and organize our ideas, and understand so we can express those ideas, learning is so much deeper. Math is not really about the result, but how you got there! Teaching students to write to express their ideas will really be what helps them to learn math, not just execute algorithms for a test that they will forget the second they walk out.

Picasa

I am learning other to use other technology that may be helpful in a classroom. The current one I am trying out is Picasa. so far this seems to be a useful tool. It seems kind of like a photoshop idea, but for someone who doesn't need all the many things photoshop can do, nor wanting to pay for it!  This should be a great tool in terms of helping me let parents know what is going on in their child's classroom.

Interviews with the Experts!
In conducted interviews with three high school math teachers: Don Busenbark, Eric Gubler, and Michelle Richardson, and an interview with a mathematics professor at USU, Dr. Jim Cangelosi. I asked them about their thoughts on and definition of literacy in math, the importance of it, challenges, etc.
In my classes up here at USU, I have come to understand the basic definition of critical literacy as being able to "read and write the world" not just the word. In questioning these math educators, their ideas of literacy fall into this definition I have been taught nicely. Their responses about the definition of literacy fall into two parts: 1. literacy in math is students being able to understand and use the language and vocabulary of mathematics--being able to read and understand, and also express, justify, and explain their thinking processes and procedures used, and 2. literacy is being able to recognize when and how to apply mathematical ideas to explore and solve problems in their lives.
Though their individual ideas of literacy in math were different to some degree, it was interesting to me that each agreed that literacy is essential to a student's success in mathematics. It seems as though most people in our culture think that literacy and math are almost entirely disjoint, yet those who teach it see that literacy is essential for success in mathematics.
Dr. Cangelosi talked about how mathematics has always been furthered by people making discoveries/coming up with ideas, and then expressing them so that others could learn from them and build upon those ideas. He said that literacy in the sense of being able to read and write, comprehend and explain is important--the numbers don't really do us much good without being able to explain what they mean. Mr. Busenbark talked about how if students don't understand the vocabulary, they have a hard time understanding the concept and thus fall behind. Ms. Richardson discussed about how because of the hard time they have with literacy, many students will not even try any problem that requires reading. Mr. Gubler told me that literacy is how they develop logical thinking. Each of these comments shows how mathematics and literacy are closely woven together. Each one of the things these teachers mentioned needing literacy are things we associate, of course, with math class, yet still so many think math and literacy are separate ideas.
In the interview with Dr. Cangelosi, he mentioned the scenario that has happened to all of us: we have a question, and raise our hand "teacher, teacher, I have a question!" "--Oh, never mind, I just figured it out." Dr.Cangelosi explained that when we take thoughts and put them into words, like formulating a question, our mind reorganizes and we understand better than before, thus we often figure out the answer to our question, just by organizing our thoughts in such a way that we can articulate our question.
This is similar to the idea that when you teach, you are the one that learns the most. Dr. Cangelosi said "Good math teaching is listening and reading; good math learning is writing and speaking." He went on to explain that when we teach, we need to teach the students to write and speak about what they are learning, and thus we as the educators need to be prepared to listen to them and read what they write. On the same note, he said that we need to also teach students to listen to each other and to read what each other writes. I was interested by this--generally, and especially in math class, our peers never see our work, and the only things said that they take time to notice and remember are things the instructor has said, not things their peers say. Not only will this will develop their mathematical skills, but it will also prepare them to be better thinkers and listeners and understanders in all facets of their lives.
The problem all these math educators seemed to agree on is the attitude toward literacy in mathematics. Students are coming into their classes being able to solve equations and graph lines, but not having any idea how to actually use and understand the equations or lines. People don't think that math and literacy have anything to do with each other, so they don't expect it, and are also quite resistant to it. Memorizing formulas, however, is not the same thing as understanding. To really be able to understand a formula, we need to be able to articulate it, so it is imperative that we teach students to read and write and comprehend and express math. We need to teach literacy.

RESEARCH

Lenski, S. (2011). What RTI Means for Content Area Teachers. Journal Of Adolescent & Adult Literacy, 55(4), 276-282.

Abstract: This article talks about the RTI (Response to Intervention) legislation and the role it plays in secondary schools. It discusses how content-area teachers should not be teaching their students how to read, but supporting the literacy development of students with respect to their specific content area. This article talks about the need for students to be given the opportunity to struggle through texts, but supplied with the tools to do so successfully. Students need to be taught content-area specific reading strategies. It discusses the need for content-area teachers and literacy teachers to work together so that work in one class supports the other.

Shanahan, T., Shanahan, C. (2008). Teaching Disciplinary Literacy to Adolescents: Rethinking Content-Area Literacy. Harvard Educational Review, 78(1). Retrieved from www.uww.edu

Abstract: This article discusses the idea that when students have mastered the basics of literacy, these skills will automatically transform into the complex skills needed to be literate in higher education. It talks about the increasing demand for a literate workforce, yet the decreasing (or at least stagnant) literacy levels in students our country is producing. This article discusses a study done investigating reading strategies within different disciplines, and ways to reinforce these in students.

Spitler, E. (2011). From Resistance to Advocacy for Math Literacy: One Teacher's Literacy Identity Transformation. Journal Of Adolescent & Adult Literacy, 55(4), 306-315.

Abstract: This article discusses how changing teacher literacy identity effects how teachers view literacy in their classrooms. Spitler details the experience of one of her students, a preservice math teacher, who was very resistant to the idea of literacy in math class at first, but evolved into an advocate for it. Spitler supports her student's experiences and insights with additional research and thoughts on the importance of literacy. 

These articles provided a good insight to me as a preservice math teacher. I admittedly have resonated with the preservice math teacher discussed in Spitler's article. At first, I was also under the impression that literacy did not apply so strongly in a math classroom. I have been reevaluating my thinking on that, and when reading these articles it was nice to read about how literacy has successfully been supported in mathematics teaching. Really, to teach math really well, literacy is key. The reading and writing in math thoughts I shared in my previous post are definitely a part of literacy in math, but there is even more to it. Students need to be taught more specific skills for reading and writing math, such as the implication words like "a" and "the."

The most typical texts of my discipline are textbooks. There are many mathematical trade books out there, but for the most part it doesn’t seem like books would be interesting if they were about math things, so those books don’t get read as often as they should. This comes I’m sure, from math textbooks being the only mathematical books people are exposed to. I sadly was until within the last couple years one of those who doubted the possibility of interesting math books.

My first experience really ever reading a math book came in Calculus 3 when I needed extra explanations, and realized that I could actually read my textbook. This was a “light-bulb moment” for me, because I’d never even attempted to read a math book before. When I took Algebraic Structures, my math book even had voice and a little bit of humor in it! Discovering the humor and voice in that textbook was probably the most pleasurable moment of reading in math. I still haven’t read any mathematical trade books yet, but am currently in possession of one that I am about to start (Zero: The Biography of a Dangerous Idea).

My most unpleasant moment in trying to read math books was probably when attempting to read the book for my Linear Algebra and Differential Equations book. I did not find that book at all friendly and quickly gave up trying to read it as a way to get additional help. I did not really always understand it, and it was really really dry. I can read most anything if it is written in such a way that I can feel a person is expressing opinions, but books that have absolutely no voice, and seem as though they could have been written by a very boring robot I have a hard time with.

My best idea thus far for encouraging reading in my discipline is to maybe take a little bit of time to read to my class a little bit from a math trade book that I find engaging, to show them that they really can be interesting. I am thinking that I may want to require my students to read one math trade book during the semester. If I do this, very early on I would want to read to them a bit, so they can see that what I am asking is really not such a terrible thing, but may actually be quite enjoyable.

In my own math classes, the way I was generally encouraged to express my understanding was just by solving math problems. As a teacher, I am thinking that while being able to solve the problems is important, I can encourage my students both in writing and comprehension if I have them routinely writing about the meaning of the problems they are being asked to solve, and about problems they may discover. This will help them both in improving their literacy as well as helping them reach a much deeper learning level in terms of the math. Likewise with assessments, if I have them writing and explaining with their assignments, I can incorporate this writing and explaining into their tests. In addition to their own learning being greater with this, it will allow me, as their teacher, to better see their thought process, to see what they really grasp and what they do not comprehend. One thought I have been having about testing is that it might be interesting to give them the solution to a couple of the problems and have them just explain to me how to get that answer.I definitely want my students to learn that math is about so much more than plugging away, mindlessly, at algorithms, coming up with answers that they do not understand. 

                I have always considered myself to be a fairly good reader, though not the best. Strangely enough I would probably consider my younger, early teen self, to be a better reader than I am now---but probably just because I did it more then. I used to read books upon books upon books. Admittedly, my favorite genre when I was young was the sappy, mindlessly predictable romance novels, made dramatic by someone dying, or being kidnapped in the beginning, and then two people getting thrown together, in the midst of the conflict, two people who always seem to start of loathing each other…and then those two fall in love. Now I’d probably say that my favorites are fantasy, historical fiction, and any other book that my little sister (who is a more avid reader than anyone I have ever met!) recommends to me.

                As long as I have had something good to read, I have always loved to do so. In school, I always loved the silent reading time, especially when I had a Nancy Drew mystery novel to fill that time. When I was in middle school, in fact, when reading began to finally really click with me, I used to get so caught up in my reading that I would not notice the rest of the class moving on to other things. My little sister and I shared a room when we were young, and every night our mother would come to check on us and “tuck us in.” As soon as she left, my sister and I would turn on our bedside lamps and read for hours. We missed out on a lot of sleep because of this, but it was so fun and sneaky! The only time that I would say I have disliked reading is when I have been required to read boring things.

                I was definitely encouraged in reading by my family, friends, and church. A couple of my best friends are, in particular, incredibly avid readers. This was awesome for me because it was like having my own library---they had all kinds of books and would recommend ones to me that they thought I would particularly enjoy reading. Then we would all have fun quoting funny lines from these books later. My family, as I have discussed in my previous blog post, have also been a huge encouragement for me with reading. We didn’t watch that much television, but instead loved to move the couches by the fireplace, make hot chocolate, and have a “Happy Reading Party.” I am a member of the Church of Jesus Christ of Latter-day Saints, and the leaders of this church have always encouraged the members to read daily from the scriptures, which advice I do my best to heed, both personally and with my family, when I am home.

                I don’t really think I had any social discouragements from reading. The biggest thing that made me read less was just when school got harder and demanded more time. When this happened, there was less time that I could spend reading things that I enjoyed.

Based upon what I have said thus far, I would say that the best way I can think of to encourage my students to read texts about math subjects, would be to occasionally have a bit of silent reading time, or maybe to sit down with them and read to them from an engaging book about math or the history of it. I loved it when my teachers would read to me. This may be a great way to help them to realize that there are actually many very interesting books written about math. (Probably most students will not believe that until they hear it or read it for themselves.) To help the students build their self-perceptions of themselves as readers, I think it would be a good idea to have books available for them to read that are on a variety of skill levels. My self-perception of myself as a reader probably grew the most when I was able to be engaged in reading, not necessarily when the reading was anything brilliant, but when I could understand it and had something to think about. Having texts available to them on a variety of skill levels will give all of my students the opportunity to become engaged in the reading and build up their view of how they see themselves as readers. 

Implantation in the back of a skull…someone crawling under a fence… trying to escape something really bad…lives in danger. These are some of the earliest memories that I have. When I was little, the favorite thing of my family was to read books together. I remember us reading this book long before I could read myself. This book left a mark on me. I remember loving this book, and years later would remember things about implantations, and such, and finally asked my mother if she knew what book that it was we had read so long ago, including those. It being one of her favorite books, she immediately knew that I was referring to Gerald N. Lund’s The Alliance. Since I was little, and since rediscovering this book, it has been my all-time favorite novel.

The credit for almost all of the literacy I possess is due to my family. Reading wasn’t something just to be learned in school, but reading was “the thing!” at my house. As I have mentioned, our favorite thing to do together as a family was to read books. Every night before bed, when I was young, my mom or dad would read me a story (or sometimes more than one if I had sufficiently irresistible puppy eyes). Before I could ever read for myself, I could quote the story of George Washington and the Cherry Tree from The Book of Virtues.

Each night before we went to bed, my family would gather to read from the scriptures together. At first, before I could read, when it came my turn to “read,” my parents (or whatever older sibling I was sitting next to) would whisper to me parts of a verse, which I would repeat, so I was also able to participate in family scripture study. As I began to learn to read, I would get to read a verse when it came my turn. As I got better at reading, I got to read more verses like the rest of my family. I still remember the first time I correctly read the word “Jerusalem.” I was slowly reading from The Book of Mormon to my patient older brother (not during family scripture study), when I saw the word, knew it was a really big word, but decided to try reading it. He was so impressed and I was so proud of myself---we immediately ran to find my mom!

Though there was an atmosphere in my home that encouraged reading, I definitely struggled at first. When I was in the first grade, I remember one parent teacher conference in particular. I was sitting with my mother and the teacher, to the side of the teacher’s desk. I can see the scene in my head. I was sitting with my mother on the left of me and the teacher was sitting facing us, her desk to her right and a window behind her, the light brown carpeted walls around us. She told my mom that she wanted me to start going to Title I (a program for struggling readers). I guess I started to glare noticeably at the teacher, because I remember her telling my mother that I was upset because my birthday hadn’t been celebrated in class. I thought this was just the craziest thing ever because I knew very well that my birthday was during the summer—and I reveled in not ever having school on my birthday. I knew why I was glaring at her, and it was because she was sending me to Title I, but I did not say anything. And thus my years in Title I began.

Even though at first I had glared at my teacher for deciding to send me elsewhere during reading time, this turned out to be a great thing for me. We used to read lists of words, and were timed for doing so, though we had to be completely accurate for our time to count. I do not know if we read each new list on Monday and got our first time recorded then, or if we read through the lists twice on Friday. But on Fridays, if our second time reading the list was faster than our first recorded time, we got to choose a free book to keep! I remember one time during third grade that I read my list of words (about 20 words on it, I think) completely accurately and in only 10 seconds! Everyone was so impressed! Because of the praise that we would get for reading our word lists, the free books that we would get, and my little girl competitive spirit, I always wanted to do better.

Looking back on my elementary school years (K-3), I have realized that I am very grateful that my school did not use normal letter grades on our report cards. Instead they used letters like M for “mastered” and PM and NM for “Partially Mastered” and “Not Mastered.” My report cards were not actually that great when I was in elementary. I struggled more in school than I did later…but I did not know it, which was a blessing. All of my siblings were straight-A students, so of course I wanted to be one too. Had I realized that I was not a straight-A student when I was getting some NM’s and PM’s on my report cards, I fear that I would have been really discouraged, and I may not have done so well in school in my later years when stuff in school started to make more sense.

When I went to middle school (4^th -6^th grade) reading suddenly seemed to click for me, and I discovered Nancy Drew books. Thus began my years of devouring books like cookies. When it came to Nancy Drew books, I would get so engrossed in the story that I would fail to notice the class moving on to other things and can remember more than once coming back into reality only to find the class engaged in other things.

I cannot remember too much about how my writing developed. What probably really helped is that I have always LOVED to receive letters, and the way to receive them was to write someone first. So, I used to write letters to my grandma and grandpa in California. Then I increased my letter writing to include my great aunt Mona. When my older siblings went on LDS missions, I wrote them letters, too. As a now amusing side-note, I don’t think I actually finally got all my letters facing the correct direction until sometime during my 4^th-6^th grade years.

In Jr. High school they taught us to write in the format of a five-paragraph essay. I learned how to do this, but unfortunately after learning that, I do not think I learned much of anything more about writing until I was at Utah State University and my professors really expected a lot of me. An experience with a professor that I really valued is when one of them told me that what I had written was terrible. Saying things like that is probably not generally a good thing for teachers to say to their students, but in this case, I really appreciated it. I had written something that would have satisfied my teachers in high school, but this professor ripped it to shreds. I did not see this as a personal attack, rather as my professor saying that he knew my best could be better, and was demanding nothing less than perfection. I may have done my best in the first thing that I had written, but my professor understood that our best can always be made better, though it may require help.

As far as the other side of literacy: listening and communicating academically, I could not say when there was a difference made in these. My greatest teacher in this was my mother. The daughter of an English teacher herself, she never let us use incorrect grammar at home. Her biggest pet peeve was hearing “these ones” and would always correct us by saying, “’these’, not ‘these ones.’”

My biggest holdup, however, was though I learned to read enjoyable books like the Nancy Drew series, in school I was never taught how to read a boring textbook. The ideas I am learning in my literacy class right now are something I really wish I had learned much earlier in my schooling.

When analyzing my reading, I would say is that I am fine with reading things written for entertainment purposes, and am also just fine reading textbooks that are written more informally and are “friendly” (i.e. are written in the first person or otherwise include personal pronouns). I would much rather read a my math book where the author used language including “I” and “you,” than read a Psychology textbook I had that spoke referring to a person as “one”---even though you would assume that a math book would be boring and a psych book interesting.

As far as my writing goes, for the most part I write the way I speak. (Well, I probably throw in “however” and “thus” a few more times in my writing than in my speaking!) Similar to my preferences in reading, I am just fine writing things when I am allowed to include my personal voice. I can write formally when necessary, but that requires much more concentration.

While I thought I was literate growing up, I think now I was less so than I presumed. I could read, but didn’t, unless it was something interesting. Thus there is much knowledge that I could have had, but didn’t, because it wasn’t very interestingly written. Being literate, as I am coming to understand it, includes more than just what we are technically capable of reading and writing, but also what we actually will read and write. Being truly literate includes not just being able to read written word, but being able to reason with it and question it. Growing up, I probably would not have questioned boring texts at all. If required to read them, I would probably just read them quickly, not retaining much, but doing it so that I could honestly say I had read it. There would be no thinking critically about boring things. We could just say that everyone should instead learn how to write in a more interesting manner, but lets face it—that isn’t going to happen! To really be literate, I believe we need to be able to engage our minds in both things that we find interesting and things we don’t.

In my classroom, I intend to help my students to become engaged in reading more than just novels. The world of the written word is so much bigger than Nancy Drew. I didn’t realize growing up that there could be interesting books about subjects like math. There are, however, a plethora of enjoyable things written about mathematics. I hope to help my students learn to read the things they may find boring by interspersing them with things that are really interesting, and prodding them to question all of them. When I am pushed to learn, I push back and learn. When I was young, my family pushed me to read things like the scriptures that used large words, but when pushed I responded accordingly. In elementary, when pushed to improve, I likewise responded and worked harder, just as in college. The impact this has made on me is that I have come to understand the value of pushing students, and pushing them hard! From my own experiences I have seen that I always have reached (maybe not immediately, but eventually) the bar that has been set for my performance, no matter how high. This has taught me that to really bring out the best in my students I need to set the standard really high, and then as my teachers and professor did, follow through with them, helping their best to reach that standard.

Hey folks, here goes blog post number 1! For this I shall give you an intro of sorts and tell you a bit about myself and why I'm doing what I'm doing!

My name is Julia and I am currently attending Utah State University, majoring in Mathematics Education and minoring in Speech Communications Teaching. I enjoy reading a good book (one of my top favorites: The Alliance, by Gerald N. Lund) , finding adorable clothing on a ridiculously good sale, drinking hot chocolate, and dancing in my apartment with the music on and the curtains closed. I have also recently developed a special affinity for Peanut Butter M&M's -- strange since as a general rule I dislike peanut butter. I love spending time with my family, and they are a large part of what defines me. I have five brothers and two sisters--yes, eight kids in my family!--and a mom and dad. I LOVE being a big sister,  I LOVE having older brothers, and I LOVE having two sisters with which to share clothes and thoughts. My family is simply my favorite thing!! My fondest memories, for the most part, involve my siblings and I all in the kitchen, singing songs at the top of our lungs that we are composing on the spot, as my mother tries to tell us that we need to keep it down. :)

I love math, and I love to talk to people, so even though my two subjects of study (Mathematics and Speech Communication) do not seem to be the usual combination, they are what I love! I was very shy as a child, so the communication interest of mine is not one I was necessarily born with, rather it is one I have become interested in as I have forced myself to overcome the shy side of me. My intrigue with numbers, however, is something I think I've always had. I can still tell you the phone number of the first cellular phone my oldest brother had and I was only about 6 or 7 years old when he had it. I have always liked to find patterns in number sequences or experiment with the them in other ways. For instance, my childhood home phone number ended in "5862." --In my head I would play with these numbers in ways like the following: The difference between 5 and 8 is 3, which is 6/2. 5+8=13, and 6+2=8, and 13+6=19, and 1+9=10, and 1+0=1. 58+62=120, and 1+2+0=3. 

When I tell people that I plan to be a math teacher, I generally see the same look of "Why-on-earth-would-anyone-in-their-right-mind-want-to-do-any-more-math-than-they-absolutely-have-to????" on their faces. I generally laugh in response to this, but this particular look is one of my main reasons for pursuing this major, and eventual career. So many people unfortunately think that math is their enemy--something to be feared, shunned, detested, and shied away from. They do not realize that math is the key to understanding the world they live in! We use math in all kinds of situations, from a mother shopping at the store and trying to get the most amount of groceries for the least amount of money, to the engineer designing bridges, to the physician who must spend time thinking logically and analyze problems, to the gambler in Vegas who needs to understand probabilities---and everywhere in between!
Math can be so much fun, so useful, and so empowering--my goal is to share this!