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.