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.