To Infinity...and Literacy!

Literacy and math. Who would have ever thought they work together so perfectly. Not I that's for sure. When I saw the title of this course I'll be honest is saying that I was bracing myself for a long semester of enduring a class I didn't think I'd get a lot out of. Sure I knew there were opportunities to teach literacy in math but I thought math was so different and so foreign to most education professors that it would barely be touched upon. I am happy to report that I couldn't have been more wrong.

There are so many opportunities to teach literacy in math that I don't even know where to start. I'd have to say that the thing I hope to apply from this course to my own classroom is creating a math library. I was blown away with how many absolutely fascinating and downright cool books there are about math. Everything from elementary to college level books that are actually interesting. I loved building my text set as well as hearing about the books that the other math teachers mentioned. As a lifelong reader I have found a way to work another of my passions, math, into it. I plan on highlighting these math books in my teaching as well as using them for ideas on presenting material. I'm excited to see how large my library will grow and hope my students will utilize them as the great resources they are.

I have also had my eyes opened to ways that writing can be effectively integrated into a mathematics classroom. I think pre-writing is something that could be used to gauge a student's background knowledge on a topic at the beginning of a unit. I also think that articulating mathematical principles in writing is a difficult skill to develop but an important one nonetheless. I know my skills in that area didn't really develop until college and I regret that. There is something about putting words on paper that really forces you to understand what you're talking about. Otherwise the writing just sounds really bad. I want to have my students write during their assignments and tests in order to truly get a feel for what they know.

Finally I've learned not to criticize it until you've tried it. What I mean by this I that I didn't think I'd get much out of many of the assignments we did in class. But I actually learned the most about my content, strengths and weaknesses, as well as my teaching style by writing lesson plans. Some were easy and some were not. But actually having to incorporate real mathematical principles with good literacy practices was a great experience. They taught me that teaching literacy in math doesn't have to be a huge, drawn out process. Rather, it's just in the small things I do as a teacher that will have a big impact on the literacy achievement of my students. A comment here, a small writing activity here and special attention to how I introduce new words and almost any math lesson can become a literacy building lesson as well. I never would have seen that without getting my hands a little dirty with it.

Overall I really enjoyed the course and felt that math was given just as much attention as any other subject, which I've found to be rare. I enjoyed the hands on lessons and the opportunities to collaborate with peers from my own discipline. I've definitely come to see that there really is literacy beyond the numbers.

As usual my thoughts tonight are focused on our latest class discussion on critical literacy. There's so much I could ramble on about dealing with this subject. But I've decided to approach it as it relates specifically to math. This is a topic I've dealt with in other classes in my major and the things I've learned and thought about have surprised me. Among other question I've considered things like, Isn't math just cold hard facts? Numbers can't lie right? and How on Earth could someone possibly know that? Unfortunately it's taken me until my college years to have these questions come to mind. I truly wish I would have been taught critical math growing up or better yet, critical thinking in a mathematical way.

I think the distinction between what I'll call critical math and critically thinking in a mathematical way is an important one. While both require interpretation and careful examination of the motives and context of a mathematical work, one is computationally driven and another is logically driven. I feel many teachers are scared away from critical literacy in mathematics because they interpret it only as teaching critical math. Critical math in my mind is mathematics that can be applied to mathematical claims to validate or disprove them. This falls into the realm of analysis which can get very complicated very quickly. Of this type of math I myself feel I've barely scratched the surface even after 4 years of college. In a sense I would call critical math the proofs behind mathematical claims. However, this is not the type of critical literacy I advocate for in a secondary education math class because quite frankly much of it goes well beyond high school math levels.

I advocate for my second category, critically thinking in a mathematical way. To me this is basically asking some very simple questions of any mathematical claim. These questions include things like, Does it make sense and why or why not? What would I need to know to determine if it is true or not? and What could contribute to bias in this claim? Questions like this don't require a student to know advanced math, only to be able to put the mathematical information into context. I think that it's ok for teachers not to always have the "right" answer and therefore we don't have to prove everything. Inspiring our students to question what appear to be cold hard facts is critical literacy at its finest and that is what we need to nurture in our students.

This practice lends itself particularly well to statistics. Student's don't need to know how to calculate the the joint frequency distribution for two exponentially distributed random variables in order to judge the validity of most statistical claims. While certainly we want them to apply what they have learned, basic principles are often the best grounds to stand on. I've heard statistics referred to as the study of mathematical lying and I can definitely see why that's true. There are so many ways to skew data sets that who knows what the truth really is. I certainly don't and nor do I always expect my students to. I only hope that they will be able to recognize the limitations of the claims and value them accordingly. That is critical literacy to me and that is achievable with any age group.

A Discourse on Discourses

I decided to focus this blog on our class discussion a few days back and the thoughts and ideas it generated for me. I also would like to stress these thoughts are my own personal feelings and not meant to be directed at any one person who may disagree. If you disagree with what I have to say I will not be offended by any comments you might leave. In fact I would welcome them. After all this is a learning experience and if we're afraid of opinions we won't ever strengthen our own.

I would like to start off by revisiting the subject of teachers' roles in regards to molding a student's primary or secondary Discourse(just for clarification I will be using the same capitalization scheme as in the reading). I still stand by the assertion I made that as teachers, our primary responsibility is to teach students our specific content in a way that they will understand it. That is what our employers expect of us, that is what parents expect from us, and quite frankly that is what our students expect from us. Now please don't mistake me for a cold-hearted, only logical never feeling, constantly analytic math teacher. I'm not. I don't want to be and hope I never will be. It is just a fact that remains a part of our profession. To quote a professor at our very own university who, among other classes, teaches a classroom management course, "You're not hired to be their friend, you're hired to be their teacher."

I think the temptation is there for all of us to want to make something more out of our students than they enter the year with. It's a natural inclination for all of us. If we weren't compassionate and caring towards others we wouldn't be working so hard to get a job that pays so little and requires so much. So I fault no teacher who has a desire to reach out and help a struggling student become a "better" person by somehow influencing their primary Discourse. But who's to say what a better person really is? I certainly can't help a student of Jewish heritage become a better Jew. I wouldn't even know where to start to with a student from South America in order to make that student a better person according to their culture. And I wouldn't even attempt to try and make a young lady a better woman because her entire gender confuses the heck out of me (just ask my wife). The list could go on but I think you get the point. I'm not qualified to make those kind of judgments about students. My Discourse is not shared by them. When teachers try and force good values and beliefs onto their students they can often time do more harm than good. It's just not something I think we as teachers should be doing.

Now I would like to make special mention of the word force that I used in the paragraph above. To force or even try to force a set of beliefs or values on a student is wrong. However, that doesn't mean that we should be lifeless blobs that are only good for reciting facts. No, we are people of value too. We have a primary Discourse as well as many secondary Discourses. It's part of who we are and without them we wouldn't be teaching. We shouldn't hide them at all. But wait you might say, doesn't that go against what you just said about not forcing things on students? I don't believe so would be my response. By being ourselves we are exposing our students to a Discourse. However, the distinction comes by us not extending our Discourse beyond ourselves or evaluating our students based solely on that Discourse. Part of learning is making choices. By being ourselves we are only throwing more options into the pot of Discourses that a student can choose from. As long as their choice is free from our direct influence I believe we have stayed within out bounds.

I also really liked the comment in class about how removing bias from our teaching is impossible because we wouldn't be teachers if we weren't biased towards our subject. With this concept I heartily agree but I would question the word choice slightly. I think enthusiasm would be a better word. To me enthusiasm is a driving force, something that motivates us to become better than we currently are. On the other hand, I think bias is judgmental in nature and a lens through which we evaluate others. I believe it is possible to have enthusiasm, and indeed I encourage it, without having bias. To put it more concretely, I love math and will teach it with passion but I will never dislike students solely because they don't share my love. That's what I meant when I said we need to eliminate bias from our teaching. It's the judgmental aspect that has no place in a classroom designed to foster learning. If we can master that then I know every student who walks through out door will benefit, regardless of what Discourse they bring with them.

I could probably go rambling on for quite a while more but I think I'll stop. Hopefully my point came across with some semblance of clarity. I realize that I made no direct application to teaching math but this principle is universal in nature and thus applies as well as any other to my subject. It's these subtleties of teaching that make it such a complex art form and which challenge and drive me to become better. To quote one other professor in the math department, "Teaching is nothing like brain surgery. It's far more complex." And I wouldn't have it any other way.

Learning to Read and Reading to Learn

I love to read. Now this wasn't always the case though. Somewhere in my later elementary or early middle school years I had a life changing experience/punishment. My parents were concerned with how much TV my sister and I watched every day. While we were both active in sports it seems like that was all we did, sports or TV or sometimes TV with friends. Well my mom decided enough was enough and took the TV out of our house. I thought I was going to die! At this point I was a good student and an above average reader but I rarely picked up a book for fun. All that changed when the TV left. I found myself bored a lot. Shortly thereafter, I somehow I ended up turning to books for my entertainment. It was like a revelation when I discovered the "shows" in my head were way better than anything on the TV. I started reading so much that my mom ended up yelling at me multiple times because I wasn't going to bed and just staying up all night reading. A little over a year later when we got the TV back I wasn't nearly as interested in it and really only used it to play video games based on the books I was reading. I will be forever grateful to my parents who forced reading on me by banishing the TV.
However, I must add that I am a very picky reader. Growing up I was enthralled by Science-Fiction and especially Star Wars books. I read every Star Wars book my library had and even requested ones from other libraries. I still enjoy those books but not as obsessively as when I was younger. I feel that the Science-Fiction genre of literature really helped push me toward mathematics. Everything in those books is advanced. Even simple things that you wouldn't think of needing technology for are improved upon in those books. I wanted to have all those things from an early age. I don't remember any specific light bulb moment or anything like that but at some point in my middle school years it dawned on me that mathematics was the key to creating the world that I loved to read about. I didn't know how exactly math could do this but I knew that math allowed us to improve technology and that especially computers where powered by math. This has been a huge driving force behind my love of mathematics; it's potential for creation of new advanced technology. And I feel it stemmed from my love of Science-Fiction
Sadly, my public education math classes never really lived up to my dreams. I struggled to see the connections because all I was given to read was text book. Now I love math but despise text books. They're not written to be read, only referenced, in my opinion. It wasn't until 11th grade in AP Calculus did a teacher give me small bits of what I had hoped to discover. Still, there was no reading to back it up.

It wasn't until college that I was exposed to math reading material that I actually enjoyed. In college I was introduced to trade books on math that read like a conversation with a well versed mathematician rather than a stuffy old lecturer. I love those books because they expose me to the capabilities of math without bogging me down with extreme details of how to do every step. If my interest is peaked enough, I can always go back to the text books and look the steps up. I've also discovered in college that reading my peers' thoughts and ideas through online forums is very useful. They often explain things in ways that I actually understand rather than in a prescribed manner that the teacher has been using for years. My final discovery of mathematical texts has come from the use of applets that illustrate mathematical ideas. These creations are wonderful at conveying powerful ideas with little or no text to get bogged down in. This in turn allows me to write my own texts in my head in a language that makes perfect sense to me.

I think my experience with reading mathematical and mathematically themes texts will help me with my future students. I've experience the drive that can be created in someone when they truly have an interest in something. Math applies to just about everything in life and all I need to do is identify my students' interests and then open their eyes as to how math applies to it. That is much easier said than done but I know it can work. I plan on using trade books to further my students' understanding of the math they are interested in. I know the common perception is that these books are too advanced for secondary education students but I beg to differ. The students may not understand the details but just like my Star Wars books, even completely foreign or new words can be learned over repeated exposure and with time things become clearer. My love of technology is also a benefit I will bring to my classroom. The youth of today are always striving to have the latest technology. Then why not use it in my class? I love it, they love it and all I need to do is introduce it and I think my students will just run with it. Before they know it they will be reading texts they never dreamed of reading before and possibly even enjoying it. And heaven forbid any student actually enjoy math :)

Oral Language in the Mathematics Classroom: Does it Really Mater?

So I thought I'd try and put some of my thoughts about oral language down in writing with the hopes that it will help me clarify my thoughts. I really enjoyed the video clips and discussion we had in class about African-American English and Appalachian English. It really got me thinking about what a language is. Initially upon being presented with the topic of the class I thought it would be interesting to learn about but not too applicable to teaching math. After all, I don't plan on assigning any huge writing assignments and math has a very unique vocabulary that I would most likely be exposing my students to for the first time. Therefore I figured I could teach my students correct math vocabulary and I could deal with whatever oral language preference my students had in their other speaking. However, as I thought more about it I realized I needed to take off my rose-colored glasses and see that it was going to be harder than I thought to deal with oral language.
Two challenges really stood out to me. For starters, the "language" of mathematics is a precision one. Words take on very specific and literal meanings in a mathematical context. Therefore, if my students bring a more ambiguous or less understood oral language into the class the specificity of the words and the message they need to convey could be lost. I would be doing my students a disservice if I let that happen. Mathematics is a language understood globally. My students need to understand that and I need to hold them accountable for speaking that language ti ensure their future success in mathematics.

The second challenge appeared when I considered my classroom as a diverse place where multiple forms of oral language will be present. To my mind came the image of a school I once worked in that had very dichotomous student population, students' families were either very well off or economically struggling. I observed that those that had more well off families didn't interact as much with the students from struggling families. I now believe part of the reason for that was that they didn't use the same oral language. This same problem carried over into the classroom. Even when students were forced to collaborate in groups assigned by the teacher, there was a resistance and lack of flowing communication. Oral language, I now believe, was a huge contributor to the wall that was between them. If I expect my students to collaborate, and I assure you I do, then I will have to work on breaking the wall that differing oral languages create.

Finally, my thoughts on oral language have turned to myself. I fully acknowledge that being raised in Utah for all but 6 years of my life that I have developed a "Utah accent." That fact, coupled with my desire to teach for a time outside of Utah, means that my oral language might come into conflict with that of my students. While I don't consider a Utah accent a separate language, I do foresee some students having a problem with some of the things I say. To overcome this I feel the best approach is to make sure my explanations are clear and that I give directions, instructions and explanations in various methods beyond just speaking. Things like written material, dialogue between peers and visuals will all help me overcome language barriers.

All in all oral language is a big deal. There's no way to avoid it and only a teacher who cares nothing for their students would disregard it. Although my knowledge and experience with its diversities and challenges is limited, I'm glad to have at least been made aware of it and my need to address it. Even in what I thought would be my isolated math class.

Starting It Off Right

Hello my fellow classmates and the world beyond. My name is Eric Arthur and I am studying Mathematics education with a coaching and physical education minor. I also have plans to get into educational administration somewhere down the road of life but for now I am satisfied to teach and coach. You’d think that after an entire first week of classes I would have this introduction thing down. However, that doesn’t seem to be the case at the moment but I’ll do my best.

A brief background of myself would probably be the best place to start. I was born in Salt Lake City, UT and claim West Jordan, UT as my home town after living there throughout my entire childhood. I was also born on the 4^th of July so for all those who didn’t know the fireworks are actually for me and not for any other reasons you might have been given. I have attended the University of Utah and Utah State during my college years. I transferred up here two years ago after getting married in the summer of 2009. While it’s taken some adjusting, I’m glad I came up here because it prompted my change of majors into the education field. I still have a few semesters left and plan on graduating Dec. 2012.

Growing up I always considered myself an intelligent jock. I think I have almost a split personality disorder of some sort because I couldn’t be more different in these two areas of life. I am pretty quiet and reserved when it comes to my academic life (although I have been known to passionately debate on topics I feel strongly about) and the complete opposite in any type of sporting event. I become super competitive, aggressive and command much more respect and attention while playing. My passion is and always will be for soccer but I also play/enjoy basketball, ultimate Frisbee, and distance running. In fact I’ve taken very well to running and have run many races including two marathons.

My other passion in life is mathematics and teaching. I love seeing those light bulb moments on student’s faces when something just clicks and becomes perfectly clear to them. There’s nothing better to me as a teacher than knowing that a student has left my classroom with a better understanding than they entered with. I consider myself a very logical person and I think that is why I’m so drawn to math. While there are many ways at arriving at an answer, every path must follow a logical progression of ideas in order for it to be valid. Navigating that path to its logical conclusion, especially when there are obstacles to overcome, is extremely satisfying to me.

I can’t really identify one major event in my life that set me on the path to a teaching career. I’ve had my fair share of influential teachers, only one of which actually taught math, but I can’t say that I have one that pushed me here. I’ve worked a lot with underprivileged youth as a tutor and mentor and I’ve seen firsthand how desperately good teachers are needed in the world today. I’ve also seen the influence a good teacher can have on troubled students and I hope to have at least one of those experiences in my life. I’m not delusional enough to think that I’ll change every student in my class but nothing is worth doing if you don’t shoot for the moon with it. I look forward to this semester and class because I hope to expand my understanding of what it takes for a student to really learn in any given content area. Then, with any luck, I'll be able to turn that knowledge to good use and be a better teacher for it. Here's to a great semester!