Synthesis of this Course

This course has helped me to realize the importance of incorporating the following ideas into my future mathematics classroom:

-evaluating and being aware of student comprehension as I teach, since comprehension allows students to grasp concepts and relationships found in mathematics;
-teaching and using vocabulary in a way that students can understand and master for themselves;
-encouraging oral discussions as a form of student-to-student teaching and as a way of communicating ideas on mathematics topics;
-using writing as a way to express ideas and understanding, as well as a form of assessment;
-creating a classroom that is conducive to supporting high self-efficacy levels and motivated learning by choosing affective dimensions of literacy (i.e. text selection that is appropriate for diverse audiences);
-becoming a critically literate teacher who values the empowerment of the student and who hopes to teach lifelong learning skills;
-differentiating instruction by providing students with choices and by educating them through different viewpoints, as well as being aware of the needs of English language learners.

I feel, after learning about all of these different areas, that each of these topics change and impact the teaching of an educator for the better. I have been convinced by research and by our class discussions that the implementation of these ideas and teaching styles can help to change the mathematics classroom from a training center to an empowering place of learning, education, and discovery.

As we started and continued through the semester, some of these subjects seemed distant and unconnected for me. However, as we took our oral final and discussed each area in depth, the big picture seemed so clear to me - it all came together. To incorporate a single one of these ideas is not enough because they are all interlaced and overlapping; to get the fullest effect, a teacher has to try to implement them all. I know that I will have a lot of struggles in the beginning of my career with these goals. But I also know that as I become more experienced, that it will be easier for me to notice changes that need to made in order to use and incorporate these ideas more effectively.

Discipline-Specific Writing and Assessment

As I have thought about my experiences in mathematics, I have realized that my experiences with writing have been somewhat limited. I say limited due to the fact that writing in mathematics may be considered different when compared to writing in other disciplines. The main type of writing that I have done in mathematics has been mostly numerical when computing and completing assigned textbook problems, tests, and quizzes. The only assignments that I remember having to write in a "standard English" sense (i.e. a paper or report) are a few reports on a mathematician from history and a project on fractals. So, overall, my math teachers in grade school typically encouraged me to express my understanding through numeric problems.

I feel that my experiences with writing in mathematics changed drastically when I entered college and began to complete upper-level course work. Much of the assignments in my classes required written proof, which was something new to me. However, I have come to appreciate the precision that comes from explaining and comprehending the driving forces behind mathematics because of this shift. I think that my professors have encouraged me to express my understanding by thorough investigation and detailed analysis of my work.

I honestly cannot think of any types of expression that I feel would be considered alternative or creative in presentation. However, this aside, I have been learning a lot this semester about how to incorporate technology related activites into the mathematics classroom. I feel that I have learned a lot of different ways that would display student understanding of mathematics in creative and alternative ways. Some of these technologies include math applets, blogs, and screen-cast videos. I have found that most research supports the use of these technologies in the math classroom, as they help to engage students in higher-level thinking, as well as encourage students to become doers of mathematics and make the discipline their own.

As a whole, I feel that most of the assessments that I took at the grade school level were limiting because they usually did not include questions that explored student understanding and comprehension in writing. Most tests were merely computational. I think that the tests that I have taken in college have been a little bit more diverse in this area, but only for certain classes. I feel that it will be important for me to include assessment prompts that ask students to explain how they would go about completing a problem, rather than always asking students to perform a computation. I think that knowing students' thought processes will help me to adapt my teaching to enhance their learning. I also think that I want students to create either a video or an applet of a proof as another type of assessment. I think that these types of assessments will help to educate students in mathematics rather than just train them in the discipline.

Introductions are a Must

Hi class! My name is Melissa Andersen. I am from Logan, UT. In the event that you missed the title which occurs at the top of this blog, I am majoring in Secondary Mathematics Education. My minor is School Library Media, which means that I would either love to eventually become a math teacher or a school librarian. I love to read books, play the piano, and watch old movies in my spare time. I also enjoy sleeping and eating ice cream. I definitely prefer vanilla over chocolate. An interesting fact about me that few people know is that I love rocks, and I own my very own rock collection, which is continually growing (even though rocks don't really grow :).

In the beginning of my college career, I had no idea what I wanted to do or become. I had always kind of wanted to be a teacher, but I didn't know what subject I wanted to teach. I was good at math during middle school and high school, and did well in all the math courses I took during those years. So, after my first year at the university, I finally put the two together and decided on this major. I honestly don't know why I like math so much. I think I like it mainly because I love solving puzzles. I love working on a problem, even to the point of frustration. And then, when I solve that problem, the feeling of satisfaction that I figured it all out is so worth it!

And allow me to put a small plug-in for school librarians at this point. They can help you all so much as secondary education teachers! They are highly involved with the literacy aspect which we will be focusing on in this class, as well as the research skills that students need in the world today. Collaborate with them, and you will be amazed at what they can help you to accomplish with your students. This is something that I am very passionate about, so don't be surprised if you hear more comments like this in the future. :)

Mathematics to me is a rich language of numbers, dealing with their values and the manipulation of their values. I feel that mathematics can be as difficult to learn as a foreign language would be to learn. Some people learn the "language" of mathematics a lot quicker than other people do, and not all people like to "speak" the language of mathematics. Mathematics is also a great discipline to me because there can only be so many answers to a problem or question. In this aspect, mathematics is quite absolute - there is usually only one right answer. It is easy to tell if you have worked a problem correctly or not; I love that set structure.

I want to teach math to students because I want them to know that they can learn something that is difficult. Math will come easily to some students, and not so easily to other students. I want to be able to teach and help all of my students to have confidence in themselves. It may take a lot of work to understand the use of variables in algebra, but I want to be a main support for those students as they struggle and eventually achieve an understanding of math. I definitely am not the smartest mathematician out there; I have to get help from my classmates from time to time in my upper-division math courses here at the university. I think that those types of experiences have been very humbling for me because I will be able to understand the frustration and overwhelming feelings that my future students experience as they stumble through their homework.

I hope and anticipate that this class and you, my classmates, will be able to help me understand and improve my teaching methods, implement literacy into my future courses, and aid the learning of my future students.