Reading Journal Week 1

        a. Recall Casey Rudd. Of Casey's list of classes that he has taken, which have you had and not had? What are his worries about being a teacher? How are his worries similar and different from your own worries?

Casey's listed the following classes: multivariable calculus, linear algebra, differential equations, analysis, algebraic structures, geometry, number theory, historical foundations of mathematics, discrete structures, probability and statistics, computer-aided mathematics for teachers, educational psychology, special education for classroom teachers, motivation and classroom management, multicultural foundations of education, content-area reading and writing, cognitive science, assessment of student achievement, and methods of teaching mathematics in secondary and middle school.

Of these classes, I have had multivariable calculus, linear algebra, differential equations, analysis, geometry, historical foundations of mathematics, discrete structures, and probability and statistics. I have not taken any of the others (notice that I have not taken any of the professional education courses in Casey's list).

Casey worries that, even though he has a solid understanding of mathematics, he won't be able to conceptually explain things or provide applications while teaching. Although he learned the basics of how to do these things in his methods class, he only had a couple of professors actually exhibit the kind of teaching skills that he has studied about. He worries that his basic understanding of these teaching strategies won't be enough when he is solely responsible for his own classroom. He also worries that he will have trouble planning out units that cover all of the necessary curriculum and offer a good pace in his classroom since he has never had experience with this large-scale planning.

I can completely relate to Casey's worry that his adequate understanding of mathematics will not be enough when actually trying to teach concepts to classrooms full of students. I worry that I don't have the skills to communicate what I know in a way that is understandable to students. I also worry that I am not creative enough to come up with applications to concepts that excite students and inspire them to continue learning. I was always one of those kids that thought math itself was fun - if you could give me an exciting application, that was great! But all I needed were the practice problems to enjoy it. I know that many students are not this way, and I want to become skilled at making math fun for all types of students. I just don't have the skills to do that yet, so I worry that the math I someday teach will be boring. Also similar to Casey, I am overwhelmed at the thought of planning out units of material to teach. I have had no preparation in this area yet (I am a pure math major, and plan to pursue a licensure program after I graduate), but I will cross that bridge when I come to it, I suppose!

        b. Recall the first category of Casey's working portfolio (Cognition, Instructional Strategies, and Planning). Give a short sentence describing what each subcategory means. 

"Cognition" refers to your understanding of how students' minds work, i.e. the ways that they learn. "Instructional Strategies" means the specific ways that you know how to teach students in light of your understanding of the different ways that they learn. "Planning" refers to your practical ability to organize lessons, taking into account instructional strategies (and cognition).

        c. Recall the 7th category of Casey's working portfolio (Historical Foundation). List a historical anecdote that you think is important to include in your mathematics teaching. Explain how you might integrate it into a lesson. 

One topic in mathematics that I think a historical anecdote is not only helpful, but also necessary for is the classification of numbers. I will not go into the detail of this anecdote, as there is enough information to occupy a large chunk of a lesson. But in algebra, we ask our students to classify the natural numbers, integers, rational numbers, real numbers, and complex numbers (and sometimes more obscure sets as well). This seems like a rather pointless activity, apart from the familiarization of set notation, unless we teach them where these numbers came from! For example, the natural (or counting) numbers stemming from the practical need to count everyday items, such as fruit, days, etc. At this point I would discuss the controversy over the number zero (the Greek philosophical dilemma: 'how can something be nothing?' This is incredibly interesting to me since it is so commonplace today to think of zero as a number!). Next move to integers (debt), rational numbers (fractions), real numbers (architecture: talk about the result of applying the pythagorean theorem to a right triangle with two legs of length one unit - the hypotenuse is sqrt(2)). This is just a brief overview, but I would present all of these sets of numbers to my classroom in the context of their history. This would make the potentially boring lesson of learning set notation and classes of numbers much more interesting!

        d. Write down the nine questions that describe what school administrators are looking for during their interview with you (pp. 8-9). Of these nine questions, pick one of them that you think may be most difficult for you. Explain why you think this will be challenging and what you can do between now and your first teaching interview to prepare yourself.  

1) Will your strategies  for  motivating  students,  engaging  them  in lessons, and managing your classroom be effective for this particular school's population? 

2) Will you interact with students, parents, colleagues, other school  personnel, and visitors to the school in a  highly professional  manner? 

3) Will  you  respond  positively  to  instructional  supervision  and  further  develop  your talents for teaching mathematics during your tenure at the school? 

4) Is there a good fit between your professional goals and this particular teaching position? 

5) Is there a good fit between your teaching style and the needs of the particular students with whom you will be working? 

6) Besides effectively teaching your mathematics classes, in what other ways will you contribute to the school (e.g., serving on faculty committees, being involved in cocurricula activities, and collaborating on special projects)? 

7) Will you teach in a manner that is consistent with the National Council of Teachers of Mathematics'  Principles  and Standards  for School  Mathematics  (PSSM)  (NCTM,  2000b)?  

8) Will you uphold PSSM's equity principle so that you teach from  a  multicultural  perspective  and equally value every student's right to learn? 

9) Will you take care of the mundane tasks required of all faculty (e.g., completing administrative forms)?

I think (5) would be the most difficult question for me because ultimately I want to be a teacher who can relate to any group of students, but this is a huge goal. For any given student or group of students, I want to be able to figure out how they learn (Cognition), and accordingly structure the ways that I teach them (Instructional Strategies). As I previously mentioned, I haven't had any preparation in these two areas, so one thing I could do to prepare myself is to take courses that would instruct me in these areas, and apply myself well. Another way I could prepare to answer this question in an interview is to practice with students. Even now, I work at a high school where I tutor students with all sorts of different learning styles. If I could practice assessing how they learn, and then try out different ways of teaching them concepts and observing where I have the most success, I would begin building some valuable experience in this area.