MATHEmily

Hi.

I anticipate that, when I student-teach (someday...), I'll have something of an easier time of grading because I'm going to be a math teacher. However, I don't have specific areas of confidence right now because I'm kind of overwhelmed. I think that one of the challenges I will have is time management as far as grading goes. Hopefully I can come up with a system that works for me.

Probably the scenario that would be the easiest for me to accommodate would be the student without computer access at home. In that case, I would make sure that the student has the homework assignments for the unit, as well as giving him or her extra review problems. Both of these (in my ideal classroom) would have also been posted on a class website of some kind. The one that would be the most difficult to accommodate would be the impromptu assembly, since, unlike (hopefully) the WKCE testing, I would not know about it in advance. Although it may not technically be “best practice” to do so, I would probably try to build in some relevant activities, but also ones that could be cut in case the need arose. For the classes that did meet, I would try to schedule a movie or activity which, although relevant to math, would not be necessary for the completion of the unit.

While talking and listening to my classmates and my content area advisor, I realized more deeply not only what I needed to work on for this current unit plan, but also some things that I would need to keep in mind when writing future plans. First of all, I realized that my order of presentation and what I include may not be the same as some textbooks, so consulting a textbook while writing a unit plan is a good idea. Second, after we were playing around with what material I presented and when I presented it, it occurred to me that writing out a unit calendar was a great idea before writing out lesson plans because the unit calendar is far more malleable and easier to change than the lesson plans. Finally, after struggling some with what sorts of accommodations I should include, it occurred to me that something as simple as a filled-out graphic organizer would work. It is not a shiny, glamorous accommodation, but it is practical and helpful. It made me realize that not everything I do in my lessons needs to be different, completely original, and exciting. While I understand the need to maintain student interest, sometimes a good, clear aid to understanding can go farther than a complicated accommodation.

For my unit plan, I am going to do trigonometric functions.

My essential questions are:
 * 1) What is a trigonometric function?
 * 2) Why are trigonometric functions important?

My [tentative] learning objectives: Students will:
 * Be able to name the three main trigonometric functions.
 * Be able to prove the law of sines and the law of cosines, and to use them to solve triangles.
 * Be able to use trigonometric ratios and values to solve right-angled triangles.
 * Be able to use the law of sines and the law of cosines to solve acute-angled triangles.
 * Be able to explain how the trigonometric ratios are derived.
 * Be able to explain the relationship between the sine and the cosine of complementary angles, and use that relationship to solve problems.
 * Be able to use trigonometric functions for real-world applications.
 * Be able to derive the formula A = 1/2 ab sin(c).

I am thinking that, for most things which are graded, I will use a policy one of my high school teachers used: if it's a day late, it's a grade late. Eventually, the student will end up with a zero on the assignment if he waits too long to hand it in, so it takes care of the problem of having a cut-off time for accepting late homework. I think that this would be a good policy for math because math tends to move quickly and material tends to build off what went before. I do not think it is wise to have a zero tolerance policy regarding late work, since situations may arise where it would have been unnecessarily burdensome for a student to complete an assignment by the due date (student was throwing up for the last few days, student's parent died, etc.).In situations like these, I think that meeting with the student and coming up with an individual plan for completing the work is appropriate.

Also, for make-up work, I think that I will allow students as many days as they were absent to make up the work without penalty. Again, if students have an extended absence, I think that coming up with alternate assignments or an individual plan for completion is appropriate.

Two insights I gained into assessments for mathematics are:


 * 1) Instructions for assessments, especially assessments other than tests, need to be very clear.
 * 2) There is such a thing as a group test/assessment. Jill showed us one in class. The class is divided into groups and each group must complete one of the tests.

[NOTE: Anything in brackets is questionable concerning its inclusion in my final draft.]


 * Intro
 * Thesis
 * Educators need to be concerned with what they teach, how they themselves present it, and how other resources they are using either aid or detract from the learning process. In light of this, this research paper will cover content standards, technology in the classroom, and textbooks, all in the context of the secondary mathematics classroom.
 * More introductory comments
 * Many of the claims are research-based.
 * Kilpatrick (2001) talks about research and evidence in light of recent education trends.
 * He discusses that there is a need for education research, not so much because it will convince people who are obstinately unconvinced that newer pedagogical techniques work, but so that educators can have solid evidence to back up their own teaching practices. Also, the evidence may encourage teachers to try some new techniques.
 * Technology
 * How should teachers incorporate technology into their classrooms?
 * Some schools are allowing students to have devices such as music players and cell phones during the school day, and are using these devices to help their students learn.
 * Hodges and Conner (2011) talk about the effect of using technology in an introductory calculus class.
 * There are websites which have different programs (such as java applets) which serve to illustrate certain mathematical concepts in a dynamic way, which static textbooks cannot.
 * Also, some textbooks now come with either cds or links to websites for additional material.
 * Content Standards
 * The NCTM put forth new math standards in 2000, which it recommends to increase proficiency in mathematics.
 * Further, the Common Core Standards website lists its standards for mathematics, which Wisconsin has adopted.
 * [Bring up Awash in a Sea of Standards (Marzano and Kendall, 1998).
 * Acknowledge that this was written in 1998, which is before NCTM came out with their new proposal for mathematics standards (2000), but that it raises an interesting issue.]
 * Kilpatrick (2001) and Reys (2001) both bring up math standards and textbook development.
 * Textbooks
 * Reys, Reys, and Chavez (2004) discuss "traditional" vs. "standards-based" textbooks.
 * They come out in favor of the latter.
 * Not only do Kilpatrick (2001), Reys, Reys, and Chavez (2004), and Reys (2001) see the textbooks as a very important part of the math classroom, but so do Kajander and Lovric (2009).
 * Kajander and Lovric (2009) discuss the issue of how mathematics textbooks may be encouraging students to form or maintain misconceptions about mathematical concepts.
 * Conclusion

The article is divided into three main sections. In the first, Burns talks about why writing in math class is beneficial: “Writing in math class supports learning because it requires students to organize, clarify, and reflect on their ideas - all useful processes for making sense of mathematics” (Burns, 2004). The second section talks about four specific kinds of writing assignments that Burns has used in her classroom: “keeping journals or logs, solving math problems, explaining mathematics ideas, and writing about learning processes” (Burns, 2004). In the final section, she discusses several strategies for implementing writing into the mathematics classroom.
 * What are the author’s main arguments or points?**

Personally, I do not need much convincing of the importance of writing, even in the math classroom. That being said, I think that the author did a good job of backing up her thesis that writing is a useful tool in the mathematics classroom. She cites examples of how she learned about her students from their writing, especially one example where a students thought that 1/16 was the smallest fraction. Because she learned about this student’s misconception, she was able to go about correcting it in a subsequent class. However, I would have liked to have seen more evidence that the writing helped her students to hone their reasoning and mathematical abilities.
 * Does he/she support those arguments or points convincingly? Explain.**

Before I read this article, I was definitely considering using writing in my math class. I was not quite sure how, though, especially since neither of my field observation classrooms used writing on a regular basis. This article helped me to see more concretely what something like using a math journal would look like. Also, it provided some helpful suggestions about helping students to write. Writing may scare some people, and students may not be expecting to write in math class. Writing does not tend to be difficult for me, so getting some ideas to help jump-start more reluctant or struggling writers was useful.
 * How does the information in this reading support what you will do or do in your classroom? Cite some specific examples.**

I have noticed myself that writing about a topic aids my understanding of it. In my undergraduate studies, I wrote a math paper on Euclid’s use of the words “construct” and “describe”. An initial glance at his usage of the two terms seemed to indicate that there was not much difference between the two, but upon further investigation, I realized that there was a difference. I would strongly consider using a similar writing assignment to help students to distinguish between some closely-related mathematical terms or ideas. This article helped to cement my inclination to use writing in my classroom.

During our meeting with our content area advisor, Jill, we learned more about how she enjoys working with at-risk students, so we talked about that for a bit. Also, we talked for a while about technology in the classroom, which included everything from using things like ipods and cell phones for education to briefly touching on using more "business"-type programs such as Excel. Jill mentioned that, at the school she is working at, they are going to allow students to have their cellphones and ipods with them during the school day. Finally, we talked about assessments, especially homework. I remember talking about whether homework should be graded. It was definitely an interesting meeting, especially since I learned more and more that classrooms now may not look like my high school classroom.

Thesis Statement: Educators need to be concerned with what they teach, how they themselves present it, and how other resources they are using either aid or detract from the learning process. In light of this, this research paper will cover content standards, technology in the classroom, and textbooks.

Textbook Survey—Mathematics

As you peruse your content area textbook, please complete the following activities and/or questions. You may place your responses on this page.

Brumbaugh, D. K., & Rock, D. (2006). Teaching secondary mathematics (3rd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.
 * 1. Write a bibliographical entry for the book using APA format.**

Brumbaugh teaches K-12, college, and in-service teachers. Rock is the Dean of the College of Education at Columbus State University. He teaches both children and adults about math; he teaches children about math when they are in a school setting, and adults about math education.
 * 2. What are the authors’ backgrounds in education?**

Students asked the profs to write this book. This book as internet references.
 * 3. Read through the Prefaces. What are 2 things that you learned about the book or author?**


 * 4. Looking at the Table of Contents, what are the 3 main sections of the book?**

1. General Fundamentals 2. Mathematics Education Fundamentals 3. Content and Strategies

I should read the second chapter, which is titled, “Learning Theory, Curriculum, and Assessment.”
 * 5. Which chapter should you definitely read before you begin the unit project?**


 * 6. What do PTHND stand for?**

P - Problem Solving T - Technology H - History N - NCTM D - Do

It is similar in that it includes most of the major factors of readiness, input, and output. However, it seems to be missing some of teacher readiness, explicit connection to standards, and is vague about formative assessment and guided practice.
 * 7. A general format for a math lesson plan is provided on page 7. How does it compare to the RIO format? (What is similar? What seems missing?)**

Chapter 4 looks interesting, since it appears to talk about how (generally) to teach mathematics.
 * 8. Of all the chapters in the book, which one interests you the most? Why?**

I will probably not read the chapter specifically devoted to calculus because calculus, being a topic I still feel the need to learn more solidly, will not be one which I choose to write a unit about.
 * 9. Of all the chapters in the book, which one will you probably not read during this course? Why?**

Possibly chapter 4, since it would apply to all of the members of my advisory group.
 * 10. What is one section in particular that you would like to discuss further with your content advisor?**

Instructor Recommendations for Reading: · For Research Essay and Unit Planning—Read Parts I and II. Highlight as you read a chapter. Then stop and list your “Top 5 Ideas/Tips” from the chapter. Read only one chapter at a sitting. · As you do you the unit plan and summative plan, read the chapters in Part III that are applicable.