Content Knowledge (Course II)

CONTENT KNOWLEDGE

1.   Describe how outside-school experience(s) have expanded or deepened your subject   area content knowledge, and tell how it enhanced or changed your understanding.   Include at least one specific experience.

During my credential program, I got to work part-time at Sylvan Learning Center.  I had the opportunity to tutor and work with high school students who struggled with Algebra and Geometry.  This experience gave me a detailed insight on what students had troubled with the most.  In Algebra, I noticed that graphing lines, factoring, and solving word problems were the most commonly struggled topic.  In Geometry, it was the proofs.  Working at Sylvan was very beneficial.  I got the practice and skill needed to explain and help these students.  It not only enhanced the students’ understanding, but mine as well.  Each time I cover the same topic, I get better and confident in getting the message across to them.  This is how I grow and learn as a teacher. 

Even when I’m not in school or Sylvan, I use math every day in the real world.  You need good number sense and strong arithmetic skills to balance your checkbook or figure out the discount price when a store is having a 20% off sale.  It’s also useful for comparing scenarios.  When I go to the bowling alley, they give me the option to pay $5 to rent a lane for an hour or pay $3 for each game played.  This makes me ponder which one is the better deal.

2.    Respond to the class discussion of Ball’s “The Subject Matter Preparation of  Teachers.”  Have your initial judgments or opinions changed based on the discussion? 

No.  I find a teacher’s knowledge of the subject matter is developed during their K-12 and college education.  Even if we don’t retain or remember much of the material taught to us, that is why we review and study to understand the concept better so we can explain it well to our future students.  Hence, this is why we have the CSET to motivate us to obtain subject matter competency.  The long, lengthy discussion from Tuesday solidified and deepened my understanding of the article. 

3.    Where are you in developing and pursuing a line of inquiry?  What is your question?  Are you satisfied with your question?  At this point, what do you know about the research available in this area?  What ideas do you have for possible experiential learning sources? 

I want to focus my research on how students can learn mathematical formulas.  Besides memorizing or making flashcards, I want to find other practices or methods students can do to remember them.  These formulas include:  the special right triangles & the area and volume of plane and solid figures in Geometry, the sum and difference of cubes & the quadratic formula in Algebra 2, and all the trigonometric identities in Pre-calculus.  Over the past few days, I have been searching for articles and journals from the St. Mary’s College Library.  I seem to have more luck finding articles/journals that focus on the content knowledge and how to better present and explain it to the students.  For instance, I found a journal titled “A New Look at Some Old Formulas” which indicates how to understand and recall the quadratic formula in a wide variety of ways.   

I will also bring in music to my research.  In my six years of teaching, my students have found it helpful to remember formulas if I incorporate a well-known tune with it.  I want to understand why they respond well to this type of practice.    

In regards to the experiential learning sources, I will interview a couple of veteran teachers who have taught Pre-calculus.  I will pose a set of questions with the main focus of how they have their students remember all the trigonometric identities.  I have not taught Pre-calculus before, so this is a good opportunity to get some helpful tips.  This will also help me remember them using their technique and words of wisdoms.  The other two will mostly be attending workshops (TBD).         




I commented on the following classmates' blogs:  


Tammy Enjaian 
Jonathan Parks
Karen Vigna
Jessica O'Connell
Eddie Izumizaki

Ball article discussion

THE SUBJECT MATTER PREPARATION OF TEACHERS

By Deborah Loewenberg Ball and G. Williamson McDiarmid

1) How did your K-12 education influence your subject knowledge?

In my pre-college years, I really had a strong foundation in arithmetic, pre-algebra, algebra, and geometry.  Therefore, I have enjoyed math and retained a lot of the concepts and skills.  I just wish I had a better teacher who was able to explain the how and why aspect when I got into more of the abstract part of mathematics (i.e. pre-calculus and calculus).  For instance, I don’t really have a deep understanding on the trig identities or how to get the graph of a derivative by looking at the graph of the original function.

2) How did your college education influence your subject knowledge?

During my college years at UC Davis, my major was math with an emphasis on teaching in the secondary level.  I was a student intern at Davis Senior High School where I observed and tutored an Algebra class.  The students were working on finding slope and writing the equation of a line, which was good for me because I got to review these concepts.  I also got to see how they understood FOIL where they used Algeblocks to see the idea visually.  They had to use the Algeblocks to form a complete rectangle because the two binomials given to them were the dimensions that made up the rectangle.  In short, FOIL is like finding the area of a rectangle.   

I also took abstract math (Advanced Calculus and Euclidean Geometry).  Like high school, I wish I had professors who could explain the how and why part better.   

3) How has your “outside of school” experiences influenced your subject knowledge?

Even when I’m not in school, I use math every day in the real world.  You need good number sense and strong arithmetic skills to balance your checkbook or figure out the discount price when a store is having a 20% off sale.  It’s also useful for comparing scenarios.  When I go to the bowling alley, they give me the option to pay $5 to rent a lane for an hour or pay $3 for each game played.  This makes me ponder which one is the better deal.

Questions:

a)      I was struck at this remark on pg. 17 under the College Curriculum discussion.  “As a result, we understand far too little about what prospective teachers learn from their college study of specific areas.”  How can we fix this so that the researchers can understand better?  Would it be better to assign one researcher to each subject matter (the researcher would be a master of that area) to investigate what these prospective teachers are learning? 


b)   I noticed that math was used more often as an example to illustrate subject matter knowledge than the other subjects.  Were the authors of this research report math teachers/professors?  

Guiding Questions

1) Why do students have so much trouble learning logarithms?  What approaches have been successful in teaching logarithms?

2) How has Algebra instruction changed over the years in the U.S.?  What are the most successful approaches to teaching it?

3) How do students memorize formulas or concepts, such as the quadratic formula, special right triangles, or Trig identities?

4) Why do students have a difficult time simplifying negative and fractional exponents?

5) It's no surprise that the majority of students are intimidated and afraid of word problems.  The dilemma is there are too many types (mixture, work, consecutive integers, distance, geometry, etc).  What teaching practice/methods can we use to boost their confidence?  How can we get those helpless hand raisers to attempt the problem (set it up) by themselves without asking for the teacher's guidance?