Blog 6- The Last One!

1.  Thinking about Ravitch- a game:  Scenario:  After the resignation of the Secretary of Education, President Obama has called you on the phone and wants to know what you think are the first five things to be done about education.  What is your response?

a) First, read Diane Ravitch’s “The Death and Life of the Great American System”.  This is to serve as a wake-up call on where education has gone wrong.  Test scores, accountability, and choice seem to be the nation’s top priority when schools are evaluated.  What ever happened to curriculum, content, and instruction? 

b) Get rid of NCLB.  George W. Bush made the biggest mistake during his presidential term by signing a bill indicating that all schools must reach 100% proficiency in math and English from all students by 2014.  As 2014 draws near, I don’t see this happening at all.  I also find it preposterous that the fate of a teacher’s employment and the school status is determined by standardized test scores.    

c) Provide the funding needed for Professional Development, Workshops, and Professional Learning Communities.  Every year teachers all over the country would like to improve on their teaching craft and explore projects & other activities to enhance the curriculum.  There just aren’t enough opportunities for these to occur. 

d) Lower class sizes.  This continues to be a factor every year.  Classes consist up to 45 students.  Think about how much and how long grading will take the teacher.  What if the class was filled with English Learners or students with a learning disability? 

e) Support teachers.  Teachers are easily the hardest working people.  However, their hard work and dedication gets overlooked.  They deserve a raise!  It’s long overdue. 

2.  What has been meaningful for you about Ravitch?

I really feel that Ravitch is genuinely concerned about education and is hoping positive changes will occur.  Who else would take 45 pages to write an epilogue (the longest I’ve ever encountered in any book) and take the time to recap what is wrong with the school system today?  I appreciate how she provides solid evidence to support her claims and theories.  Sometimes she just gets carried away with her rambling, but I know she means well. 

For me, I just get carried away with my own teaching practices and helping my students that I don’t consider the economic and political issues of education.  This book has certainly opened my eyes.  I was not aware of the “dangers” behind testing, accountability, and choice, so I am extremely grateful that this book was assigned for us to read.   

3.  Given the current state of American education, what can you do as a teacher and as a citizen?

As a high school math teacher, I will continue to do what I do best.  That is, to teach and inspire my students to work hard and be responsible individuals.   Every year I always hear that schools are in need of math teachers.  Let’s face it.  There just aren’t enough good math teachers today who are capable of explaining the material well enough for students to comprehend.   From the praise and positive feedbacks I’ve received from administrators, parents, colleagues, and students these past six years, I’m so grateful I am not one of those “bad” teachers.  Therefore, I plan on teaching and touching students’ lives until I declare retirement.    

As a citizen, I can take part in making the right choices towards the political and economic aspects of education (i.e. lower class sizes and higher salary pay J).  I am also a member of the Parent Teacher Student Association (PTSA), an organization designed to support the school, teachers, and students by contributing funds to make clubs, sports, and after-school programs possible.      

4. Find two national or state associations from your subject area and describe what you find from each website.  

American Mathematical Society (AMS)  http://www.ams.org/home/page

AMS is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship.  It does this with various publications and conferences as well as yearly monetary prizes and awards to mathematicians.  AMS meets every January to review the research made from these mathematicians.  Prizes, such as the Cole Prize or the Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student, are awarded to those mathematicians who get their research published.    

National Council of Teachers of Mathematics (NCTM)  http://www.nctm.org/

NCTM is a public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.  Each year, national and regional conferences are held for American teachers to publish their four print journal of either elementary, middle school, or high school mathematics.  Their research is published in one of the four journals depending on the grade level, content knowledge, or pedagogical knowledge.  They are:  Teaching Children Mathematics, Mathematics Teaching in Middle School, The Mathematics Teacher, and Journal Research in Mathematics Education.  

5.  Because it was impossible in six weeks for you to find all the resources you might wish to find in your content area, and/or investigate all the experiential resources held in the Bay Area, please respond to the following:

Over the next three years, if you could, what would you...

a) still like to see in the Bay Area?

Bay Area Math Project

Lawrence Hall of Science (workshop for math teachers)

Math Teachers’ Circle Network

Mathematics Umbrella Group

Academic Summer Camps (math)

b) still like to read?

How Math Works (How It Works) by Carol Vorderman

Punk Mathematics by Tom Henderson

Teaching Outside the Box:  How To Grab Your Students By Their Brains by LouAnne Johnson

Savage Inequalities by Jonathan Kozol

Who Moved My Cheese (about time management) by Spencer Johnson

c) still like to investigate?

The Electronic Journal of Mathematics and Technology

The Cornerstone:  Math Journals

d) still like to attend?

California Math Council Conference (Asilomar:  Finding Common Ground with California Common Core Standards)

Key Curriculum Press (Addressing Common Core Standards in Alg. 2 for Statistics & Probability with Fathom)

e) still like to see in the world connected to your subject area?

Cairo, Egypt (to see the pyramids)

London, England (to see the Big Ben)

Sydney, Australia (University of Sydney has a prestigious school of Mathematics & Sciences)

Manhattan, New York (Museum of Mathematics)

Orlando, Florida (Go to Disneyworld.  Math can be incorporated by planning a budget.  How much will it cost to fly round trip, to stay there via hotel, and to get in the parks?)  

Blog 5

1.  Discuss what was the most relevant part(s) of Dr. Robert's presentation for you.  What further questions do you have regarding this subject?

I found Dr. Robert's presentation on the use of media and media multitasking of 8-18 year olds very insightful and disturbing.  I say disturbing because I'm just stunned that kids/teens today are exposed to media on average of 7+ hours a day.  As he pointed out, this could make them socially awkward.  It is one thing to be able to communicate with their friends on social networks such as Facebook or Twitter, but having a face-to-face conversation is another story.  This could affect vital skills, such as eye contact or speaking eloquently, which is needed to make them successful when they are faced with job interviews or delivering a speech publicly.  Dr. Robert's study on media is very fascinating and I hope he gets the grant to further his study for the next 5 years.  I guess my only question is what other results and effects will he gather if he includes iPads, smart phones, and other innovative gadgets that are revolutionizing technology and media.         

2 and 3.  Discuss the implications for education, for your school community, and for your own teaching.

The question is in regards to the article "More Pupils Are Learning Online, Fueling Debate on Quality".  In the article, I saw some pros and cons.

Pros:
Saves money
Students who were unable to attend school due to circumstances could take the course via online
Higher graduation rates

Cons:
Plagiarism
Online advanced placement courses (because not enough students signed up for the traditional class setting)
Less teachers needed, thus more layoffs

Based on that, here's my take on online courses.  At the high school I teach, online courses are discouraged and frowned upon, especially math.  The school district only grants credit if the student is repeating the class a second time.  Therefore, they cannot take it to get ahead or move on to the next course.  My concern with online courses is that students don't get enough (or any) direct teaching from the instructor.  Is there any rigor on the topics covered?  Does it cover all the necessary topics needed to prep them for the next course?  I feel that students who are deprived of the face-to-face instruction and interaction won't get much from the online course.  Will they retain any information after the class is over?  For instance, I had a student who retook Algebra 2 last summer via online and passed.  However, she had to drop out of Statistics this year during the first semester because she did not have a solid foundation of the Algebra skills.

I think online courses should only be open to highly motivated students (like my 402 classmates) who abides by the rules and maintains integrity.  I have a difficult time seeing students in high school doing this since they are tempted to plagiarize and take the easy way out.  

4. Review the "Technology Resources for the Teacher" document on Moodle.  Explore a minimum of four links with which you are unfamiliar and discuss how each can support student learning in your classroom- now or in the future.  

http://www.dropbox.com/


A new math teacher is coming into my school this year and she mentioned about having this software.  I didn't know what this was until I encountered it here.  This would be very useful for me to save all my important documents (notes, course policies, worksheets, etc.).  I like how you can use dropbox to access your files on another computer or a smart phone.  This could also serve as a back-up copy if I misplaced my flash drive or if my hard drive crashed and lost all my files.



http://prezi.com/


I didn't hear about prezi until this summer when one of my classmates mentioned it during a class presentation for my Master's Program.  A few weeks ago, I got to see how it worked.  I think this is better than Power Point because prezi takes the viewers on a path (journey) to learn.  I know my students would love it and be engaged with the lesson.



http://www.chatzy.com/

Some students may get very impatient and want a response for their question/concern right away when they send an e-mail to their teacher.  This may be the perfect solution for that problem.  Time and date would need to be established to have this work.  Speaking out of context, chatzy could be an alternative solution to the Web Ex requirement for the 403 class.    


http://rubistar.4teachers.org/


I wish I knew about this website a few years ago.  It would have made my life a whole lot simpler to grade my students' projects if I had a helpful, reliable rubric system.  This year I designed a music video project for my Algebra classes.  The challenging part was coming up with the rubric because no other teacher in my department had done it.  In the future, if I design another project, I can use the website to guide me in developing the rubric system.

Interdisciplinary Teaching

Choose a topic you commonly teach, and find at least two resources outside of your subject area that you could utilize to enlarge, broaden, and enrich understanding.  How would you use them?  What are the challenges and value of interdisciplinary teaching and learning?  You must include the appropriate links and/or files.  


One topic I teach in Geometry that can lead to many fun activities is finding the surface area, ratio, and volume of solids (3-dimensional figures).  The solids I cover are prisms (two polygonal bases), pyramids (one polygonal base), cylinders (two circular bases), cones (one circular base), and spheres (circles in space).  If you click on the following link, you will find that I've provided two activities.  Since the blog did not allow me to attach WORD documents, I had to post them on my Teacher WebQuest (which still works after 6 years).

http://teacherweb.com/CA/SMC/MrPang/photo7.aspx

The first activity gives students the opportunity to select a product (i.e. cereal box, bottle of lotion, carton of milk) and change the design (the shape or the dimensions of the original solid).  Once they have changed the design, they need to make an oral presentation and convince the Founder, Owner, President, or CEO of that product why their design is much better than the original one.  Students can work by themselves or with a partner to work out the proposal and details.  This allows the students to get a dose of what to expect in the business world.

The second activity is a lengthy worksheet that allows the student to investigate how solids can relate to science and economics.  Here the students can see why calculating ratios of the solids is relevant to cell biology and the economy rate.

I haven't personally done either activity, but the first one seems intriguing and worthwhile for the students.  I just may assign this project for my Geometry classes this year.

My main concern is if I had English Learners in the class.  Both these projects will pose as a big challenge to them since they are in the process of mastering the English language.  Just look at the text and the instructions of each activity.  I think they would be overwhelmed.


I read the blogs of Christina Baronian, Alex Iwaszewicz, and Mary D'Arcy.

I responded to MJ's blog.  mjdarcy.blogspot.com

Mind the Gap: session 2

1.  Chapter one:   In recounting her journey through many educational reforms, Diane Ravitch makes a number of provocative statements.  Choose two, quote them, and personally respond.  


1st quote: "School reformers sometimes resemble the characters in Dr. Seuss's Solla Sollew, who are always searching for that mythical land '"where they never have troubles, at least very few."'  Or Like Dumbo, they are convinced they could fly if only they had a magic feather.  In my writings, I have consistently warned that, in education, there are no shortcuts, no utopias, and no silver bullets.  For certain, there are no magic feathers that enable elephants to fly."  (pg 3)


Response:  This is very true.  This is the real world, not a fairy tale.  Miracles do not realistically or automatically get handed on a silver platter.  If a positive change were to occur towards education, hard work and excellent decisions need to be made for that to happen.


2nd quote: "I grew increasingly disaffected from both the choice movement and the accountability movement.  I was beginning to see the downside of both and to understand that they were not solutions to our educational dilemmas.  As I watched both movements gain momentum across the nation, I concluded that curriculum and instruction were far more important than choice and accountability.  I feared that choice would let thousands of flowers bloom but would not strengthen American education.  It might even harm the public schools by removing the best students from schools in the poorest neighbor hoods.  I was also concerned that accountability, now a shibboleth that everyone applauds, had become mechanistic and even antithetical to good education.  Testing, I realized with dismay, had become a central preoccupation in the schools and was not just a measure but an end in itself.  I cam to believe that accountability, as written into federal law, was not raising standards but dumbing down the schools as states and districts strived to meet unrealistic targets.  (pg 12-13)


Response: I agree wholeheartedly with Ravitch here.  I like how she illustrates her concern on choice using the analogy of blooming flowers.  Curriculum and instruction would be the top two items on my list to focus and improve on.   




2.  Chapter two:  On page 16, Ravitch gives a brief definition of well-educated person.  How would you characterize a well-educated person?  What should any well-educated person know in today's world?


A well-educated person is someone who has developed valuable knowledge and skills from (hopefully) a solid K-12 and college education.  They need to be able to speak, write, read, and think effectively and critically when faced with a mathematical word problem, a scientific experiment, a literary novel, or any major challenges posed in the other subject areas.     


In today's world, a well-educated person is capable of making the decision that is best for them.  Along with the knowledge and skills they have obtained from school, they must also have common sense.  Without it, they won't survive in the real world.  



3.  Thinking about the class discussion on the book, what stands out for you?  What would you have liked to say that you did not say?


The one issue that stood out to me during our seminar was teaching and prepping the students for what is covered on the standardized tests (CST, STAR).  Since we (as teachers) are held accountable on how the students perform, we are pressured into doing the state's bidding (thanks to NCLB).  I am all for curriculum and want to make sure all the standards are addressed.  I do not like to be "controlled" and be required to teach a particular unit that does not flow or connect with the previous unit just to ensure that my students know it before the standardized test.  


The one thing that wasn't mentioned was study skills and how the majority of students lack this type of practice. This was brought up in my group when we were looking at the ANAR document.  We suggested that teachers should devote some time in class to teach and help students practice & develop their study skills.



4.  Choose one gap you listed from your subject area and identify 3 resources:  a web site, an article, and a book that can help you fill that gap.  List these and discuss what you learned from one of these.  


One gap of my content knowledge that I would like to have a deeper understanding is the concept of pi and why its constant is 3.14.  


A website I found is the following link:  http://www.youtube.com/watch?v=5Ei7KmyTctY.  This is a video of a teacher showing how the ratio of 3.14 is obtained by performing an experiment involving circular objects and a piece of string.  The hands-on activity was very helpful and effective.  I will try this out with my Geometry classes this year.   


An article that helped me solidify my understanding of pi is Making "Pi" Meaningful written by Hillard C. Tripp, published in The Mathematics Teacher.  


The book Math through the Ages by William P. Berlinghoff & Fernando Q. Gouvea devotes a couple of chapters on the history of circles.  It talks about "Measuring the Circle" and "The Story of Pi".    




5.  Your annotations of resources are meant to be both scholarly and brief.  In the blog, discuss in detail why/how any two of these articles were useful to your topic/question(s).  Consider such things as listing specific information you learned that you didn't know before; how this new learning leads to other questions or sources; why this writer was convincing; whether you would seek this writer out for other articles he/she has written, and anything else you'd like to state in a blog that others can learn from and read.  




Korenman, Lisa M. & Peynircioglu, Zehra F. (2007, Spring). Individual Differences in Learning and Remember Music: Auditory versus Visual Presentation. Journal of Research in Music Education, Vol. 55, No. 1, pp. 48-64

This research article examines the effects of presentation modality and learning style preference on people's ability to learn and remember unfamiliar melodies and sentences.  Throughout the research, music is brought into the experiment to see how it affects the auditory and visual learning process.  The more meaningful the material was to the participants, the easier it was for them to retain the information.  This understanding between the two types of learning with the musical element is intriguing and helpful towards my research.  I am trying to come up with other methods and practices for students to remember mathematical formulas.


Jarrett, Joscelyn A. (1987, March). A Geometric Proof of the Sum-Product Identities for Trigonometric Functions. The Mathematics Teacher, Vol 80, No. 3, pp. 240-244.


This journal goes into more depth on how to prove the sum and product identities for trigonometric functions.  Each step of the proof is explained in detail and a visual aid is accompanied to illustrate the meaning behind the process.  I think deriving a formula and addressing the origin of where it comes from is very helpful and powerful.  This is one of the practices I want to address in my research.  



6.  Ask Meg a question.  


For our experiential resources, could we also interview former students who have taken Trigonometry or a course of mine?  I figure if I can get responses from both sides of the spectrum this will make my research more rich and worthwhile.


This blog and the previous one took the whole day for me to complete.  Hope the next blog has lesser questions. :)



Blogs I've commented on: 


Jennifer Arnold   jennsmc14.blogspot.com
Ashley Devers     adventuresinmait.blogspot.com
Melina Rinehart   MAIT-MelinaR.blogspot.com
Christina Baronian missbaronian.blogspot.com

State Framework vs CSET

1.  Examine the State Framework and CSET Overview.  Are there discrepancies?  If so, where?  In your teaching experience, how closely have you aligned to the standards?  Deviations?

As I'm comparing the State Framework and the CSET Overview for Mathematics, I see a couple of discrepancies in Algebra and Geometry.  On the Algebra portion of the CSET, we are expected to "know why the real and complex numbers are each a field, and that particular rings are not fields".  This topic is focused in college when you take 'Discrete Mathematics'.  On the Geometry part of the CSET, we must "know the variants of the Parallel Postulate produce non-Euclidean geometries".  In a high school Geometry course, we only cover the Euclidean Geometry aspect.  Non-Euclidean Geometry is more advanced and is addressed in college should you decide to be a math major.  Neither of these expectations are in the standards of the State Framework.  


I've taught Algebra 2 and Geometry for the past six years and I cover most of the standards that are addressed in the State Framework.  The only thing I don't get to cover in Algebra 2 is mathematical induction. In Geometry, some of the standards indicate that students need to prove statements/relationships, such as congruent triangles or Pythagorean Theorem. I don't necessarily derive the Pythagorean Theorem as I dive straight into concrete examples.  If numbers cannot be incorporated into the discussion, then I do spend the time proving the concept (i.e. congruent triangles).     


On the CSET, there is a section where we need to master Number Theory and the History of Mathematics.  Neither of these topics are really addressed in High School Math courses since these are considered college courses.  Therefore, these deviate from the State Framework.

2.  Using the State Framework and CSET Overview, you will examine three increments (Hint:  You have already examined one of the three years) and detail your gaps in subject knowledge.  Choose one or two and SPECIFICALLY state how you plan to bridge the gap.


I have already listed my gaps for Algebra 2 (see hard copy).  I mentioned that I wanted to have a deeper understanding on those topics.  By having that new found knowledge, I can explain those concepts better with ease and confidence.  


In Geometry, I want to expand my knowledge on circles.  For instance, why is pi 3.14?  I could do an activity on pi day (March 14th), in which the students will investigate the ratio of the diameter and circumference using a string and a circular object (i.e. pie).  If they have shown me that their result is in fact the constant 3.14, then they can eat the pie.  :)  


In Pre-calculus, I have some difficulties with the Trigonometric Formulas and Identities.  The main problem is retaining the set-up and where they came from.  If I can derive them or come up with a mnemonic device (preferably a song or a meaningful phrase), then I will learn and not forget it the next day.  Visual aids may be helpful as well.  

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?