Tuesday, January 15, 2013

Freedom of Choice

I grabbed a book from the public library's book shelf just because its colorful cover caught my eyes.  And I looked closely.  There is a beautiful young woman looking down covered by a multi-bright colored cloth; I assumed it was a traditional outfit for women.  As its subtitle shows, it was about an Afghan woman who defied her fate which was extraordinary inspiring.  The author Saima Wahab shared the journey of her life with readers quite beautifully.  It made me feel more thankful for being in the U.S. than before after reading this book.  But at a same time, I felt terrible about the living situation and women's states in Afghanistan, which made me depressed.  Really deep.  One of the reasons was this; As I became more confident in understanding about Afghanistan in depth, I wanted to share my knowledge with my 3rd graders.  Yet they are too young to understand the whole picture.  I got frustrated.  I didn't make them depressed.

When I returned it in the library, I found another book.  It's called;
My husband glanced at it on the kitchen counter and started reading.  In 15 minutes, he said, "You must read it.  It must have a kids version."  So I googled it and found the Author, Jon Gordon's site.  Then, I clicked away several times.  Now I found The Energy Bus for Kids. 


"What a wonderful book, " I thought aloud.  The driver of the Energy Bus is Joy who teaches how to stay positive and overcome challenges in life with of course, a kid friendly setting.   One phrase from a song goes, "I am a driver of the bus, I know where I'm going."  Jon Gordon invites and encourages children to visualize their life goals and dreams.  No one can stop you.  You can choose to fuel yourself with positive energy or now.  You can choose to accept bullies in your bus or not.  I was stunned.  In our country, we have choices regardless of the ages, gender, whatever you can see as differences among people.  If you make wise choices, your life would be full filled.  It totally made sense.  Then, my prior lament about the Wahab's book turned into the positive thoughts.  While I may not directly introduce terrible things about other countries right now, I can teach gratefulness of being in our country.  There were many sacrifices over the years, for example, Dr. Martin Luther King. Jr.  When my students visit me 10 years later, I would love to share about the suffers that some countries have been experiencing. 

The final gratitude of a day is here;  I can choose what to teach my students to prepare for their real life.  And my students, too, can learn how to make wiser choices each time.  I am very grateful to be a part of their lives.

Thursday, January 10, 2013

Number Order in Multiplication

I am throwing a question at you.  Stick with me and have some discussions!

Ordering numbers in multiplication equations has been a headache for a long time.  As a 2nd grade student and a Elementary School teacher myself, it was always the same.  It is called the "Sandwich Rule" .  Number of objects in each group x Number of Groups = Total Number of Objects

Quite interestingly, although this rule is so common in educators in Japan, it is not necessarily clearly stated in their world widely famous national standards.   According to the English Translation for the Japanese Mathematics Curricula in the Course of Study, 2nd grade D. Quantitative Relations states; (2) Student will be able to represent the cases in which multiplication may be applied by using mathematical expressions and will be able to interpret those expressions.  A Japanese teacher in Tokyo told me that teachers assume the students' understanding of the multiplication situation  by which numbers students are using for multiplier and multiplicand.  Since teachers stress about the number order, students should be able to demonstrate the proper number expression.  For example, three children are at the park.  Each child is holding 2 balloons.  How many balloons are there in all?  If you are Japanese 2nd grader, the answer is 2 x 3 = 6.  Your teacher will love you because you put the numbers in the right order.  Your answer proves your ability to identify what kind of number your are dealing with, therefore you can apply multiplication concept in your own life.  A teacher can analyze it by just a glance.

Whereas American styles vary.  Every time I teach the multiplication unit, I ask, research, and google math lessons and concepts.  Some text books favor the Japanese way, some are strongly against it, and some don't care much.  It has been a frustration because no one seems to explain why they use number orders the way they use although they have strong opinions about it.  No wonder kids get confused while their teachers are not sure...

One bright piece of news is that Common Core State Standards Mathematics stated clearly for the guidance. Grade 3 Operations and Algebraic Thinking. 1. Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each.  For example, describe a context in which a total number of objects can be expressed as 5 x 7.  Hooray!  It is totally opposite to what I am familiar with, one way or another.  The committee decided to put it in this way because of how we use English language, in my opinion, which is okay.  I can deal with it. 

But when you see the question like this; A baby whale is 3 meters long.  A mother whale is 2 times longer than her baby whale.   How long is a mother whale?  What would you do?  3 x 2, right?  2x 3 just doesn't make sense.  Here is my theory.  Objects in each group and the base number (baby's whale) seem like the same category while number of groups and ratio (2 times longer) could be similar.  So, I suppose American students are required to manipulate numbers in multiplication in case by case.  My concern is how smoothly flexibly they can accept the different ways of thinking as the grades going up.  Do they have a strong enough foundation? 

I am open to any ideas, especially, the newly coming Common Core.  In fact, I share one of the worksheets I have created below.  Of course, Step 1 used to be Step 2....  Anyway, I would like to hear some clarification.  I want to be confident and consistent.  Keep our conversation alive!




Multiplication Word Problem Analysis
Name ___________ Date________
  
Page/ #
Step 1
# of Groups
Step 2
# of objects in each group
Step 3
Total # of objects
Step 4
Equation
Labeled Answer
1






Write a story Problem.
_______________________________________________________________
_________________________________________________
_________________________________________________
_________________________________________________
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Friday, January 4, 2013

R.I.P in Rapport

If you have a rapport with someone, you can find "Respect", "Intention", and "Patience" in your trust relationship.  There are so many relationships everywhere in different styles and different degrees.  It doesn't matter if the relationship is just beginning or if it's over 30 years... Your comfort level has been allowed to flourish into a positive relationship with a particular person.  This is what I found as "R.I.P". 

First, any communication starts with mutual respect regardless of what or who you are.  If you find yourself judging a person in certain ways, such as how he dresses, what he values, or where he lives, etc., a rapport might be difficult to build.  Accepting is respecting.  It is okay to be different to your appearance or your opinion.  Next, if you would like to develop a positive relationship, your must be intentional.  Your intention is to want to feel good about each other by mutual respect.  So your approach must be friendly and kind with a smile.  Your body language is soft and open.  Your eyes are meeting with others.  Show your interest in what he does.  Acknowledgement opens anybody's heart easily.  Furthermore, don't wait for the accidental occasion (like hoping to see him at Costco).  If that person and the relationship with him is important for you, initiate to call, email, and make an appointment. Last, be patient when you disagree with that person.  Allow extra time and room to develop a rapport with someone.  If you are respectful and intentional for the purpose of the true relationship, it will come.  But it might take a longer time sometimes because personal experiences vary depends on each individuals. 

After all, patience pays off.  You will feel safe to open yourself up.  Positive relationships enrich your life.  I would love to be happy by connecting with many individuals, new and previous, close and distant, young and old, in 2013.

Wednesday, January 2, 2013

Array Finder

I met a book written in 1970s.  Its author is a famous Japanese mathematician/educator, Toyama, Hiraku.  In his book, I have learned how to manipulate 10x10 tiles so that young students would develop the concrete concepts of multiplication.  In addition, memorization will no longer be such a pain with 10x10 tiles.  I made a large classroom presentation 10x10 poster and laminated it.  I also made mini version for individual students, all laminated.  You can manipulate another color, like "L" shape, to show array quite easily, for example, a photo above indicates 7x8.  It is exciting for the creative teachers and students because possible multiplication activities with this tool are endless!  In fact, when you make lines on 5s vertically and horizontally, you can see one fourth areas.  The array finder will tell you one quarter of 100 is 25, just like a dollar.  So the product of 7x8 must be larger than 25, etc....  Bridges Math Curriculum, our district uses as the math curriculum supplement, shows a beautiful partnership with Array Finder.  The Bridges 3rd grade Unit 4 was an apparent collaboration to enhance multiplication instructions and activities along with Toyama's 100x100 tiles.  East meets West beyond four decades.  What else can you say?