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Introduction:

Education is becoming more competitive.  Teachers around the world are questioning how to generate the next Einstein, Gershwin, and Cummings.  A mathematician, musician, and poet sent forth to grace society with brilliance.  However, why not strive for something greater?  A super student who has the ability to converge desired talents and abilities to gain a higher understanding.  Better yet, a classroom full of students who excel in all areas of the curriculum and embody intellectual abilities.  Geniuses.  “Any intelligent fool can make things bigger and more complex... It takes a touch of genius - and a lot of courage to move in the opposite direction,” said Einstein.  How do you make a genius?

Changing Traditions:

Classrooms all have commonalities.  Comparisons can be made between brick walls, desks in neat rows, and #2 pencils.  Students all receive an education in math, reading, writing, science and social studies.  The traditional organization and delivery of education has been consistent for years upon years.  But growth will not occur without change.  “To change means to learn new patterns of attention.  To look at different things, and to look at them differently; to learn to think new thoughts, have new feelings about what we experience” (359, Csíkszentmihályi).  Education is not a static ritual, but rather a living, limitless, continuation of understanding connected to the well being of society.  It is imperative that common educational traditions are broken down with the introduction of creativity.  The time has come to foster creative individuals in an effort to make geniuses.  How do you teach creativity?

Creative License:

Creativity is not divided between the haves and the have-nots.  It is a skill that can be developed over time in anyone, anywhere.  “People in every creative endeavor use a common set of general-purpose thinking tools in an almost infinite variety of ways.  These tools reveal the nature of creative thinking itself; they make surprising connections among the sciences, arts, humanities, and technologies…” (Preface, Root-Bernstein).  The book of origin, Sparks of Genius, denotes a combination of tools: Perceiving, Patterning, Abstracting, Embodied Thinking, Modeling, Playing, and Synthesizing.  All of which impart creative thinking.  “At the level of creative imagination, everyone thinks alike.”  Where do we start?

The Very Beginning:

Young boys and girls are thrust into the hands of educators at an early age.  This primary education lays the pathway for thinking about thinking.  Students must be led in the right direction from the very beginning so that creative habits become the habits.  My first grade classroom is the ideal starting place to implement Root-Bernstein’s Tools of Creativity.

Perceiving:

Perceiving is the act of interpreting what you observe in context.  Perceptions change based on a variety of conditions such as environment, prior knowledge, or outside influences.  Young eyes are constantly observing their environments as they shape their understandings.  What my students see most often is what they will most often remember.  Student perceptions are so important to building connections between background knowledge and new knowledge at school. Therefore, linking classroom academia to the real world broadens these perceptions.  In my classroom an addition symbol is linked to the volume button on a television remote.  Both increase a product.  Letter sounds are linked to childhood favorites like McDonalds, and Sponge Bob.  “We cannot focus our attention unless we know what to look at and how to look at it” (42, Root-Bernstein).  Changing perceptions in a creative way in an effort to cement understandings makes teaching and learning powerful.

Patterning:

Patterns are one of the first concepts covered in elementary school due to their presence in most every learning domain.  My first grade students are encouraged to seek out and apply patterns to better understand a variety of content.  Patterns can be discovered in repetitious books, familiar songs, and on number grids that help with addition.  “Nurtured patterning skills are at the root of the success of many artists, scientists, and professionals in various occupations” (Sparks of Creativity Wiki).  Seeking patterns and building connections across areas of studies will enrich student understanding in my classroom and encourage creativity.

Abstracting:

Abstractions are different representations that hold the same meaning.  Abstractions in elementary school help to yet again build connections.  Many first grade students in my classroom abstract content to gain a common ground.  Their bodies become a stick figure, the word love turns into a heart, and numbers become corresponding blocks.  Nietzsche stated, “The more abstract the truth you wish to teach, the more you must allure the senses to it.”  Turning big, complex ideas into something that can be felt, manipulated, and communicated will bring meaningful teaching into the classroom. 

Embodied Thinking:

Embodied thinking is engaging your body in the act of problem solving.  Embodied thought can happen whether you are solving the problem of art, music, or math.  Young students are whole body individuals.  Their excitement comes out in jumping up and down, their anger shows up in swift kicks, and love can be felt with a hug.  Therefore, it is important to use this natural form of communicating to solve problems across the curriculum.  In my classroom, hopping on a life-sized number line can solve a complex number sentence and humorous picture books can evoke laughter.  “Mind and body are one, and we must learn how to facilitate and make use of the interconnections (174, Root-Bernstein).

Modeling:

The purpose of a model is to represent an object or idea that is most often too large or too small to grasp.  Using models creates a common understanding between imagination, visualization, and physical representation.  Modeling in the classroom links the skills of perception with abstractions.  In my classroom, students model story problems with Unifix cubes, they tell a tale with puppets, and build maps with the help of Legos.  Encouraging students to model their thinking is a way of making internal thoughts into hands-on creations that can be used as a learning tool by a wider audience.

Playing:

Play is fun!  Play occurs at every age as a way of actively engaging with others in a risk free environment.  Plato enlightened, “Do not…keep children to their studies by compulsion but by play.”  Learning can and should be fun in the classroom.  Play is a tool that supports student engagement in such a creative way that learning becomes natural.  I use play in my classroom during Math Workshop to make new learning accessible to everyone through the use of games like War, Bingo, and Sorry.  This way number sense becomes something enjoyable and cooperative.

Synthesizing:

Synthesizing is the act of coming together to gain an insightful understanding across modalities. “No major problem facing the world today can be boxed neatly between a single discipline or approached effectively by analysis, emotion or tradition alone.  Innovation is always transdisciplinary and multimodal” (314, Root-Bernstein).  There are so many puzzle pieces to education, but the focus should not be on individual pieces but the picture as a whole.  All disciplines in my classroom must be connected in order to form a perfect understanding.  The days schedule should not be broken up by traditional standards: reading, writing and arithmetic.  The integration of subjects is key to not only building connections in the classroom but building connections in the brain as well.  “Creativity is just connecting things. When you ask creative people how they did something, they feel a little guilty because they didn’t really do it, the just saw something. It seemed obvious to them after a while,” Steve Jobs.

A Creative Education:

The competition in education is between tradition and creativity.  Both have a place as learning grows and changes, but only creativity can organically meet the needs of all students.  A synthesized education must start today in all grades but especially at the beginning of this race to enlightenment.  Students just starting school must be shown the tools of perceptions, patterns, abstractions, embodied thought, models and purposeful play so that these skills can be applied now.  This is an urgent task that requires immediate attention for a higher understanding by administrators, teachers and students as a collective whole.  “After creative energy is awakened, it is necessary to protect it.  We must erect barriers against distractions, dig channels so that energy can flow more freely, find ways to escape outside temptations and interruptions.  If we do not, entropy is sure to break down the concentration that the pursuit of an interest requires.  Then thought returns to its baseline state-the vague, unfocused, constantly distracted condition of the normal mind” (351, Csíkszentmihály).

Immediate Sources:

Csikszentmihalyi, Mihaly. Creativity: Flow and the Psychology of Discovery and Invention. New York: HarperCollinsPublishers, 1996. Print.

Root-Bernstein, Robert Scott., and Michèle Root-Bernstein. Sparks of Genius: The Thirteen Thinking Tools of the World's Most Creative People. Boston, MA: Houghton Mifflin, 1999. Print.

"Introduction." Sparks of Creativity. N.p., n.d. Web. Dec. 2012.

"CEP 818." CEP 818. N.p., n.d. Web. Dec. 2012.

How Do I Love Thee: Play

http://goo.gl/HA8NC

Playing:

Play is fun!

Play occurs at every age as a way of actively engaging with others in a risk free environment.

Meaningful Play:

Jet Ski Addition is a great way to introduce addition to young students and promote review among those who are experienced with the foundational skill.  There are endless possibilities for students to set up a successful and safe learning environment with this learning tool.  Competitors, individuality, pace and much more can be determined by each and every player.  Furthermore, the fast-paced, engaging game is online making it accessible to any student anywhere with an Internet connection.  

A Playful Activity:

The activity above is a game that turns addition into a fun experience with a twist.  Jet Ski Addition allows players to practice addition in a non-threatening way online.  The customizable features provide players with anonymity or publicity.  The style of a race encourages safe competition and a thrill to win.

• Players begin online by creating a game, either public or private.  Public games have already been started by other users in Jet Ski Addition.  These users are anywhere online and ready to add!  Games can also be set to private with passwords that allow specific players into the same game.  This way friends can be sure to play with one another.  There is also an option to play with just the computer.  The many ways of playing Jet Ski Addition lets each individual player customize a his or her preferred environment.  

• Once a game is selected, there are more ways that the game can be tailored to each player.  The player's name will self populate for an anonymous user.  The player can also type in a pseudonym or student name in a private room.  Finally, the player can select a jet ski color to keep track of progress in the game.  These personal touches help players connect to others and establish an identity.

• The game begins at the start of a jet ski race.  Players advance by correctly answering addition problems.  With each correct answer, the players colored jet ski moves ahead until the finished line is reached.  Throughout the game all players can see where they are in comparison to other players on either side of their jet skis.  The race is also limited in time so attention is kept throughout the entire practice period.  The end of the game awards trophies to all players involved.  Jet Ski Addition is a safe and efficient way to practice addition and enjoy the timeless challenge and thrill of a race.

How Do I Love Thee: Modeling and Dimensional Thinking

M.C. Escher

Modeling: 

The purpose of a model is to represent an object or idea that is most often too large or too small to grasp.  Using models creates a common understanding between imagination, visualization, and physical representation.  

Dimensions of Addition:

The topic of addition seems pretty simple when discussion begins in a first grade classroom.  It all comes down to putting numbers together.  However, the broader terms of addition and its uses both inside and outside of the classroom can support student understanding.  

Patterns:

The foundation of first grade is that of patterns.  Students begin recognizing patterns all around and then represent patterns with a variety of resources.  Patterns can be found on the side walk, the bark of a tree, and the colors on a shirt.  Furthermore, students show different types of patterns that can be 2 dimensional and dimensional.  The use of colors, words, and blocks bring out creativity in designing patterns.  Patterns on a paper, patterns they will look...patterns on the playground, patterns in a book.  The topic of patterns directly connects to counting by 1s, 2s, 5s, and 10s on a number grid.  Coloring in a number grid to show different ways to skip count will reveal a variety of patterns and designs that mystify students.  

Subtract:

Skip counting and identifying number patterns on a grid are the early stages of addition as well as subtraction.  Both skills work hand in hand as students learn to count forwards and backwards, up and down, and from side to side.  The formal terms of addition and subtraction are not always enforced, but students apply known patterns to explore counting in all directions.  Problem solving begins to take shape as real life examples are used to give meaning to the use of numbers.  For example, I have 4 balloons in one hand and 3 balloons in the other.  How many balloons are there altogether?  OR the oposite...I have 4 balloons in one hand and 3 balloons popped!  How many balloons are left?

Opposites:

Opposites in math are a natural part of problems solving.  Students are taught that items can be given out and then taken away.  Addition is connected with words like, altogether, more, in all, and both.  All of these words tell a student to combine numbers in order to find the total.  The same can be said for subtraction: take away, minus, left over, and so on.  Over time students become comfortable with the rules that govern problem solving.  This leads to a flexibility between addition and subtraction where students use one and then the other to check their work within a fact family.  For example, 4 + 3 = 7 and 7 - 4 = 3 AND 3 + 4 = 7 AND AGAIN 7 - 3 = 4.  Eventually the boys and girls are adding to subtract and vise versa.  

Graphical Representation:

At first glance, M.C. Escher's artwork does not appear to represent the topic of addition.  This idea came to be after rethinking my topic.  I first began with a simple representation of a growing pattern...counting by 1s and the adding on of manipulatives.  Students do this task in first grade and become shocked and surprised that they have created stairs.  However, these unifix stairs do not fully capture the dimensions of addition.  Students are adding up and taking down, but the fluidity of positive and negative combinations is not represented.  This led me to M.C. Escher's complex piece of art where stairs are growing and changing depending on the individual's perspective.  

How Do I Love Thee: Embodied Thinking

Embodiment:

Thinking with the body involves a combination of muscle movement and thought.  Sometimes our bodies move in such a natural way that it seems like there is hardly any thought at all.  

The task of finding a way that the body moves to accomplish simple addition problems brought me to the use of fingers.  As a young child, I remember using my fingers to add...but there was always a problem.  I only had ten.  My first graders have this same problem, and while some try to count their toes, there is a better way.  However, if I am being honest, I had no idea that this existed until today.  

Below is a video of a 3 year old girl using "Finger Math." Watch carefully to see if you can identify the pattern in her counting...

If that didn't impress you then here is another video of a young boy using the same strategy...

Embodied Thinking:

Engaging your body in the act of problem solving.  Embodied thought can happen whether you are solving the problem of art, music, or math.  

I'd like to say that I have been using Finger Math in my classroom for years, but I just stumbled upon the idea during my course investigations.  I first noticed the young boy on YouTube, and I thought it was a spoof.  I could barely keep track of the instructor's commands let alone the finger manipulations.  After some more video explanations, and a lot of practicing, I watched his video again and kept track up until he moved into two hands.  The three year old girl is more my speed!

Both videos have commonalities that I have noticed after several viewings.  The finger movements seem to happen naturally while the children are focusing on one command at a time.  When both children are adding or subtracting multiple numbers, they are starting from the number in their hands at all times.  (The three year old girl is given the problem, 3 - 2 + 5.  She makes the number 3 with her pointer, middle and ring fingers, puts down her middle and ring, and then puts up her thumb for a final total of 6.)  She never starts over, repeats a command or even counts her fingers until asked to do so.  Both children in the videos problem solve in this same way with finger math.  They don't seem to be keeping track until they count up the answer once the commands stop. It's as if their finges are moving at their own accord, and their brains catch up to read the answer at the end.

This seriously impacts my topic of addition.  Finger Math is a way to use the body without the limitation of ten finges.  The problem solving method also frees up space by allowing students to keep track of one number at a time and build or take apart that number.  This same strategy works for addition, subtraction, multiplication and division.   Once the strategy is understood, the possibilities are endless and the boundaries of age or grade disappear.  I can't wait to try it out in my classroom!

If you haven't figured out the pattern, here is a video with the concept mapped out.  

If you're STILL not impressed...you may want to keep a calculator on hand!

How Do I Love Thee: Abstracting

Abstracting: 
Addition is made up of several components.  The most obvious being numbers, symbols and words.

(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, +, =)

http://goo.gl/1zKYi 

Others include the specific concepts of combining quantities and items as well as the actual sum or total.    All of the above are abstractions.  Abstracting is the process of narrowing down a topic or idea to a single, simple, important element.  

I will be taking a focused look at the concept of adding, or +.  Now the symbol alone is an abstraction for the idea of addition.  However, I'd like to further abstract the thought.  A new baby in the family is often thought of as a "new addition."  A family grows larger and changes with new life.

Furthermore, addition can be seen with a different take on "addition."  A train can grow and change by the adding on of cars.  This can be realized while waiting for a long train to pass at a train stop.

Abstractions:
Abstractions are representations that hold the same meaning.  The abstraction of a human could be a stick figure.  Both are humans, but range in representation.

I chose to represent the concept of adding through the use of "new additions."  Both images above represent growth and change.  When you add together two numbers like 2 + 3, you will observe a larger number that is different than both parts...5!  The addition of a baby into a family is just that.  A family may start with two people and grow to three.  This particular abstraction can be further represented with the number sentence, 2 + 1 = 3.  Relating the concept of addition to growing and changing families will support student understanding.  Furthermore, number models can be represented to capture student families in multiple ways.  For example, mom and dad (1+1) or my parents and I (2+1) as well as the people who live with me, my grandparents, and my cousins (3 + 2 + 5).

The second representation is another type of "addition."  This form of addition takes shape with the adding on of train cars to make a long extension that passes, one after the other.  The adding on of train cars can be related to the classroom with the adding on of manipulatives.  Boys and girls can use unifix cubes to build number representations and create a concrete visual that supports addition.  For example, 5 red cubes and 7 blue cubes equals 12 cubes altogether.  It appears that a "cube train" has been built with the connecting of colored cubes. The manipulatives demonstrate the same growth and change as the new addition to a family.

These ideas impact my topic of addition while both simplifying and clarifying the overall concept.  Whether you are adding numbers, objects, money or thoughts the process will result in a larger total that is different from its parts.

Below is a link to a company with its own play on abstract addition...
http://identitydesigned.com/addition/

How Do I Love Thee: Patterning

Patterning:
Patterns are one of the first mathematical concepts covered in elementary school due to their presence in most every learning domain.  First grade students are encouraged to seek out and apply patterns to better understand a variety of content including addition.

Counting in itself is addition since you are adding 1 to the first number to arrive at the second number in a number sequence.  If starting at 0, 0+1=1 and so forth.  First grade students master counting by 1s followed by 10s, 5s, and 2s.  This is often called skip counting, otherwise known as adding on, or the beginning stages of multiplication (repeated addition).  These counting patterns can be easily seen on a number grid with the help of a little color...

• Counting by 10s can be connected to a color and students begin to recognize that all of the numbers have commonalities.  There is a 0 in the ones place and the tens place is counting by 1s.  Students can connect this with addition and subtraction.  One hop straight down will add ten to any number, or hoping up will do the opposite, subtraction.  
• Counting by 5s with the addition of color is a back and forth motion on the number grid.  Students are encouraged to notice the overlay of 10s and 5s.  In doing so, students recognize the number pattern of 5, 0, 5, 0 in the ones place with the tens place counting by 1s yet again. 
• Counting by 2s on the number grid is a reaffirmation of place value patterns with additional connections to both the tens and the ones place.  Students also gain a better understanding of even and odd numbers as well as the addition of evens and odds.  
• Adding on with different numbers becomes exciting as students discover new patterns.  They look for new number grid designs that can be found when adding on by 3s, 6s, 12s and so on.  Students also notice what numbers are most frequently used in patterns, and those that are often left uncolored.  

Patterns on the number grid initially help cement learning and provide a resource for students to independently check their work while adding on.  However, this knowledge also provides a short cut that can be used ineffectively if a student is not secure in his or her foundation of number sense.  Those who try to fill out a number grid with strictly the pattern in mind often end up skipping rows and losing their place.  Other students absentmindedly memorize patterns without the understanding of how the patterns are formed by adding on the same numbers over and over again.  Furthermore, these patterns on the number grid will only help those when adding numbers from 1 to 100 (or as high as the number grid will go).  The limitations of the number grid can be harmful if students do not have other foundations in mind such as place value.  Adding together 2,o46 to 15,334 will take quite awhile on a number grid.  These misunderstandings can be dangerous and cause a large amount of reteaching.

Re-patterning: 
Patterns are a repetitive form or plan (Bernstein, Sparks of Genius).  They are discovered when understandings are layered to build new connections.

First grade students are originally guided to discover number patterns with adding on, or skip counting. This usually becomes a rote memory procedure with a sing-song rhythm.  Young children are taught to drag out the numbers before the new group of tens so that they will later recognize these stand out patterns.  When given a number grid, the oral counting is transfered to the written numbers.  This is when students recognize the visual similarities in the numbers they have been singing all along.  New patterns can be found when students color counts by 10s, 5s, and 2s.  This provides students with a visual representation of repeatedly adding on by the same number.  It is important that students take ownership of these patterns so that the number grids do not hold limitations.  Students who know how to count to 100 by 1s, 2s, 5s, 10s, and so forth should be able to count on and on, or backwards for that matter.

Later in first grade the number grid is deconstructed and put back together to support patterns of addition.  The numbers are no longer in order, but connected on a grid by combinations from 1 through 10.  The numbers on the top of the grid can be traced down while the numbers on the left side of the grid can be traced over.  The answer can be found to an addition problem by tracing rows and columns until they intersect at the answer.  (For example, by placing your right hand on the top 2, your left hand on the side 5, and tracing down and over until the lines intersect will bring you to 7.  2+5=7!)  The color coding on this new tool further supports patterns in addition and helps students recognize new ways to combine numbers.  (For example, 9+2=11 but one more over is 12, so 9+3=12.)

http://bte2.wikispaces.com/Addition+Timed+Tests

This impacts the topic of addition and the learning process.  Different students learn in very different ways.  Some students find it useful to organize information with pictures, words, colors, numbers and more.  This new representation of a number grid to support addition is simply another resource that will reach students on a new level of organization and pattern building.  However, it is important that the understanding of patterns within addition continues beyond the visual representation.  Such visual enlightenment should only be used to cement pattern recognition and inspire future pattern seeking as well as pattern creating.

How Do I Love Thee: Perceiving

Observing:

The topic of addition will be the object of my studies in first grade.  It is introduced to most in kindergarten and pops up over the course of a life time.  This little symbol, a side-ways x, a stumpy t, two intersecting lines...usually means to add in a number sentence.  Students perform addition problems with ease such as, 2 + 2 = 4. 

It can be drawn with a pencil, pen, crayon or marker.  It can be typed on a keyboard or scribbled in the sand. Students recognize this symbol when doing math more than any other symbol such as, ÷, <, >, or the similar ×.  Some students say plus, some say add, or addition when reading this symbol.  In first grade, students are taught other key words that go with this symbol like and (2 and 2 makes four) or altogether (what is 2 and 2 altogether). 

No matter how the symbol is written, spoken, or pictured...it most often means to add in a number sentence.  The combination of two numbers to find the sum.  Unless it's red...

Re-Imagining:

Now what do you see?  This re-imagined character brings with it the values and emotions of the Red Cross.  An emblem traced back in history that gives courage and inspiration to those who need it most.

Perceiving:

Perceiving is the act of interpreting what you observe in context.  Perceptions change based on a variety of conditions such as environment, prior knowledge, or outside influences.

The addition symbol is most often perceived as a prompt to combine two or more numbers within the confines of a math class.  But, take the same figure out of the classroom and it carries a whole new meaning.  The Red Cross was declared as a symbol of protection at the 1864 Geneva Convention.   The red emblems on a white background were to be placed on medical vehicles and buildings to protect them from military attack(*).  Since then, the Red Cross holds the message of help and hope.  It can be found in hospitals, on first aide kits, and badges worn with honor.

This new perspective only supports my teaching of addition in first grade.  What my students see most often is what they will most often remember.  Whether the addition symbol pops up in math class or on the front of a building - black, red, pink or purple, it is present in our everyday lives.  Building connections between what we know and the like broadens our understandings of the changing world.

What More:

Take the red cross on a white background and flip-flop the colors.  Add a pole...

Véjà Du Revealed

How Do I Love Thee: Véjà Du

Guess What...

CEP 818

Welcome to my new Blog for CEP 818!