Preschool Beginning Counting

Many parents, and educators, have trouble knowing what beginning counting should involve. It is so simple that it is hard to imagine or remember trying to “learn” counting for the first time. Keeping it simple and not rushing are the keys to success now and in your preschooler’s future.

"A hundred years ago, researchers in logic discovered that virtually all of the concepts used by working mathematicians could be reduced to one of two extremely basic operations namely the operation of counting or the operation of grouping objects into sets. Most people are able to perform both of these operations before they enter kindergarten." John Mighton from The Myth of Ability Nurturing Mathematical Talent in Every Child

EveryDay Mathematics, the pervasive curriculum in U.S. schools, have two early childhood counting goals. The first, being able to count 1 to 10 objects with one-to-one correspondence (not counting the same object twice). Organization is the key to developing one-to-one correspondence. Excellent objects to count are caps of any kind like orange juice or milk container caps. Begin a collection so your child is counting the same objects. 

Generally without any education, a child can grasp the number of their age; anything above their age needs to be taught and taught slowly. The concepts of adding, subtracting, multiplication and division can be taught well, avoiding place value, using just the numbers 1-9. The mistake in educating a child to count is the constant push to higher numbers, when there really is no need.

Remember this, if the child cannot count backwards from the number they count up to, then it is not mastery of the counting goal. Think of counting numbers as staircase, if you cannot come down them, they are only half useful and won’t bring you back to where you started. Equal praise and emphasis on counting down is missing in education. 

When working with your preschooler start at their age. Give them that number of caps, they can count or guess how many the have. To check place the caps on the number organization paper they believe it is.

The second early education goal is performing rote counting from 1 to 20. This is akin to learning the alphabet in a song. Actual understanding comes with using a number board and pointing to each number. This reinforces one-to-one correspondence and the idea of larger numbers taking up larger areas. The number board shown below develops the left to right reading pattern when counting up or down. Find the resources for these goals at the ColorMyMath store.

Kindergarten Numberlines- What's Wrong with this Picture?

The simple reason why ColorMyMath number line is better than others is we focus on formatting for the child to understand counting and not formatting for the publisher to print.

Bad number lines start with 1 basketball and finish with 20 sticks.

One big basketball and lots of little sticks?! What's wrong with these pictures?

If we start out counting basketballs, then we finish counting basketballs. This takes up too much space and formatting becomes a problem.

Many number lines on the market have the flaw of changing the objects that are being counted, putting smaller objects in for the larger numbers so the objects fit on the page.

The objects/dots in the ColorMyMath  number line simply stay the same size.

Counting is more logical by simplicity than the previous example. By adding the same "measure" a dot, the child can now see the relationship between counting to larger numbers and making bigger groups.

The ColorMyMath number line also reinforces the previous learning goal for the child: recognizing bigger and smaller. The number line beautifully displays small, big, bigger, bigger still, biggest!
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Daniel Tammet Likes Pi

Today is 3rd month and 14th day of the year. When math people write this date every year, too often they think of the first three digits of Pi, 3.14.

 
Daniel Tammet  is an interesting resource for today's teacher. He fits in with Pi Day because one day he recited 22,514 digits of Pi!  Daniel raised money for Epilepsy.  Besides math, Daniel also can learn languages in a matter of weeks as well!

When Daniel was young, he suffered from epilepsy. In Daniel's memoir, Born on a Blue Day,  he recounts how after nearly dying from a seizure he began to "see" colors when thinking about numbers. This is known as synesthesia and the famous physicist, Nikola Tesla is also known to "see" colors in thoughts.

Daniel's own drawing of a part of Pi.

The Boy with the Incredible Brain, start here, is 50 minute show about Daniel. Daniel shows scientists how he sees numbers by making them out of clay. These scientists are amazed when they show Daniel a corrupted version of the digits of Pi, he gets physically upset just watching. I was amazed to watch students in Japan use an imaginary abacus. Also, Daniel meets Kim Peek, the "real" Rain Man, and plays blackjack in Las Vegas.

In the book, Born on a Blue Day , Daniel describes his struggles with Aspergers syndrome and he writes about going on David Letterman and having to concentrate on making eye contact and smiling. Daniel tells David he looks like the number 117!  here.

Happy Three Point One Four Day!

Marie Curie

Marie Curie 1867 - 1934

As teacher and a father of a daughter, Marie Curie has always been an exceptional female role model in the field of science and math. Born in 1867 as Magna Sklodowska,  Marie was of Polish nationality and her parents taught her to read Polish at a time when it was illegal! 

Her mother died early and the house was turned into a boarding house and school by her father to make ends meet. Magna found respite in her studies. Her sisters and brother would try to distract Magna to no avail.

Around 1890, Magna changed her name from the Polish to the French pronunciation. This is the time when Marie began studying Physics at the Sorbonne in Paris, France. After graduating with top marks in Physics she began her second degree in Mathematics.

During the time at the Sorbonne, Marie met, married and work side-by-side with Pierre Curie. There is a wonderful 1943 movie, Madame Curie , based on a biography written by one of her daughter’s, Eve. The movie depicts the hardship of their lab conditions, and the work that goes into separating pitchblende into its elements. At the time pitchblende was a source of Uranium, however Marie and Pierre discovered two other radioactive elements hidden in it : Radium and Polonium, named after her native Poland.

In 1903, Marie was the first woman awarded a Nobel Prize when she and Pierre were awarded a Nobel prize in Physics for their discoveries in the new science of radioactivity. 

Alpha particle ejected from the nucleus of atom.

Three years later, Pierre tragically was run over by a horse and carriage crossing the street on a rainy day in Paris. Marie Curie became the first female Professor at the Sorbonne when she took Pierre’s position. Marie had a difficult time going back into the the lab because she and Pierre worked so closely for so many years.

Marie was awarded a second Nobel prize in 1911 in Chemistry. Now Marie was the first person to win two Nobel prizes in different fields.

When World War I broke out, Marie put science to work to save many lives. X-rays are excellent at showing pieces of metal like bullet shrapnel, in a body. If the surgeon does not find all of the metal, greatly increases the chance the patient will not recover. At the time, x-ray equipment was only in the bigger hospitals in the cities. 

Marie knew that the x-rays machines were needed at the front-line hospitals. Marie figured out how to put the x-ray equipment in a truck. The truck traveled between army hospitals supplying x-ray images and giving its life saving information. The trucks that drove the x-ray equipment were known as “Petite Curies” or “Little Curies. 

Marie in a "Little Curie truck"

The courageous Marie and one of her daughter’s drove to the front-line and trained others on how to run the x-ray machine. We found an enjoyable children's movie depicting this part of Marie's life called Marie Curie- More Than Meets The Eye at the library years ago and loved it.

Marie received the French Legion of Honor because she was beloved by France even before the war.

Marie and Pierre honored on French money.

Marie’s daughter, Irene also was awarded a Nobel prize in Chemistry in 1935. This was a year after Marie’s death at 66.

Madame Curie is now accessible to kids in graphic novels about her amazing life. This book my daughter enjoyed Marie Curie (History Maker Bios).

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Geradus Mercator Map Maker

Gerard Mercator was born, March 5^th 1512, in the hospice of St Johann in Rupelmonde. Gerard’s older brother Gisbert was a priest at the hospice. Gerard was the 7^th of 11 children. The father was a poor cobbler, and the family survived mainly on bread for the first 5 years of Gerard’s life.

At school Gerard studied Latin, religion and arithmetic. By the time he was seven years old he was able to speak and to read Latin fluently. Although others in his family became priests, Gerard could not accept the teachings of Aristotle. He was not going to publicly disagree with Aristotle because it would be heresy against the Catholic Church. Gerard could not believe the Catholic Church’s creation story either. What he could believe in was the land that god had made, he traveled extensively and fell in love with geography. Gerard found his calling mapping God’s creation.

Mercator is Latin for “merchant”. Gerard did not take the name Mercator until after his mother’s death around 1528. Maps at the time were very political because they showed which countries owned what, which cities were bigger than others.

Mercator returned to the school in Louvain in 1534 where he now studied mathematics. He had difficulty until he found the math that dealt with cosmography. He also learned to be an engraver and instrument maker and taught at the school for his income.

In 1538, Mercator produced his first world map. This was the first map to show the Americas stretching from the north to the south and the first time that North America was called North America.

In 1569, he first used straight longitudinal and latitudinal lines in a “Mercator projection”. Mercator also coined the word “Atlas” for the 18 wall maps of the world he produced.

On December 2 1594, after a third stroke, Gerard Mercator passed away. One of his sons completed the maps in progress.

Addition's "Buddy" Carl Guass

Gauss at 51.

Not that long ago, in a town called Braunschweig there lived a young boy who would grow up to be known as the prince of Mathematicians!

His name was Carl Freidich Gauss and was born on April 30, 1777.

Carl was a child prodigy. At the age of seven, little Gauss started elementary school, and his potential was noticed almost immediately. His teacher, Büttner, and his assistant, Martin Bartels, were amazed when Gauss summed the integers from 1 to 100 instantly by spotting that the sum was 50 pairs of numbers each pair summing to 101.  -- Ref. Mac Tutor History of Mathematics archive.

ColorMyMath's "Buddies" addition goal is a simpler example that the prodigy Gauss employed as a boy. Gauss spotted pairs that summed to 101, we spot the pairs that sum to 10.  

ColorMyMath names the pairs that sum to 10  "Buddies".  For example, nine and one are buddies:  9 + 1.  8 + 2,   7 + 3,  6 + 4,   5 + 5 are all buddy pairs. 

Beginning understandings of the buddy pairs is a matter of asking the child "why" they are buddies. The answer is of course, "They add to ten". The buddies is the third of four goals in achieving mastery of  Everyday Mathematics easy addition facts. 

In addition to teaching the easy facts ColorMyMath introduces two other simpler patterns . Teaching the Buddies to elementary students is one reason why ColorMyMath builds better foundations for the future. 

Visually, the Easy Facts and its four goals look great in a triangle.

 

The first addition goal from the well known Everyday Mathematics curriculum is sums that add to 10 or less. These 25 "Easy Facts" are lumped together as one big goal. What makes ColorMyMath different and better than Everyday Mathematics  is that we organize these  "Easy" facts into 4 smaller parts. Additionally, the child is shown 2 other patterns in  goals 1 and 2. 

First Day on the Blog

Hello and welcome to the official start of my blog. Number one question a writer should ask "Who is your audience?"  My target audience for today's blog: People that read white papers.

To the astonishment of many educators, myself included, children can learn to read at a much earlier age. It stands to reason that kids could learn to count at an earlier age.

Beginning the foundations for success in math is a difficult task and educators have clung to what works. Although these styles vary greatly, many carry a common theme: the pinnacle of expectations for math computation is the "Multiplication Tables". Either a 10 x 10 multiplication table or a 12 x 12. Unlike the Tiger Mom, the average school in America has not raised the basic math expectations in 40 years.

I would like to see that change, right now. A look into the average elementary school in America we see math taught verbally combined with digits and variables written on the chalk board. In the K through 1st grades, verbal teaching methods i.e. "count by 2's" are still in use. It works! for the auditory learner. Another practice is the use of  a number line or number grid. The learner is taught the correlation between number and distance. A very one-dimensional view of numbers. The success in teaching computational skills and expectations have remained stagnant  for 40 years in America.

ColorMyMath proposes to change that. These low expectations and in turn performance for the average student is a thing of the past. A breakthrough in math education is inevitable and ColorMyMath leads the way by continuing a child's math education where many start: playing with blocks. ColorMyMath's advantage over blocks is the blocks are organized and quickly relay visual information by color and shape.

Why aren't bowling balls black anymore?

Android applications.