Data Collection and Graph

According to Wikipedia, “Data Collection is a process of preparing and collecting data, for example, as part of a process improvement or similar project. The purpose of data collecting is to obtain information to keep record, to make decisions about important issues, or to pass information on to others.  Data are primarily collected to provide information regarding a specific topic.”

So, we went on to collect data about the class age group. Below was the result.

We were asked to tabulate the data in to graph. This was what our group came out with.

Although the answer was not wrong, we did it the wrong way as the main idea that we were given a strip of paper was to see that the graph can be turned into a pie chart when the edges are connected. It took us a while to visualize the concept but after looking at what the other group came out with, we managed to understand.

From the graph, we can find the:-

Mean – is the average. To find mean, add the numbers and divide the sum by the number of    addends.

Median – is the middle number in the data set that is ordered from the least to greatest. When there are two middle numbers, the median is the mean of the two numbers.

Mode – is the number that occurs most often in the data set.  Some data sets do not have a mode while some have more than one mode.

Geometry

One of the best ways to learn Geometry – use the geoboard. With children, it is best that the real geoboard and elastic bands are used rather than having dots given on a piece of paper.

A geoboard is a mathematical manipulative used to explore basic concepts in plane geometry such, as perimeter, area, and the characteristics of triangles and other polygons. It consist of a physical board with a certain number of nails half driven in , around which are wrapped elastic bands.  

Geoboard were invented and popularized in the 1950s by an Egyptian mathematician, 

Caleb Gattegno (1911-1988).

During our lesson, we were given a paper with dotted lines and were asked to draw any polygons which only connected to 4 dots. Of coz, the first thing we all drew was a square. When we explored around, we realized that the possibilities were endless. We could draw on and on. Then, we were asked to find the area of the shapes. We found out that the shapes that has no dots in the middle are of 1 unit, the shapes that has 1 dots in middle are of 2 unit, shapes with 2 dots in the middle are of 3 unit and so on. We began to see a pattern and it was decided that:-

Area = x + 1

Let x = number of dots inside

We came out with an equation!!! Yeah we felt like mathematicians. Why didn’t the math teachers teach this way back then? It would make learning math so much easier! And I wouldn’t have flunked on math!

Click on the link below to try on the virtual geoboard!

http://www.mathplayground.com/geoboard.html

Fractions

Fraction is part of a whole.

This is a hexagon. The hexagon can be divided into 6 equal parts.

Now, each divided piece of the hexagon is 1/6.

We call the top number the Numerator, it is the number of parts you have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

Now you can try to count in Fractions.

How much of the hexagon is red?

   5 red pieces 

    6 total pieces

So 5/6 of the hexagon is red.

How much of the hexagon is blue?

1 blue piece

6 total pieces

So 1/6 of the hexagon is blue. 

I found this link which is very useful for the teachers to use when introducing Fractions to the children. 

http://www.mathsisfun.com/fractions.html

Whole numbers

Whole numbers are simply the numbers, 0,1,2,3,4,5,6…. (and so on). Whole numbers are used for counting, adding, subtracting, multiplying and dividing.

So why do young children need to understand whole numbers? It can make it easier for children to understand the properties if integers. Integers and whole numbers are NOT the same, but all whole numbers are integers. The difference is that integers include negative numbers, while all whole numbers are non-negative. Zero is neither positive nor negative.

When the teacher asks students to round their math answers, the students will need to figure out simple math in their heads. For example, the price of the pencil box is $1.95 and a marker cost $0.99 and the child needs to figure out the total amount to make payments. He will need to round up or down to the nearest whole number to determine the estimated total. Thus, the price of the pencil box can be rounded up to $2.00 and the marker to $1.00 to make the total of $3.00.

Teachers do take note:

Please use the correct terms when teaching.

More than NOT bigger than

Less than NOT smaller than (use fewer than)

Numbers, Numbers, Numbers!!!!

What are numbers? According to Wikipedia, "A number is a mathematical object used to count, label and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers,   and complex numbers."

Rational Numbers??? Irrational Numbers??? Complex Numbers??? WHAT???

Ok, let's break down the Math jargon.

Cardinal Numbers

A cardinal number tells "how many." Cardinal numbers are also known as "counting numbers," because they show quantity.

Here are some examples using cardinal numbers:

• 4  cats
• 10 friends

Ordinal Numbers

Ordinal numbers tell the order of things in a set—first, second, third, etc. Ordinal numbers do not show quantity. They only show rank or position.

Here are some examples using ordinal numbers:

• 2nd fastest
• 5th in line

Nominal Numbers

A nominal number names something—a telephone number, a player on a team. Nominal numbers do not show quantity or rank. They are used only to identify something.

Here are some examples using nominal numbers:

• Bus 147
• Phone number 91234567 

Rational Numbers

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers.

• The number 8 is a rational number because it can be written as the fraction 8/1.
• Likewise, 3/4 is a rational number because it can be written as a fraction. 
  

Irrational Numbers

All numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction.

An irrational number has endless non-repeating digits to the right of the decimal point. Here are some irrational numbers:

π = 3.141592…

Although irrational numbers are not often used in daily life, they do exist on the number line. In fact, between 0 and 1 on the number line, there are an infinite number of irrational numbers!

And you think it ends here? Think again, there are also Prime Numbers, Cute Numbers, Perfect Numbers (yep that’s right CUTE and PERFECT), Complex numbers, Odd and Even Numbers, and the list goes on. So think twice if you think that teaching young children is an easy job!

Mathematics and Young Children

How do we teach Mathematics to young children? I strongly agree that the teachers need to thoroughly understand the concept and content that they are teaching. Equipped with the essential mathematical knowledge, teachers will then be able to be an effective math teacher who will provide high quality mathematics education for the children.

In school, we teach math in a fun way by using games and real life experiences. For example, when teaching ordinal numbers, we get the children involved in a race using toy cars. The children will stand side by side behind the line and push their cars across. The children will get to identify and label which car came first, second, third, etc. We like to emphasize to the children that math is used in everyday life and is all around us. We bring the children out to walk in the neighborhood and identify all the numbers and shapes. When teaching about money, we set up a supermarket corner for the children to get involved in counting money. Apart from that, the children also went to the local supermarket to have the real experience in purchasing with real money.

According to Jean Piaget, constructivism is the key to learning math. He believed that learners are not blank slates but rather creators of their own learning. It is said that children build or construct their own knowledge by integrating new concepts into existing mental structures. Children create or recreate mathematical concepts in their own minds.  Lev Vygotsky on the other hand, believed that information which is internalized depends on whether it was within a learner’s zone of proximal development (ZPD). It refers to the difference between what a learner can do without help (on his own) and what he can do with help. Teachers need not strictly choose between the two theories, but in fact we need to create opportunities for the children to construct ideas or to provide tools to promote mediation in the classroom.