Sunday, August 18, 2013

Paper Art

Square papers are being folded into triangular shape. A triangle is being cut out at the "Right Angle" area of the papers.

Figure 1: Two folds were made.
Figure 2: Three folds were made.
Figure 3: Four folds were made.

Question of the day: How do you think the 4th figure will be like?

Posting this activity for the children would spur their ability to visualize and reflect on their inference and findings. Children will have to be able to see the patterns in the 3 figures and visualize what they think the 4th figure will look like.

Children should be ask to pen down their learning onto a table form with three different questions.

  • What do you see from the three figures?
  • What do you think of the three figures?
  • What do you wonder the 4th figure will look like?

This activity does not require the children to come out with the correct answer but to assess their ability to see patterns, visualize the next figure, and provide a reason for their inference.

Before you start scrolling down to see the answer, try to wonder how the forth figure will look like and provide a reason for your inference!


Find The Angles

Question of the day: How many ways can you find out that the different angles match to 180 degree?
When I was posted this question by Dr Yeap, the only thing that came to my mind was "By using protractor". I couldn't thought of any other ways to measure the different angles. However, 30 brains are better than 1 brain. The class started brainstorming different ways to find out the answer.
  • Use a protractor.
  • Tear out all the angles and put it together in a straight line (Because a straight line represent 180 degree).
  • Identifying alternate angles on parallel lines.

The approaches that the class identified can be classified under the CPA approach.

C - Concrete
P - Pictorial
A - Abstract

Challenge of the Day: Try identifying which method is using the concrete approach and which method is using the abstract approach.

Friday, August 16, 2013


Geoboards are concrete materials that can be introduced to children when they are doing multiplication or problem solving activities.

  • How many different shapes can you make with one dot / two dots untouched in the shapes you made?
  • Find out the area of the different shapes you made.
When I did the activity during lesson time, I came to realize the pattern between the number of dots touched with the area of the shape. Children can come to realize Mathematical concepts when they are manipulating with Geoboards too.

Thursday, August 15, 2013


Question of the day: How much is 2 1/4 (2 and 1 quarter) take away 1/2 (1 half)?

Many of the adults would use one method to solve this problem.
The most abstract method that they were taught.


Denominator multiply whole number, add numerator.
Minus 1/2.

Why do we have to teach children the same way that we were taught?

Using diagrams and graphs make learning easier for the children because they proceed from concrete to pictorial to abstract. Jumping straight to the abstract approach often confuses children.

Challenge of the day: 
Think of as many ways as possible to solve the question that caters to children under the concrete and pictorial level! :)

Wednesday, August 14, 2013

Whole Numbers

Learning addition, subtraction, multiplication and division might seem like an easy task for adults because we are using our prior knowledge to help us construct new knowledge. Children start from the basic of recognizing numbers and adding numbers. It is teachers' and parents' ability to scaffold children in constructing knowledge with the usage of concrete materials. Even though the course is designed at the Elementary level, there are a lot of ways teachers can design it to the Kindergarten level.

Ten Frame

It was the first time I came across Ten Frame during Dr Yeap class. I was surprised that this can be a very helpful tool to allow children to learn about whole numbers. Ten Frames are the cheapest tool because teachers and parents or even children, can make a Ten Frame themselves using paper.

Benefits of Ten Frame:

  • It allows children to see patterns through different Ten Frames.
  • Children who are more advanced will be able to visualize patterns.
  • There are many ways to calculate the total number of beans/buttons with the use of Ten Frames.

Parents and teachers should start using it now!

Tuesday, August 13, 2013

Learning About Equal Parts

Math is not all about doing numbers with paper and pencil. As learned from the first lesson, teachers need to apply the CPA approach (Concrete, Pictorial, Abstract) when teaching children. Math for young children should start from the manipulation of lots of concrete materials. Even though the Mathematics course we are taking are for Elementary level, but teachers can always simplify the Mathematics ideas and fit it into the Preschool or Kindergarten level.

Problem Posted:

  • Imagine the rectangular paper as a pizza.
  • How many ways can you divide the pizza into 4 equal parts?

Strategies that were learned:

  • Fold the rectangular paper equally. If the rectangular paper overlap each other nicely, it means that the parts are equal.
  • If the folded rectangular paper does not overlap each part, try cutting it out. It is trail-an-error approach.
  • For older group of students, calculating the area of each part to ensure that all parts are equal.

If the above problem is too difficult for a preschooler or Kindergarten child to solve, below are some of the simpler methods of conducting lessons on equal parts:

Thursday, August 8, 2013

Mathematics For Children (Reflection - Chapter 1 & 2)

No one child is good in all subjects that are covered in school. This sentence applies to adults as well. It is often our own beliefs and attitudes that affect our learning towards Mathematics. With a positive mindset and a "never-give-up" attitude, adults are more likely to influence children's interest in Mathematics. As teachers and parents, we might have learned Mathematics in a form of memorization. It is time to ask ourselves these questions:

  • Do you still remember all the formulas you learned in school years back?
  • Can you apply the formulas as and when it is needed?
Rote learning enables children to remember concepts or new content easily. However, it is ineffective in constructing new knowledge. Therefore, both teachers and parents have to understand the importance and methods of educating Mathematics to children. 

When teaching Mathematics, we have to provide opportunities for children to construct new knowledge from their prior knowledge, allow children to be engaged in reflective thinking and sharing, encourage children to use a variety of approaches to solve a problem, engage children in experiencing productive struggles, give children opportunities for learning from their errors, scaffold children in learning new content, accept the differences among children, as well as using multiple tools and manipulative and technology in teaching Mathematics.

Learning Mathematics is not about getting the correct answers but about the justification and adaptive reasoning.