A parent recently asked me to find him a Singapore method math tutor for his daughter. He said that he wanted her to get ahead in that subject and become fluent in English too. I offered to help and then decided to write this article to explain why the Singapore method of teaching math is best.
Like all academic subjects, no one is born with mathematical ability. Singapore has a strong belief that “effort” is the human characteristic that makes kids “smarter” at math.
Effort is a choice
As humans with free will, we can choose to either work hard or not. But giving effort when the method is flawed may not make us smarter at math. So we need to control the method too. When we use a sound method and choose to give full effort, we start to take control of whether we become smarter at math or not.
“Children usually give full effort when they play – which is probably why the Singapore method is so popular with students.”
In the 1980s, Singaporean schools developed a curriculum that focused on fewer topics but studied them in greater detail. Students learnt how and why equations worked. They refined problem solving skills using pictures and diagrams. To understand why this is important when teaching math, we need to remember how we learnt in kindergarten.
Kindergarten math starts with blocks, numbered cards, or counters like on an abacus. These are concrete objects that young learners can touch and feel in playful tactile discovery.
Later, when we went to primary school, many of us were expected to study equations such as 1 + 2 = 3. As easy as this seems to us now, it is abstract and rather difficult for young children to grasp.
The Singapore method added a “pictorial” stage, as a bridge between the concrete and abstract stages of learning.
Based on the work of Jerome Bruner’s Constructivist theory, Singapore’s curriculum developed a system of teaching that makes learning easier because it focuses on understanding how and why! Students start with hands-on group activities with concrete objects like buttons or dice. Then students learn the pictorial stage, drawing pictures of these same concrete objects before moving onto the abstract equation stage.
It is really important that each stage of development constructs new ideas or concepts based upon current/past knowledge. If the students started counting coins or buttons in stage 1, then they should open the book and see coins or buttons in stage 2. Only in stage 3 will the abstract appear and build on what was learnt in the concrete and pictorial stages. If stage 2 is neglected, then understanding at the stage 3 level could be underdeveloped.
In the Singapore method, this 3 stage approach, of concrete – pictorial – abstract, is not abandoned after kindergarten but kept alive throughout primary and secondary education. We know that children need to play in order to learn. By making math fun we are able to help them understand why things are.
4th Grade Fractions Example
The traditional way of teaching fractions was to learn a method and do lots of practice. Teachers didn’t always explain why the method worked, maybe they couldn’t, they simply barked instructions!
Do you remember being told to just multiply the top numbers together, and then multiply the bottom numbers together?
Thus ½ x ½ = ¼
Having been taught this method, students often knew how to find the correct answers but they didn’t know why. This caused major problems later on in school life, when equations became more difficult.
The Singapore method teaches children “why” by adding a pictorial stage. Think of a whole one as a circle or a whole pizza. Pizza is a concrete object that we all understand. If there is 1 pizza for 1 person we have 1/1 or one whole pizza each. If we share 1 pizza between 2 people we have half each, we need to cut it with a knife to get half a pizza. Students draw a complete circle to represent the pizza and cut it in half. To multiply ½ x ½, students know they must cut the half circle in half again. They are left with two quarters and a half pizza.
The pictorial pizza stage builds on the concrete pizza stage. When the students understand why ½ x ½ = ¼, they begin to master the abstract stage 3.
Common Core Standards
New textbooks have been introduced which align with Common Core standards. Unlike the old approach, where material appeared in a spiral, each skill set in the new curriculum is a foundation for future lessons. Schools are now opting into the Singapore method of teaching math.
“As a teacher it’s easy to see the appeal. For parents however, it is not always straight forward.”
The main reason parents stumble over these phrases is because schools are switching over from old methods of problem-solving to new ones. I learnt concepts like “carrying and borrowing” when doing addition and subtraction problems. Students today are learning concepts like “regrouping.”
Let’s look at some other vocabulary and then watch a video.
Singapore’s 7 Step Solution Strategy
- Read the problem carefully.
- Determine the variables, who and what?
- Draw the unit bars.
- Break down (chunk) the word problem, re-read it and adjust the unit bars to match.
- Place the question mark.
- Write the number sentence and solve it.
- Write a grammatically correct answer.
Special thanks to Amy Cantone for making this educational video.
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