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What’s Singapore Math?

addWritten by: By Laura Lewis Brown    Source: http://www.pbs.org

Parents in the United States often hear (and stress about) how students in other countries perform better than our children in math and science. With that in mind, many schools and homeschoolers are implementing an approach to teaching elementary math that is common practice in Singapore.

Singapore math, which refers to the teaching methods or the actual curriculum used for kindergarten through sixth grade in the small island country, has become popular due to Singapore’s consistent top ranking on an international assessment of student math achievement called the Trends in International Mathematics and Science Study (TIMSS). In the latest TIMSS report in 2007, Singapore was ranked in the top three in fourth- and eighth-grade math scores, while the United States ranked ninth and eleventh, respectively.

Mastery, Not Memorization
Supporters of Singapore math credit the Singaporean methods of instruction and curriculum for its students’ success. While American math instruction often relies on drilling and memorization of many skills each year, Singapore math focuses on children not just learning but also truly mastering a limited number of concepts each school year. The goal is for children to perform well because they understand the material on a deeper level; they are not just learning it for the test.

“The sequence of topics in Singapore math has been carefully constructed based upon child development theory,” says Jeffery Thomas, president of Singapore Math Inc., the primary producer of Singapore math products for the U.S. market. “The means to mastery is problem solving, and the beauty of the approach is that the majority of students are well prepared to tackle increasingly difficult topics, such as fractions and ratio, when they are introduced in the third through fifth grades. Those students are also then typically ready for algebra and geometry in middle school.”

Students in the same classroom may learn the concepts at different paces, but ultimately they all learn them and help develop their own solid foundation for further math learning. This prevents the need for reteaching as students move to the next grade.

Thomas and his wife, Dawn, a native Singaporean, helped bring Singapore math to the United States in the late 1990s by adapting Singaporean textbooks and workbooks for the U.S. market through their company. Now Singapore math is part of the core curriculum at schools in 40 states, Thomas says. Many schools have adopted Singapore math as their core, others have brought it in gradually, and still others are using it for gifted and talented students, or for struggling students.

What Type of Students Benefit from Singapore Math? 
There is no guarantee that the Singapore method will make your child a math whiz, but teachers who use it believe it can help any child. “Most any child would benefit from this program,” explains Kevin Mahoney, a math curriculum coordinator at a private school in Massachusetts, who also maintains www.singaporemathmentor.com. “That’s because of its reliance on understanding number sense, problem solving and conceptual understanding of what these kids are doing. Singapore math requires children to understand how something works, like long division. But they’re also going to understand why long division works, not just the how but the why.”

Singapore math also relies heavily on visualization, which is often neglected in the American classroom. “In typical American math teaching, you use a concrete-abstract approach. If I’m going to teach about multiplication I will bring out physical objects and demonstrate how to multiply, then move to the abstraction of lining up numbers in a multiplication equation,” Mahoney says. Singapore, on the other hand, introduces a middle step between the concrete and abstract called the pictorial approach. “It asks students and teachers to draw a diagram of the concepts going on. This is not an idea that’s exclusive to Singapore, but it’s so well expressed in a coherent idea in the curriculum in a comprehensive way,” he says.

Students also learn to use model drawing to solve those word problems that many of us remember fondly from elementary school. Instead of trying to picture the problem in their heads, then writing out the equation to solve it, students in Singapore math diagram the elements of the word problem. “Model drawing is really exciting to Americans because they’ve seen never anything like it,” Mahoney says. “It gives American teachers a tool to help students decode those sticky word problems.”

Success Stories
Since Singapore math was added to the core curriculum at Pennacre Country Day School, an independent K-6 school in Wellesley, Mass., there has been a noticeable change in student performance. Mahoney says a recent assessment found 20-percentile gains in standardized testing of third graders compared to previous third-grade classes. The school also determined that 89 percent of parents said their children had a very positive experience with Singapore math, and were more competent in problem solving and arithmetic thinking.

In Hawaii, students and teachers at Shafter Elementary are also taking to Singapore math in a big way. “The students just grab onto it because it makes sense to them,” says Robin Martin, principal of the Honolulu school that is using Singapore math in its K-6 curriculum. “I don’t exaggerate: every day a teacher was coming into my office and saying, ‘Oh my god, the kids are getting this.’ The kids are just so excited about it. When the teachers see the kids excited, the teachers really put effort into it. They see that it’s really having an impact.”

A Parent’s Role in Singapore Math
Singapore math instructors encourage parents to be open-minded. Singapore math is not what most parents in the United States studied in school, but that doesn’t mean they need to resist it. While you may want to help your child learn the times table the way you did, you should also consider this different approach.

“Many parents want to tell their children not to do a math problem this way, or they discourage, saying there is an easier way,” Martin says. “Part of Singapore math is children making meaning of the math. Just because the parents understand it one way doesn’t mean the children won’t another.”
Char Forsten, a consultant and writer who helps schools implement Singapore math, explains, “When I was in school, the emphasis was on getting the correct answer; here it’s about understanding the math and explaining your answer. That’s a big thing that parents need to understand.” We may want our children to get the right answer, but we also want them to know why it is the right answer.

Even though Singapore math may seem strange to you, you can still help your child access it. If your child is not learning Singapore math in school, you can purchase materials on your own. Singaporemath.com offers a placement test to determine where your child may be in the curriculum, so you can select the right textbook and workbook combination.

Be aware, however, that although doing practice problems is helpful, it cannot replace learning in the classroom. “Just looking at textbooks themselves can be misleading. The textbooks don’t include all the rich teaching and dialogue that go on in a Singapore math classroom,” Mahoney says. “To an untrained eye they look simple, but the math involved is really quite deep, and that really gets drawn out in the Singapore math classroom.”

Regardless of your child’s relationship with Singapore math now or in the future, your goal should be to support and encourage the style of math learning that works for them. “The parent is the supporter. The parent is the guide in asking questions,” Forsten says. “I believe the best thing they can do is question their children. Questioning children is an excellent way to develop their thinking.” So when your daughter or son comes home with a math problem that you don’t understand, simply ask what they know about it, what they were taught in school, and so on.

A parent should also be open to playing games that rely on math skills and pointing out math in the environment, such as asking what shape the kitchen cabinets are and other real-life math questions.

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10 Top Tips for Trying the Singapore Model Method with your Kids

Source: http://www.bbc.co.uk/skillswisetop-10-tips

Count things with objects

Try counting familiar things together like the number of people in the room, kids’ ages, or goals in football matches, using concrete objects like counters, buttons or small stones, lining them up one by one. If nothing’s to hand use fingers.

Get some interlocking cubes

Interlocking cubes are great and can be bought for a few pounds, or your child’s nursery or school may be able to lend you some. Try carrying round a few to count things when you’re out and about. They are also good for kids to play with to keep them occupied.

Use cut-out pictures

Draw pictures on paper and cut them out to use as counters with your kids. Or print out our handy Singapore Model Cutout Pictures and use them at home with your kids, to count people, ages, goals, coins or fruit.

Do basic arithmetic with objects

You can talk about most basic arithmetic using concrete objects, adding objects to the line, taking them away. ‘Multiply’ literally means ‘many layers’ and you can show times tables by layering rows one on top of the other.

Use interactive blocks

If you have an iphone or Android mobile why not try BBC Skillswise’s interactive blocks: text SKILLSWISE to 81010 or if you are reading this on your mobile device preview the interactive times tables blocksPlease note texts to the BBC cost 12-15p, interactive not compatible with all phones.

Draw pictures

Give kids pens and paper to draw things they count, lined up in a row. Encourage them to draw boxes around the pictures. The fact they have drawn the pictures gives them a sense of ownership and means they’ll probably be more confident in talking about them.

Don’t rush to use figures

Hold off from using number symbols until your child is really confident with concrete and pictorial representations and can make the link. So they will always have a ready way of picturing what the symbol means as a fall-back.

Start with figures 1 to 9

When you do start using symbols to label drawn boxes, stick to 1 to 9 at first to build confidence, so one figure relates to one quantity. The leap from the figure 9 to the figure 10 involves concepts of place value and zero which can take time to understand.

Brush up your own maths to help your kids

Most of us feel a bit rusty with maths, especially the new methods used in schools these days. Why not be a learning role model to your kids by joining a local maths class for adults? You can find out more about local courses/workshops from MathsExCEL programmes. Or brush up your maths skills online with maths websites for adults like BBC Skillswise.

Go slowly to build confidence

It takes time for children to get really confident with the basics. The Singapore curriculum actually covers less than the UK national curriculum in the first few years, instead taking more time to build confidence in the basics. But this pays off in spades later on.

TOP TIP: Be positive

Above all be positive. Enjoy playing with and counting objects together, celebrate effort and praise often. Real learning involves making lots of mistakes. Try to see mistakes as positive things that highlight deeper misunderstandings. Why did I think that? Kids have years of maths lessons ahead of them and every ounce of self-confidence helps them to succeed. Boosting children’s understanding with objects and pictures is key.

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Can the Singapore Method Help your Children Learn Maths?

Source: http://www.bbc.co.uk/skillswise

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Singapore teaches maths better than most countries including the UK, according to international rankings for secondary pupils.

The difference starts at an early age.

There are many reasons but one key factor is its step-by-step approach that can be used at home or in the classroom.

Young children are happy playing with blocks or drawing pictures. But they can find number symbols, like 5 + 2 = 7, mystifying.

So the Singapore method begins by allowing children to start learning about maths by playing with real objects, blocks or cut-out pictures.

They build confidence with the basic ideas of adding and taking away. There is then a second stage of drawing pictures representing the objects. And only later do they gradually start to add numbers to their drawings.

Maths without symbols?

5 planesStraight to the symbolic – a leap too far for many children?

In education systems in the UK, pre-school children are often introduced to maths and to number symbols at the same time. For instance through brightly-coloured counting books which show a picture of an apple – or a kite or a butterfly – next to a ‘1’. Two new things next to a ‘2’. Three new things next to a ‘3’. Culminating in a loose group of ten things next to a ’10’.

But number symbols like 5 or 10 as well as symbols like + or – are often difficult for children to understand. And if they are introduced too quickly, there is a risk that young children will struggle and from then on never fully recover their confidence in maths. Failing repeated tests on symbolic sums at school only deepens their anxiety and they soon learn that maths is not for them.

The Singapore method illustrated in more detail below goes more gradually – from handling “concrete” things, to drawing one-to-one “pictorial” iconic representations of them, to eventually understanding and using the mysterious “abstract” symbols with confidence.

1. Lining up objects in a row

Real objects, cut-outs and blocks

Children start by counting familiar things using blocks or cut-out pictures they can physically line up in a row. For instance counting pieces of fruit, their own ages, or people in the room. With one block or cut-out picture for each orange, or year, or person.

They can learn most basic maths concepts with these objects. For instance add objects to the row, or take them away, to understand adding and subtraction. Or split a row in the middle to understand halving.

2. Drawing boxes around pictures

A drawing of 3 oranges in boxes

Then children start to draw pictures on paper of the things they are counting, with a box around each picture. So there’s one box for each thing they are counting. Over time they drop the pictures and just draw the boxes.

3. Labelling the boxes

A drawn box labelled with a 3.

Gradually, once they are confident with drawing boxes to count objects, children start to write the number of boxes as a figure above the drawing.

Eventually they no longer need to draw all the boxes. They just draw one long box or bar and label it with the number. This step away from one-to-one representations to symbols is crucial and it may take a year or more for some children to become confident with it. But the benefits later on are worth it.

The Singapore Model Method

This model of numbers as labelled bars is known as the Singapore model, and it’s a tool children can use to understand almost any concept in maths, including multiplication and division and even algebra.

Professor Lianghuo Fan, former editor-in-chief of Singapore’s maths textbooks, has researched the reasons for Singapore’s success in maths. As he puts it: “People have different views about the reasons for Singapore students’ performance, but one thing that is universally agreed is that the Singapore model method is key.”

You can see examples of different stages of the model in this slideshow:

Algebra bar modelIn a year group there are 50 children. There are 10 fewer girls than boys. How many boys? The model can help visualize the unknown quantity. You can see that x + x – 10 = 50. If you add the 10 you get x + x = 60. So x = 30.
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Teach Your Child Problem Sums Solving

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Ever teach your child Maths Problem Sums using the Model Drawing but discover that you do  not know how to draw the diagram? If you have, you might want to know that you are not alone. Many parents are facing the same problem as you simply because you were not this way when you were young.

Model Drawing has since been widely used in the teaching of students in primary schools in Singapore. They are introduced to the method from as young as Primary One.

Students typically find word problems difficult due to several reasons:

  • they are weak in their Mathematical language;
  • they have limited understanding of the arithmetic operations;
  • they are unable to relate the known(s) to the unknown(s) when the problem structure is difficult to understand;
  • they are unable to analyse problem situations.

This method is especially useful when: you teach kids who respond better to visual stimuli (e.g. pictures, drawings, etc); you try to provide math homework help but the conventional methods do not really work well with your kids; and your kids has not learnt algebra yet and solving the math problems with algebra is not an option.

However, without proper guidance, you may not be able to experience the full benefits of the Model Drawing. The Model Drawing essentially becomes a good entry level tool to help the your child to understand and break the questions down into component parts making solving and learning math easy.

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What is a Model Drawing ?

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free-trialThe model approach requires students to draw rectangular boxes to represent part-whole relationships and Math Value. By drawing such blocks, they can visualize the math problems more clearly and are able to make tacit knowledge explicit. Word problem solving is a major part of the curriculum in Primary Mathematics in Singapore, both known and unknown values, in the Maths Problem Sums.

This technique of model building is a visual way of picturing a situation. Instead of forming simultaneous equations and solving for the variables, model building involves using blocks or boxes to solve the problem. The power of using models can be best illustrated by problems, often involving fractions, ratios or percentages, which appear difficult but if models can be drawn to show the situation, the solution becomes clearer, sometimes even obvious.

For more resources, click here.