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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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Being Engaged in our Children’s Education: – “What is it you do in school today?”

learning_stylesI keep remind myself the need for parents to be involved in their children’s education.

As a mum I want to know what’s going on with my son. And I had a number of interesting challenges to the very idea and I want to share it with you.

A friend repeated to me Einstein’s famous saying that “education is what’s left after you forget all the facts they taught you in school.” “Leave the teaching to the school and concentrate on educating your child” he said. To him, being involved in his children’s education meant providing them with parallel real life experiences and he couldn’t care a fig about tonight’s homework assignments; they are the responsibility of the child, and not the parent.

A mother of two teens commented that the best gift she could give her daughters was that of trust and self confidence. She wasn’t getting involved in the process of schooling. “Did you ever see the look of embarrassment, even horror, if your child unexpectedly sees you in the school hallway?”  “My child doesn’t want me to look over her shoulder” commented one of my daughter’s friends about her nine year old. These parents were taken aback by what they thought I was suggesting.

It is my contention that parents need to know what their children are doing at school and to become actively involved in helping facilitate their success. I am not referring to homework and test preparation. I am not referring to being cooperative with the school and teachers, which I am not denying it is very useful to engage with teachers too, to keep up and learn more about our child in school. I am more referring to make the child’s school experiences a part of the parent’s life. I believe a parent’s role is somewhere between coach and cheerleader; neither as critically involved as the former or as benignly enthusiastic as the latter. Allow me to elaborate.

Taking an active interest; or: “What is it you do in school today?”

Indeed, we forget most of the facts we cram for tests during our school years. What we are expected to retain are the skills with which will enable us to learn and discover for ourselves. Even more importantly, good teachers will have inculcated within us a love for learning to last a lifetime.

Learning skills do not develop in a vacuum; they develop through learning and internalizing the process. A love for learning develops from the satisfaction of understanding and the curiosity to know more. This too is a byproduct of learning and absorbing information, primarily in school. When a parent shows interest in the subject matter, his child is learning that says to the child: what you learned at school matters. Questioning a child about what he learned in school is an essential component in his developing a healthy respect for what he does all day; and he learns.

Questioning a child about school can be a tricky experience though. Ask a typical adolescent “what did you learn in school today” and the response, if you get a verbal one rather than some sort of primal sound, may be “nothing” or “stuff”.  The questions must be direct and specific for the child to be responsive. “What did you enjoy most about your Maths class today?” If he responds with a multi-word answer, the parent will have gotten a perspective of the child’s engagement in the Maths class. He may well say, “I didn’t enjoy it at all” — that speaks volumes too. Regardless, the parent has demonstrated interest and that the subject is important.

On the other hand badgering a child for information and interrogating him about precisely what he learned may be counterproductive from a parenting perspective. What the child might deduce from continuous pressured questions is that the less he says or pretends to remember the better off he will be. He perceives the questions as an invasion of his privacy; of course he will resist. A lot more information would be forthcoming if the question were put something like this “did you learn any interesting at the School Talk today?” or “How did the teacher like your social studies project?”

In a nutshell: the questions must be detailed and about the work rather that about the child. Specific but open ended questions will generally elicit a coherent response which can then

I did rather not head in the direction of the parent who spends the night studying with a child for a test and then asks “how well did we do on the exam?” Naturally, when taken to the extreme, that kind of “interest” will be more crippling than helpful.

Till my next post, hope this helps.

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10 Specific Compliments to Give Your Children

Fact is, children look to their parents and teachers for encouragement, and finding affirmation at home is foundational to positive emotional development. Parents need to be in the business of building our children up.  But we also need to be honest, and it’s important to use compliments that really mean something. Kids can sense disingenuousness and empty praise. Making stuff up is harmful; false praise is dishonest and the practice breaks trust.

Here are 10 compliments all kids need to hear:

  • Recognize and compliment character: We live in a world where integrity is neither consistently taught nor widely expected. When our children demonstrate honesty, kindness, trustworthiness and reliability, that’s a great time to take them aside and offer a sincere compliment.
  • Compliment obedience and respect:  It’s too easy to fall into patterns of disapproval, where the only time we notice is when kids do wrong. Rather than waiting for disobedience or disrespect (then coming down like a ton of bricks) try noticing obedience and respect: “I don’t always remember to tell you, but you are an awesome young man, and I appreciate the way you treat your mother”.
  • Appreciate them for simply being part of the family:  “Every time I see you, I’m thankful that I’m a dad.” Kids need to understand that they are valued simply because they are.
  • Compliment contributions to the family:  “Clearing the table (sweeping the porch… putting out the trash) makes a real difference. I appreciate your contribution.” Kids need to understand that what they do makes a difference, that the adults notice, and that pitching in is a good part of family life.
  • Compliment the quality of a child’s work:  “This is one clean porch, mister!” “You mowed the lawn right up to the edge.  Way to go!  I’m so glad you take this job so seriously, it shows.” Doing a job at a high standard is always worth noting.
  • We can compliment the effort, even when the result is not the best:  “Your willingness to help makes me happy! Now we need to take a look at how you can get the trash to the curb without leaving a trail!” Compliments can be an important part of our role as teachers.
  • It’s important that we compliment children when they achieve something new:  “Wow! That’s a huge leap forward for you there in math, pal.” “Awesome! I’m not at all surprised after you worked so hard.” A well-placed compliment can keep a positive ball rolling.
  • We can compliment sense of style even if we don’t exactly share their taste:   We don’t want to hedge kids into being clones of dad, or mom. “When it comes to putting together an outfit, you certainly have some flair!” “I can tell that you put a lot of thought into the way you look.” “I’ve never seen a table set quite like that before – you have an amazing imagination!” It’s not useful to limit compliments to the narrow range of our own taste.
  • Compliment steps towards a long-term goal:  “Son, the improvement you’re showing is commendable. Thanks for trying.” Waiting for perfection before we’re willing to dish out a compliment is inefficient, may dampen enthusiasm, and does little to help the process of growth.
  • Try complimenting their friends:  But only do this when you can do it honestly! “Your friends are the greatest!” “That Jimmy is such a positive young man.” “You know, it gives me a lot of confidence to know you use common sense in choosing your friends.”

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