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New Bar Modeling iPad Apps!

For many years, I’ve highly recommended Thinkingblocks.com to my students who hone their bar modeling skills while playing really fun games. These flash-based programs work great on a desktop or laptop, but required third-party solutions to work on mobile devices.

Tired of using Rover to run Thinkingblocks.com on your iPad?

Well, hop on over to the iTunes app store because Math Playground has just published  four new iPad apps based on the popular website Thinkingblocks.com that work perfectly, provide tracked progress and are FREE for a limited time:

Addition and Subtraction:

Thinking Blocks Addition and Subtraction

Multiplication and Division:

Thinking Blocks Multiplication & Division

Fractions:

Thinking Blocks Fractions

Ratios and Proportion:

Thinking Blocks Ratio & Proportion

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Can the Singapore Method Help your Children Learn Maths?

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

1

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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Motivating Your Child to Do Homework and Study

children-are-made-readers

  • Is your child motivated to do homework and study or do you need to ‘strongly encourage’ your child to do the work?
  • Has homework time become a battleground?

I understand how difficult this can be for you once things get out of hand but DO NOT DESPAIR.  In my last article  Teaching Young Children To Study, I explained the importance of teaching even young children how to study so they can become independent learners at school. A key component of being an independent learner is motivation.

Here is the brief version:

STEP 1: FIND OUT WHAT THE BLOCKAGE IS

For you to be able to help your child overcome homework problems you first need to become a detective like Sherlock Holmes. The important thing to keep in mind is that there is no point forcing your child to do work that he/she is not able to do. All that will happen is that you will both get more emotional and will not be able to think clearly or work with each other effectively. There could be a variety of reasons why your child won’t get on with homework such as:

  • doesn’t understand the work
  • hasn’t or can’t read the instructions properly
  • doesn’t know where to start
  • lacks the basic skills to do the work
  • hasn’t got the materials needed to complete the task

STEP 2: Break the work that needs to be done into a series of SIMPLE STEPS

Thus get your child to DO ONE STEP A TIME.

STEP 3: HAVE PATIENCE

Rome was n0t built in a day. Your goal should be to help your child get a few more skills and a bit more confidence every day. Research shows that the best way to build up good habits is to take small but regular steps. Just do as much in a sitting as you can both manage without getting tense. In the early stages it is often much more effective to do three 10-minute sessions than one 30-minute session.

Remember, if your child is not doing her/his homework effectively at the moment, then small positive changes on a regular basis is far better than no change at all.

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Teaching Young Children To Study

every child can shineWHAT IS STUDY? – Study is the skill of learning something independently of a teacher.

Obviously I did not mean that a 5 year-old should be reading and studying textbooks at night after going to school!

Being an independent learner in Kindergarten means things like being able to FOCUS on what the teacher is saying so the child is be able to COMPREHEND what is being said and to FOLLOW THE INSTRUCTIONS given.

Many children are not capable of concentrating enough to be able to do this effectively when they first arrive at school so they miss a lot of the teaching in class – it just goes straight over their heads. These children are dependent on the teacher instructing and monitoring them individually . . . meanwhile the independent children are getting on with their work and learning things. The independent learners will have been taught good listening and oral comprehension skills by their parents, and just as importantly, they will have been taught the social and emotional skills needed to operate successfully in a room full of people – many of whom will be disruptive of the group as they have not learned good social and emotional skills before coming to school.

By the time your child is 10 years-old, study means a lot more. By then your child will need much more developed written and oral communication skills to be able to make the most of his/her time in class, and be able to do homework with minimal supervision – a child who is not a fluent reader for example will not be able to become a very independent learner. By this age, it is also important that your child has developed the positive Growth Mindset.

On entering Middle School it is important that your child has learned how to take full responsibility for comprehension at all levels. Your child should:

  • KNOW WHAT SHE/HE KNOWS and
  • KNOW WHAT SHE/HE DOES NOT KNOW, know what to do about it, and ACTUALLY DO IT. That might mean independent research or seeking help from an appropriate person.

So you can see, study skills are important right through school. As a caring parent it is important that you monitor your child’s progress very closely, and teach your child good study skills at home – if possible, BEFORE they are needed at school.

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Mathematics Gaps that Need to be Handled with Care

The following is derived from my eight years of teaching mathematics from Primary 1 level to JC 2.

1st Gap – From Lower Primary to Upper Primary

model-drawing-h

Somewhere in Primary Three problem sums that require the drawing of simple models begin to appear and in some schools, this happens in P2 and even P1. However, these problems tend to be simple enough so as not to cause problems for students who don’t draw models. Generally, parents report their children doing badly and losing interest in math in P4. This is because in P4, complex problem sums begin to appear. It also coincides with the appearance of Decimals. Thus students who have not mastered Fractions as well as simple models by the end of P3 will find P4 a tough and demoralising year, with some probably staying away
from Math for the rest of their lives. However, in P4, Section C (problem sums) still only take up about 20% of the marks, so pupils will still survive and scoring above 75% is not a problem for the hardworking student who is not careless.

However, this ecstasy is short-lived. In P5, Ratio, Average and Percentages start to appear, on top of decimals and fractions, and only the well-taught and discerning student will understand that they are all roughly the same thing in different forms. To add to the agony, Paper 2 in P5 takes up 60% of the total marks! It is a very big jump from P4; students can no longer afford to just concentrate on their short questions in order to score A*. P5 is the year that separates the men from the boys (or the women from
the girls). In P6 or PSLE, Paper 2 weightage is 60%, wiping out all remaining students who have not mastered complex problem sums and non-routine questions. That is NOT the bad news yet. The worse news is, the ecstasy of quite a number of students who scored A-star in math at PSLE is also short-lived (I have encountered quite a number of students doing badly in secondary math even though they scored A-stars or A’s at PSLE).

2nd Gap – From P6 to Sec 1

Why is it that some students can score A-stars or A’s at the PSLE yet become average or even failures in math at the secondary level? The answer lies in two words – Algebra and presentation. It’s unfortunate that even at the upper primary level, students are not taught to form and solve equations using algebra, and they are also not taught how to present their answers in logical and coherent mathematical statements. Thus I find that many Sec 1 students provide math workings that will not earn full marks by ‘O’ level standards, and these habits are hard to change. Inability to use algebra properly also means inability to master important fundamentals such as algebraic expansion, factorisation and manipulation, resulting in poor performance at the upper secondary and JC levels.

Whenever I ask an upper secondary or JC student to state the main reason why he thinks he’s doing badly in math, the reason given is almost always that he had difficulty handling algebraic concepts and formulae while in Sec 1 and Sec 2. Thus parents and students need to comprehend fully the importance of mastering algebra in the lower secondary years.

3rd Gap – From Sec 2 to Sec 3

Even students who perform well in Sec 1 and Sec 2 may suddenly suffer a drop in their math performance by the middle of Sec 3. This is largely due to the full impact of Additional Math and the pure sciences taking place and finally being felt by students around that time. A. Math can be a shock to some students who are not used to algebra-intensive questions with solutions that are one-page long. Trigonometry in A. Math is also substantially more difficult to grasp than it’s counterpart in elementary Math.

4th Gap – From Sec 4 to JC 1

H2 Math is more shocking to new JC students than A. Math is to new Sec 3 students. H2 Math is significantly more difficult than A. Math and from my experience, students who do not get an A1 for A. Math will have a hard time even in completing their JC tutorial worksheets. This is because on top of having to write out solutions that are often more than one page long, students have to familiarise themselves with a new graphical calculator. Many topics in H2 Math are also completely new to students, such as Complex Numbers, Series and Sequences and Probability Distributions, just to name a few. H2 Math is also difficult for most students because some parts of its topics are taken from the former subject Further Math, which was meant for only top students in Math. Thus it is not surprising to find many students failing in Math tests in their first year in junior college.

✩ My main point is – Concerned parents must monitor their children’s mathematical development extra closely when the kids go through the above stages.

From Md. Ilyasa, Principal Tutor and Managing Director of Concept Learning