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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

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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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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

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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

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Improve Your Maths Marks

This article is written by  Deb Russell, http://math.about.com.

Here are some quick steps to help you get better at doing mathematics. Regardless of age, the tips here will help you learn and understand math concepts from primary school right on through to university math. Everyone can do math, be positive and follow the steps here and you’ll be on your way to seeing success in math.

Understanding Versus Memorizing

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All too often, we will try to memorize a procedure or sequence of steps instead of looking to understand why certain steps are required in a procedure. Always, always strive for understanding the why and not just the how. Take the algorithm for long division Typically, we say, “how many times does 3 go into 7” when the question is 73 divided by 3. After all, that 7 represents 70 or 7 tens. The understanding in this question really has little to do with how many times 3 goes into 7 but rather how many are in the group of three when you share the 73 into 3 groups. 3 going into 7 is merely a short cut. Putting 73 into 3 groups means understanding. The long division algorithm rarely makes sense unless the concrete method is fully understood.

Maths is Not a Spectator Sports, Get Active!

Getty ImagesUnlike some subjects, math is something that won’t let you be a passive learner. Math is the subject that will often put you out of the comfort zone, don’t worry as this is normal and part of the learning process. Try to make connections in math, many of the concepts in math are related and connected. The more connections you can make, the greater the understanding will be. Math concepts flow through levels of difficulty, start from where you are and move forward to the more difficult levels only when understanding is in place. The internet has a wealth of interactive math sites that let you engage, be sure use them.

Practice, Practice, Practice

Getty ImagesDo as many problems as is required to ensure you understand the concept. Some of us require more practice and some of us require less practice. You will want to practice a concept until it makes sense and until you are fluent at finding solutions to various problems within the concept readily. Strive for those ‘A Ha!’ moments. When you can get 7 varied questions in a row right, you’re probably to the point of understanding. Even more so if you re-visit the questions a few months later and are still capable of solving them. This too is key to understanding. Be sure to check out the worksheet section for lots of practice examples.

Additional Exercises

Getty ImagesThis is similar to practice. Think of math the way one thinks about a musical instrument. Most of us don’t just sit down and play an instrument. We take lessons, practice, practice some more and although we move on, we still take time to review. Go beyond what is asked for. Your instructor tells you to do questions 1-20, even numbers only. Well, that may work for some, but others may need to do each of the questions to reach the point of fluency with the concept. Doing the extra practice questions only helps you to grasp the concept more readily. And, as always, be sure to re-visit a few months later, do some practice questions to ensure that you still have a grasp of it.

Buddy Up!

Getty ImagesSome people like to work alone. However, when it comes to solving problems, it often helps to have a work buddy. You know the saying: two heads are better than one. Sometimes a work buddy can help clarify a concept for you by looking at it in a different way. Organize a study group or work in pairs or triads! In real life we often work through problems with others. Math is no different. A work buddy also provides you with the opportunity to discuss how you solved the math problem. And as you’ll see in this list of tips, conversing about math leads too permanent understanding and you know that understanding is key.

Explain and Question

Try to explain to somebody else how you solve math concepts. Teach a friend. Or, keep a journal. It’s often important to state either in writing or orally how you solved your math problems/exercises. Question problems, ask yourself, What would happen if…….I solved it this way because…..
Remember William Glasser’s findings:
  • 10% of what we READ
  • 20% of what we HEAR
  • 30% of what we SEE
  • 50% of what we SEE and HEAR
  • 70% of what is DISCUSSED with OTHERS
  • 80% of what is EXPERIENCED PERSONALLY
  • 95% of what we TEACH TO SOMEONE ELSE

Phone a Friend …. or Tutor!

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Seek help when it’s appropriate. Don’t let yourself get stuck and frustrated. Seek extra clarification when needed, be your own advocate! Whether you have a friend or need to hire a tutor, recognize the point at which you need help – then get it! Most of us need help some of the time, if you let it go too long, you’ll discover that the math will only become more frustrating for you.

Learn how your child can benefit at his most at MathsExCEL!facebook icon 2

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Tips to Help Children Understand Maths Concepts

model-drawing-hIn any school system one finds children who excel in Maths; but one also discovers that an equal or even greater number of school children fare poorly – probably because of their failure to understand basic math concepts at a very early stage.

In this article I would like to ventilate the following tips to help children, young and slightly older ( teens in their junior and middle High School years ) ones who have difficulties grasping math concepts, resulting in them not doing what they are inherently capable of achieving in general mathematical performance.

Tip # 1: INTRODUCE MATHS CONCEPTS PROGRESSIVELY with emphasis on developing manipulative skills and activities-based learning.

It is vital that children in elementary schools be taught the fundamental math concepts involving the usual operations (addition, subtraction, multiplication and division) and fractions, proportions and percentages. Early Maths education should be as activity-based as possible: from simple additions ( putting objects together and counting them ), subtractions ( removing articles/items from a certain number of such articles/items ), multiplications ( linking addition to the ultimate concept of multiplication ) and division ( dividing a certain number of objects equally among say 2 or 3 or more children ).

Tip # 2: EMPHASIZE both THE PRACTICAL IMPORTANCE OF MATHS and the INTERESTING ASPECTS OF MATHS – hands-on and practical approach.

Many children would question why they have to learn Maths concepts like fractions, percentage, decimals, etc.; they demand to know why they are in a sense compelled to learn sometime apparently ‘useless’ and ‘abstract’ topics. It is therefore incumbent on the teacher or the parent or anyone who is interested in the child’s Maths abilities to try a hands-on and practical approach, at least at the beginning stage of learning of the more abstract topics. This necessarily requires that the learning of these ideas be associated or linked with everyday, commonplace activities.

Children could be brought to markets, both traditional and the modern ultra-modern hypermarkets – to see and experience themselves first-hand activities and visual stimuli that involve math: fractions, percentages (e.g., on signboards in departments that offer discounts), geometrical shapes of bottles ( perfumes and toiletries department ). Slightly older children could also pay visits to local banks to find out the meaning of interest rates, exchange rates, etc. – practical matters that bear some relation to what they learn in classes.

Tip # 3: EXPOSE THE CHILDREN TO THE POSSIBILITIES OF MATHS: make attempts to encourage and stimulate children to think of areas which could make use of Maths concepts.

Although children with some form of learning difficulties in Maths are generally not whiz-kids it does not mean that they all are lacking in imagination and enthusiasm. It takes a dedicated, qualified, well-trained and inspired person ( usually an educator ) to motivate these seemingly less Maths-inclined children; with appropriate approaches and methodologies, it is not impossible for educators to unearth the potential abilities of these children.

Suitable strategies can be drawn up in attempts to pique the children’s curiosity as when the teacher poses the interesting question of how Maths concepts like game theories and stochastic processes are used to forge new and novel designs in both weaponry and machinery. Children could also be guided to navigate the huge resources offered by the Internet – with its several hundreds of thousands of useful math websites; to look for interesting, interactive Maths programs that teach basic math concepts. The possibilities offered by Maths are therefore quite limitless though not immediately tangible and practicable. By encouraging children to freely voice their opinions and suggestions (however naive and improbable) on the use of Maths concepts, they realize that learning Maths can be fun and Maths is not a dull and abstract subject at all!

Your child can achieve. At MathsExCEL we guide them Step-by-Step using Model Drawing.

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