Category Archives: Problem Solving

Problem Solving | Mathematics in Singapore

Problem solving

 What has mathematics got to do with problem solving ? Actually a lot , especially in Singapore

Problem solving | Singapore Mathematics

Singapore’s Mathematics  is very known around the world and many countries has started many programs modelling the success of the Singapore story .  This trend started when Mathematics educators start noticing  that  Singapore has been doing extremely well  in both 4th and 8th grades in the Trends in International Math and Science Study (TIMSS) comparison assessments in 1995, 1999, and 2003, and in the top three in 2007 . Solving Mathematical problems is key in learning mathematics

Problem solving | Singapore’s approach to problem solving in mathematics

The Singapore approach uses models such as bars to solve problems . They are sometimes called “bar modeling” or “model drawing” . The use of “modeling” allows the students to handle information better , deal with complexity and at the same time communicate their thoughts using the visual models that they can manipulate . Even complicated worded problems are being broken down into models to ease understanding of the problem .  The Singapore approach in mathematics problem solving allows students to identify relevant information , explore patterns and relationships , make hypothesis and apply the knowledge  and tools to solve a particular problem . [see full report ]

Watch the video below

Problem solving | The back of the napkin approach

Dan Roam’s approach to problem solving through visual thinking is very similar to the Singapore mathematics problem solving in the sense that both make use of “models” to demonstrate complex problems ,  concepts , or things that are abstract . The “models” allows communication between people and  to help understand  the problem better . Information is categorized or patterns identified so that we can establish some form of relationship or coordinates that are crucial to problem solving  . Here is an article about visual thinking in Singapore Mathematics and Dan Roam [see report]

Below are a list of websites showing examples of “models” , drawing of pictures and finding patterns that are adopted in the Singapore mathematics problem solving  .


In a n nutshell , pictures and models are important in problem solving , base on the results  in the Singapore Mathematics .   Students are not only able to retain information longer but the visual aids help to understand a complex problem easier , as seen in the case of complex worded mathematical problems .  It allows better communication and participation which is ideal in a work place .

Problem solving | Use of pictures for communication

Here is another demonstration of how a science teacher uses pictures , in fact cartoons to explain certain theories and to  generate excitement and interest among his students . Meet Singapore Engineer turn Science teacher , Otto Fong during an interview with CNA . See the video below


We use pictures and models to explain , especially when when we try to explain items or issues that cannot be seen , such as gravitational forces , electrons , or things that are abstract , or a  concept  or an architectural  design . So that is why the course “The Back of the napkin” is formulated to address this need . From the results seen ,   we certainly cannot deny the power of pictures in problem solving


Problem Solving | Visual Thinking Singapore



Problem solving



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Problem solving through visual thinking

Problem Solving | Visual Thinking


Problem solvingWhat is problem solving through visual thinking ?

When we were young , we showed our kindergarten teachers our drawings of how we see the world around us . We draw our mummies and daddies , our homes , the sun and the flowers which represent the things around us .  We see the world through our eyes and we show others what we see through our drawings . We already have this skill .. our in-born skills , a natural tendency to draw and show others , but somewhere along the way , as we grow up and acquire new (verbal and communication) skills , we put our drawing skills on the back seat .

Sometimes we imagine the flowers or even the butterflies with different colours . We draw and showed to our friends what we think . They look at what we have drawn and therefore understand our ideas and our imagination .

This is visual thinking !! How can we use it to for problem solving ?

Problem solving | our biological tools

Of all the 5 senses that we have (sense of touch , smell , hear , taste and see) , our eyes are probably the most important of all . It is one of our most valuable biological tools . Sometimes after  a short nap  ,when  we look out the window and  notice the sun setting , with the slightly dark sky , we think that  it is probably about 7 in the evening  .  How did we come to know that its about 7 in the evening ? We can make a rough guesstimate by comparing to the things around us and base on our past experience , since it is about to get dark , it is probably around 7 pm .    We can  guess time  and  we can even guess  how much time have passed by just looking out the window.  What if we lose our eyes ? Without our eyes , there will be  a lot of problems that we cannot solve . Unknowingly , we have been doing problem solving with our biological eyes .

Now , let us look at another example . Try explaining the company’s organization chart to a friend verbally . Then compare it with a visual  organization chart . In this particular situation , perhaps after 3 lines of  verbal information , our mind probably freezes up . Its hard to retain the verbal information . However the visual organization chart do away with all the explanation and probably can retain information a lot better .

In the olden days , we have silent movies . We had Charlie Chaplin then and today we have Mr Bean . Notice that the entire show or movies , there is little or no verbal communication , only actions and their  body language  . And yet we laugh for we understand exactly what they were trying to tell us .   This is the power of pictures , and pictures are extremely powerful tools in problem solving .


problem solvingLuckily , our forefathers who lived in caves then , they drew  pictures of  animals . It helps us recognize that at that time they have horses , buffaloes and so forth . Imagine if they had not drawn those picture but instead use some form of written or verbal communication . We probably would have a harder time understanding the types of animals they had then . But with pictures , its so much easier .


Problem solving | Visual thinking revisited

Visual thinking is about using what we already have in all of us , our eyes and our mind’s eyes .  In fact more 50% of ALL the  neurons in our brains are focused on visual processing . That makes our brain a huge image processor and that’s the number ONE thing our brain does  . Every time when we open our  eyes ,  our brains processed images and pictures . So why don’t we capitalize and make full use of this innate ability that we already have , for problem solving  !!

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