Problem Solving

My father used to make me memorise square numbers when I was in primary school. I had to recite square numbers up to 12 squared, which is equal to 144. I'm sure some students would have similar experiences. Now what if you are made to calculate 14 squared or perhaps a bigger number, say 108 squared. Would you be able to do it without using a calculator? Before I give the solution to the problem, let's look at problem solving in general.

Most students' experiences with problem solving come from the mathematics problem sums that they have to solve. However, in the real world, problems do not just exist in the mathematical realm. In fact, the solution would often require knowledge and skills from different disciplines. More often than not, creativity, critical and inventive thinking skills play a critical role in solving the myriad problems of the 21st century. 

Recently, it was reported that Singapore students have topped an international assessment on problem solving. This is based on results for the 2012 Programme for International Student Assessment (PISA), a worldwide study by the Organisation for Economic Co-operation and Development (OECD). 

OECD's Andreas Schleicher said, "Innovation today is no longer about you having a great idea and being able to do it. Innovation is to do with how you can connect with the ideas of others, people who share other ways of thinking, other belief systems. Those are the skills of increasing importance for success. It is important for us to see to what extent they are developed in school and even out of school. What's true is also that in a fast-changing world, the skills that are required to be successful are changing."

"This means that the education system needs to remain very, very active, and needs to be very sensitive to the needs of individual students and the kinds of skills that are valued by society," he added. 

To do well in the future, students would definitely need to learn to think critically and inventively besides doing well academically. 

Back to the question that was posed earlier. There is a very simple solution to the problem.