Empowered Mathematical Mindset

Learning Mathematics by heart is a thing of the past. Nowadays, children are expected to work out calculations using creative problem-solving skills

It is without a doubt that primary school maths is no longer limited to simple arithmetic sums. By the end of Primary one, children are expected to tackle problem sums involving topics on money, measurements, fractions and graphs (to name a few) - on top of basic addition, subtraction, multiplication and division. The key is to develop an understanding of mathematical concepts, and to acquire analytical skills that will enable the children to apply the mathematical concepts to problem-solving scenarios.

With a growing emphasis on encouraging creative thinking and problem-solving abilities in our school curriculum, it is not surprising that children need to be exposed to more challenging approaches to learning mathematics – and parents feel an increasing pressure to keep up with the latest trends.

One of the latest teaching methods, adopted in many primary schools, is the use of learning centres in lower primary classroom, as part of the Strategies for Effective and Engaged Development (SEED) programme. In brief, the SEED programme intends to integrate learning between mathematics, science and the English language, through a thematic approach. Such integration across the curriculum should give rise to fun learning activities in primary schools, while at the same time developing language skills with mathematic and scientific knowledge.

Other than the efforts made to improve the curriculum in our primary schools, what can parents do to help advance the learning of our children? With jargons like “analytical skills” and “problem-solving techniques”, coupled with various teaching methods involving models and its variants, parents are often at a lost as to how best introduce mathematics to their pre-schooler and subsequently to sustain an active interest in mathematics.

Need For Creative Learning

In this current knowledge-based economy, where the emphasis is on creative and independent learning for children, the traditional method of spoon-feeding students with information and grading them based on the knowledge they have retained is irrelevant. What the new economy requires are students with nimble, innovative and analytical thinking skills, to challenge problems that are new and unknown. Parents need to nurture problem-solving skills in their children and not merely train them to perform like calculators.

With the Ministry of Education announcing the changes to the A-level “thinking” examination in 2000, students can expect more questions intended to test their understanding and application of concepts across topics, instead of merely applying well-memorised formulae.

Nowadays, most enrichment centres have designed their mathematic classes to keep pace with teaching trends in primary schools. Through a series of carefully crafted questions, students are gently steered into discovering for themselves a magical and lively world of numbers. It is certainly more meaningful to acquire knowledge and upgrade abilities by way of self-exploration, than by a purely teacher-orientated approach. Active learning is the trend for modern education. Children can build up self-confidence and gain knowledge at the same time, in the learning process.

Importance of understanding concepts

Most people know how to count from 1 to 10,000. Although they may not have done it before, they know that they are able to do so because they understand that 1+1=2, 2+1=3…., and so forth. This means that they understand the Concept and Method needed to count up to 10,000.

Parents should try not to intimidate their children with big numerals, as it is more important to understand the concepts and models necessary to solve a problem, instead of blindly applying the same well-used method. Counting and calculation skills are by no means the only measure of a child’s mathematics ability. Several more fundamental skills need to be developed to boost mathematical learning and understanding.

Multiplication Table – Beyond Mere Memory

Despite earnest efforts to memorize the multiplication table, it is not unusual for children (even adults) to forget portions of it. The accumulation of knowledge and abilities are best achieved by way of thorough understanding of the subject matter, instead of relying solely on memory. New teaching methods in mathematics aim to replace sole reliance on memory work with real comprehension, so that knowledge can be recollected whenever necessary.

To replace the traditional ways of memorisation and drills in Maths learning, the current Mathematics syllabus features lively maths sums to help captivate and equip children with the initiative to think, and therefore rely on their own strengths to solve problems.

Different strategies in solving Mathematics problems

Primary school children are taught a variety of ways or strategies to work out their problem sums. They can use any method they are comfortable with, as long as they end up with the correct answer. Children’s mind needs to be simulated to think in a multi-model manner. A likely scenario is where a child, out shopping with his mother, is asked, “If you have $17 and you buy an item worth $9.90, how much change are you left with?” Before the mum could elaborate, he answered, “Mummy, I can take $10 to minus $9.90; then add the balance 10 cents to the $7. Or I can take $1 to minus 90 cents and $16 to minus $9; and then you add the 2 answers together!” Such a scenario would imply that the child has learnt many ways to derive a solution from a problem, instead of relying on a fixed way or method. The child is also able to relate and apply his mathematics skills in his daily life. Every child should be encouraged to develop similar abilities, with the appropriate exposure to different mathematical reasoning.

Calculation skills verses Problem-Solving skills

During the 19^th century, when Carl Friedrich Gauss (a mathematical genius) was ten years old, he was asked to add up every numeral from 1 to 100 (ie.1 + 2 + 3 +..100 = ? ). He instantly scribbled “5050” on his slate and laid it down with the proud declaration, “There it lies.” When the other students turned in their slates after painstakingly adding the numerals one at a time, no one except Gauss had the correct answer!

How did Gauss do it? He had observed that each pair of numerals - 1 and 100; 2 and 99; 3 and 98; and so on up to 50 and 51 - added up to “101”. From the resultant 50 pairs of numerals, he deduced the mathematical statement: 50 x 101 = 5050. What Gauss had exhibited was problem-solving skill, and not just calculation skill!

1 + 2 + 3 + …50 + 51 +…99 + 100 = ?

Therefore, problem-solving skills are much more important than calculation skills.

Young students are encouraged to acquire a real comprehension of Maths, not simply memorise formulae. From as young as K1, young minds should be coached to think creatively and independently for more complicated Maths concepts which they will encounter as they grow older.