Cursory thinking is thinking without paying deep attention, or rather, the inability to grasp the essence of a problem or to get an instant deep insight into the real issue, or resort to lazy simplistic thinking – the inability to penetrate beyond seemingly simplistic solutions, or, often being misled by false simplicity. Cursory thinking can lead to wrong decisions in real life and in business situations with serious consequences.
Mathematical thinking, on the other hand, is to instantly get a deep understanding about nuances in any issue, see the false as the false, see the hidden truths, seeing a problem in all its countours, as clearly as one would, if light is focused on an object.
It is possible to develop a mathematical mindset if math is learnt through deep conceptual understanding. Logical thinking, creative reasoning, open ended problems, problems to develop speed and agility etc, should also be packaged into math learning from an early stage, to help a child learn holistically and develop mathematical thinking. The focus at Cuemath is to develop this life skill called Mathematical thinking in every child from a young age. The curriculum is designed to make every child a mathematical thinker and achieve this life skilling outcome.
Let us look at two problems to illustrate the difference between cursory thinking and mathematical thinking. Most adults think cursorily and would come up with wrong answers, and instantly, misled by what seems to be false or deceiving simplicity in the problems below.
Of 100 people in a room, 99 are mathematicians. How many mathematicians should leave the room so that the percentage of mathematicians in the room will drop by one percent?
A cursory answer that is often given is 1. The cursory thinker cannot comprehend that a one percent drop from 99 percent to 98 percent would need about 50% of mathematicians to leave the room.
Deeper thinking process would be: If one non mathematician were to constitute 2%, how many others should be in the room including himself? Or, simply put, mathematically, what is 1 divided by 2%. The answer being 50, it requires 50 mathematicians to make their exit so that 49 of them are in the room along with a non mathematician The fact that it requires a large number to exit the room to move the needle by one percent is not what most cursory thinkers would see immediately.
A, B and C are in a race. B’s speed is 90 % of A’s and C’s speed is 90 percent of B’s. When A hits the finish tape at 100 metres, by how many metres is C behind?
The Cursory answer is that C would be at 80 metres. And therefore behind by 20 metres It is so convenient not to think in terms of C’s relative speed to A’s speed!
The mathematically inclined would quickly grasp that B’s speed relative to A’s is 90% and given that C’s relative speed to B ‘s is 90%, the relative speed of C to A is 81%. So, C would be at 81 metres when A finishes the race exactly 19 metres behind.
A mind that is mathematically inclined will seldom make cursory omissions. This requires systematic training with the right resources to make the child confront challenges all the time to think out of the box. Mathematical thinking skills have deep value in decision making. These valuable skills can only be imparted in a well-designed math learning system. Seldom do traditional math programs, curriculums, coaching classes in math, specific and narrow skilling programs focusing on calculation abilities etc serve this all-important need. The proof that math learning of most adults has suffered without producing the required outcomes that really matter, lies in that fact that over 90% of the adults cannot think through the solution to the above two simple problems. Obviously and unfortunately, they never learnt it right and learnt what really mattered. The earlier such right skilling begins, the deeper would a child’s cognitive abilities develop. An early beginner would reap the benefits of gaining cognitive skills, deeper, faster and better, with a clear early start advantage. Cuemath is designed to deliver life skilling of a high order that will prepare every child to rise up to the ever-occurring life’s challenges of VUCA (Volatility, Uncertainty, Complexity and Ambiguity), akin to what the world is facing in the current pandemic.
At Cuemath, we train teachers to help students cultivate a mathematical thinking approach towards problems; we continuously review and monitor their classes to check if the recommended best practices are followed and share feedback, so that, in course of time, they come to embrace these qualities, become great teachers. Anyone who wants to be a part of a movement, to change the way children learn Math across the world can become a Cuemath teacher.
At Cuemath we have a community of talented teachers who are applying the best practices focused on research to give your child sound fundamentals in computer science, critical reasoning, and artistic problem-solving abilities. Cuemath provides live 1:1 Live Online Math classes. Book a demo and get in touch with our academic counsellor to get the best course for your child.
-By Ramesh Bharathi
Ramesh heads the training vertical of Cuemath. He has over 40 years experience in senior positions in leading industries such as Airlines, Investment Banking, Print media and Education. He is a Chartered Accountant and a Chartered Financial analyst and has also taught in ICFAI Business school, a leading Management Institution in India.