Mathematics has been aptly called the language of logic, pattern, and structure. However, for most students, it turns into a language that is alien, replete with symbols and processes that appear abstracted from reality. An ongoing question is: Why is it that learners are doing well on textbook problems but can't seem to bring the same principles to bear when confronted with new, everyday situations? This disconnect between procedural and conceptual understanding is being increasingly highlighted with India's embrace of the National Education Policy (NEP).
With the new curriculum, there is a deliberate shift towards competency-based learning. For instance, students are increasingly being examined on how they can apply mathematical logic to case studies and emerging problems. Yet classroom instruction continues to focus on solving standard, textbook problems. This causes a disconnect, Students perform well in scripted formats but falter when asked to use the very same concepts under unfamiliar settings.
The imbalance in the way mathematics is taught, examined, and applied in everyday life renders even top-performing students inadequately prepared for examinations that attempt to test real understanding.
Ramana Andra, Lead Faculty, and Krishnan VP, Research Associate, Prayoga, stress that mathematics comes across as abstract and isolated for students. They point out that India's NEP emphasizes learning mathematics by intuition, practical applications, and inter-disciplinary relations.
ABSTRACT BEFORE EXPERIENCE
In most classrooms, formulae and definitions are given early on, occasionally without sufficient context. The student may understand that a linear equation has the form "ax + by + c = 0", and that such an equation graphs as a straight line. But the deeper concept, that this form describes a constant rate of change in a relation between two variables, is stressed infrequently. The result is an ability to perform symbolic operations without grasping the conceptual foundations behind them.
This lack of continuity is revealed in assessments. It is not uncommon for "sharp" students, students who have memorized solutions of textbook problems, to flunk when requested to solve or interpret a problem not encountered before. They do not fail because they are less able or less hard-working, but because they have been taught merely to remember and regurgitate rather than think and analyze.
Recognizing the Problem
The 2023 National Curriculum Framework for School Education is recognizing this problem, noting that "conventional methods of teaching mathematics directly dive into abstract symbolic manipulation". In so doing, they lose sight of the importance of building intuition and capacity to apply in the real world. As an example, a physics concept like Hooke's Law, where the displacement of a spring is in proportion to the force used.
Concepts of proportionality, variation, and rate of change are learned in separate subject areas so that students can't see the underlying patterns that mathematics is designed to reveal.
At the university level too, math students might be good at doing things with n-dimensional vector spaces and playing around with abstract symbols effectively. Yet, many of them have difficulty with fundamental principles in physical settings, e.g., torque or electromagnetic theory.
TEACHING FOR INTUITION AND APPLYING
The answer is not to cut the mathematics down to its simplest level, but to rearrange how it is first introduced and encountered. Rather than starting with symbols, students should be led to discover mathematical concepts through examples, patterns, and models from their surroundings. Visual argumentation, testing, and everyday contexts provide good points of departure for learning, like using pictures, manipulatives, or everyday examples make ideas more concrete.
Shifting beyond x and y does not imply throwing away symbols, it implies grounding them in experience, so that students can view mathematics not as a method to conform to, but as a prism to comprehend the world.
