10%10% of What They Read
At the base of the pyramid, the image shows 10% of what they read. This means that reading alone is the weakest form of learning. Reading books, notes, formulas and explanations is important, but it is not sufficient by itself.
For UPSC Maths Optional, many students make the mistake of collecting too many books and notes. They keep reading theory repeatedly but do not solve enough problems. This gives a false feeling of preparation. The student may feel that they have understood the topic, but when they sit to solve a question independently, they may struggle.
Reading is useful for building familiarity with a topic. It helps students know definitions, formulas, theorems and basic methods. But Maths Optional requires more than familiarity. It requires accuracy, speed, logical presentation and step-wise solution writing. Therefore, reading should be treated as the first step, not the final step.
For example, a student may read the theory of Real Analysis, Linear Algebra, Ordinary Differential Equations or Mechanics. But unless the student solves examples and writes answers, the concept may not become strong. Reading introduces the topic, but practice strengthens it.
20%20% of What They Hear
The next level is 20% of what they hear. This means listening to a teacher or lecture improves learning, but it is still mostly passive. When students listen to class explanations, they understand the topic better than reading alone. A good teacher can simplify difficult concepts, explain the logic behind formulas and guide students on what is important for the exam.
In UPSC Maths Optional, listening to a teacher is very helpful because many topics are technical and interconnected. For example, topics like Abstract Algebra, Real Analysis, Partial Differential Equations, Mechanics and Fluid Dynamics may become difficult if students try to understand them only through books. A teacher can explain the sequence, common mistakes and exam-oriented method.
However, listening alone is still not enough. Some students attend classes regularly but do not revise or practise after class. They understand the topic during the lecture but forget it after a few days. This happens because listening is still a passive activity. The student is receiving information but not yet applying it.
At Ramana Sri IAS, students are always encouraged to move beyond listening. A class explanation should be followed by note-making, revision, solved examples and independent problem-solving. Listening gives clarity, but practice gives command.
30%30% of What They See
The third level is 30% of what they see. Visual learning is stronger than reading or hearing alone because images, diagrams, graphs and solved examples stay longer in memory. For Maths Optional, visual understanding is very important.
Many topics in Mathematics become easier when students see the structure clearly. Graphs, geometric diagrams, coordinate systems, flowcharts, matrices, solution steps and formula maps can help students understand difficult ideas. For example, in Calculus and Analytical Geometry, diagrams help students visualize the problem. In Mechanics, force diagrams and motion diagrams make the solution clearer. In Linear Algebra, matrix structure and transformations become easier when shown visually.
Solved examples also play an important role. When students see a teacher solve a problem step by step, they learn the method, sequence and presentation style. This is especially useful for UPSC Mains, where step-wise answer writing matters. A student must not only know the answer but also know how to present it properly.
Still, seeing solved examples is not the final stage. Students must not become dependent on watching solutions. They must move from “I understand when the teacher solves” to “I can solve independently.” That shift happens only through active practice.
50%50% of What They See and Hear
The next level is 50% of what they see and hear. This represents video learning, classroom teaching and live explanations where students both watch and listen. This is stronger than only reading, only hearing or only seeing because both eyes and ears are involved.
For UPSC Maths Optional, a good classroom or video-based learning system can be very effective. Students can hear the explanation, see the steps, observe the teacher’s method and understand how to approach exam-level questions. This is why structured coaching, recorded lectures and demo videos can help students build a strong base.
For example, when a teacher explains a theorem, solves a PYQ and shows how each step is written, students learn multiple things at the same time. They learn the concept, the method, the formula application and the answer-writing format. This type of learning is stronger because it combines explanation and visualization.
But even this level is not enough by itself. Many students watch videos and feel satisfied, but they do not write answers or solve problems after watching. This creates passive confidence. The student may think, “I understood the solution,” but actual exam performance depends on whether they can reproduce the solution under time pressure.
Therefore, seeing and hearing should be followed by writing and doing.
70%70% of What They Say and Write
The fifth level is 70% of what they say and write. This is where learning becomes active. When students explain a concept in their own words, discuss doubts, write formula notes, prepare short summaries and practise answer writing, their understanding becomes much stronger.
In UPSC Maths Optional, writing is extremely important. The final exam is not an oral exam; it is a written exam. Students must write complete solutions in a clear, logical and step-wise manner. Even if a student understands a topic mentally, they must be able to express it on paper.
Writing formula notes is one of the most useful habits for Maths Optional aspirants. Each topic should have a compact formula sheet, important theorem list, common methods and standard problem types. These notes help during revision and before mock tests.
Explaining concepts in your own words is also powerful. If a student can explain a formula, theorem or method without looking at the book, it means the concept is becoming clear. Discussion also helps because doubts come out when students try to explain. Many hidden gaps in understanding are revealed during discussion and writing.
At Ramana Sri IAS, students are guided to build this habit of active writing. Maths Optional preparation must include written practice, formula revision, answer presentation and PYQ discussion. This converts passive understanding into exam-ready ability.
90%90% of What They Do
The top level of the pyramid is 90% of what they do. This is the strongest form of learning. It includes practising, solving, teaching, applying and testing. For UPSC Maths Optional, this is the most important part of preparation.
Mathematics is mastered by doing. Students must solve questions repeatedly, attempt PYQs, write mock tests, correct mistakes and revise weak areas. This is where real learning happens. Reading and listening prepare the mind, but solving and writing build performance.
When students solve problems independently, they face real difficulties. They may forget a formula, make a calculation mistake, miss a step or fail to present the answer properly. These mistakes are not failures; they are part of the learning process. Each mistake shows what needs to be improved.
PYQ solving is especially important because UPSC Maths Optional has patterns. Previous year questions show the type of questions asked, the depth required, the common areas, the marks distribution and the expected presentation style. Students who practise PYQs regularly understand the exam demand better than students who only read theory.
Mock tests are also essential. They help students improve time management, writing speed, accuracy and presentation. UPSC Maths Optional papers are lengthy, and students must solve questions within a fixed time. Without test practice, even a knowledgeable student may struggle to complete the paper.
This is why the top level of the pyramid is the most powerful: doing creates mastery.
