By Cynthia Kemunto, Mathematics Teacher · May 2026 · 6 min read
For many students, "quadratic equations" is the moment maths stops being fun. It does not have to be. After years of teaching IGCSE Mathematics at Smartious, I have found that the students who enjoy quadratics are not the ones with special talent — they are the ones who were shown the subject differently. Here are five approaches that work.
Every quadratic is a parabola — a curve with a real shape. Before a student ever meets the quadratic formula, show them the curve: where it crosses the x-axis, where it turns, why it is symmetrical. When students see that solving a quadratic just means finding where the curve meets the line, the algebra stops feeling arbitrary and starts feeling like a map.
A thrown ball, a fountain of water, the cables of a suspension bridge, the path of a long jump — all parabolas. When a student realises the equation describes the arc of a basketball shot, quadratics stop being abstract symbols and become a description of the real world. Smartious lessons deliberately anchor every quadratic in something physical.
Factorising a quadratic is genuinely a puzzle: find two numbers that multiply to one value and add to another. Framed as a logic puzzle rather than a procedure, students compete to solve them quickly. The satisfaction of "cracking" a factorisation is real — and it builds the speed examiners reward.
Give a student a wrong worked solution and ask them to find the mistake. Hunting for the error — a sign slip, a dropped term — is more engaging than copying a correct method, and it teaches the exact mistakes they need to avoid in their own work. Teaching by debugging works remarkably well for quadratics.
Factorising, completing the square, and the quadratic formula each solve the same equation. Rather than forcing one, show all three and let students discover which they prefer and when each is fastest. Ownership of the method turns a dreaded topic into one where the student feels in control.
Quadratic equations become enjoyable when students see the curve, connect it to the real world, and feel ownership of the method. None of this requires special talent — only better teaching. At Smartious, our Mathematics teachers make quadratics one of the topics students end up enjoying most.
Quadratics appear from around Year 9–10 and are a major topic in IGCSE, GCSE and equivalent secondary curricula, continuing into A-Level and IB.
Factorising first, because it builds number sense. The quadratic formula is the reliable fallback for equations that do not factorise neatly. Completing the square matters most for understanding the curve and for later topics.
Usually because they were taught the formula before the meaning. A student who understands the parabola first finds the algebra far easier — which is exactly how Smartious sequences the topic.