https://shivakumari.com/blog Short essays on how I teach — the habits, the diagrams, and the small shifts in thinking that make physics and maths click. en https://shivakumari.com/blog/the-homework-battle https://shivakumari.com/blog/the-homework-battle Sat, 06 Jun 2026 00:00:00 GMT The nightly standoff over maths homework exhausts everyone and rarely improves a single mark. Most of the time the fight isn't about the work at all — and seeing what it's really about changes how you handle it. https://shivakumari.com/blog/not-a-maths-person https://shivakumari.com/blog/not-a-maths-person Tue, 02 Jun 2026 00:00:00 GMT It's almost always said kindly, often by a parent protecting their child from pressure. But it's a quiet self-fulfilling prophecy, and in six years of teaching I've yet to meet the child it was actually true of. https://shivakumari.com/blog/exam-nerves-are-a-timing-problem https://shivakumari.com/blog/exam-nerves-are-a-timing-problem Fri, 22 May 2026 00:00:00 GMT Most students who 'freeze' in exams know the material fine. What they haven't practised is the clock. Here's the two-pass routine I drill before every board exam. https://shivakumari.com/blog/the-slope-is-a-story https://shivakumari.com/blog/the-slope-is-a-story Mon, 18 May 2026 00:00:00 GMT Before calculus is a single rule to memorise, it's a way of noticing how fast things change. Here's how I introduce it without a single formula on the board. https://shivakumari.com/blog/mistakes-are-data https://shivakumari.com/blog/mistakes-are-data Mon, 27 Apr 2026 00:00:00 GMT Most students hide their mistakes. The ones who improve fastest learn to read them. Here's the diagnostic habit I teach from day one. https://shivakumari.com/blog/draw-the-picture-first https://shivakumari.com/blog/draw-the-picture-first Mon, 30 Mar 2026 00:00:00 GMT Nine times out of ten, a stuck physics student doesn't need another formula — they need a diagram. Here's the two-minute habit that unsticks most problems. https://shivakumari.com/blog/field-lines-are-a-map https://shivakumari.com/blog/field-lines-are-a-map Tue, 10 Mar 2026 00:00:00 GMT Students picture electric and magnetic field lines as physical threads running through space. They're a drawing convention — and confusing the map for the territory causes a specific, predictable set of mistakes. https://shivakumari.com/blog/the-question-after-a-test https://shivakumari.com/blog/the-question-after-a-test Fri, 27 Feb 2026 00:00:00 GMT Parents almost always ask the same first question when a test comes home, and it's the one that teaches the wrong lesson. There's a better question, and it costs nothing to switch. https://shivakumari.com/blog/chain-rule-is-layers https://shivakumari.com/blog/chain-rule-is-layers Wed, 11 Feb 2026 00:00:00 GMT Students learn the chain rule as a formula to apply and a function to spot. It's easier than that: a composite function is an onion, and you differentiate it one layer at a time, outside in. https://shivakumari.com/blog/integration-is-adding-slices https://shivakumari.com/blog/integration-is-adding-slices Tue, 20 Jan 2026 00:00:00 GMT The integral sign scares students into thinking it's a new and difficult kind of object. It's the oldest idea in maths wearing a fancy symbol: cut a thing into slices, add the slices up. https://shivakumari.com/blog/newtons-third-law-sentence https://shivakumari.com/blog/newtons-third-law-sentence Tue, 02 Dec 2025 00:00:00 GMT 'Every action has an equal and opposite reaction' is true, memorable, and the cause of more confusion than almost any line in physics. One missing phrase is the whole problem. https://shivakumari.com/blog/past-papers-are-a-diagnostic https://shivakumari.com/blog/past-papers-are-a-diagnostic Thu, 06 Nov 2025 00:00:00 GMT Doing thirty past papers and feeling more tired is not the same as getting better. The students who improve treat each paper as a list of things to fix, not a score to collect. https://shivakumari.com/blog/circuit-diagrams-lie https://shivakumari.com/blog/circuit-diagrams-lie Tue, 14 Oct 2025 00:00:00 GMT Students try to read circuit diagrams like maps, worrying about which component is closer or which wire is longer. A schematic throws all of that away on purpose, and understanding why makes circuits click. https://shivakumari.com/blog/radians-make-sense https://shivakumari.com/blog/radians-make-sense Mon, 22 Sep 2025 00:00:00 GMT Students meet radians as a weird unit full of π that exists to make exams harder. They're the opposite — radians are the natural way to measure an angle, and degrees are the arbitrary ones. https://shivakumari.com/blog/projectiles-are-two-problems https://shivakumari.com/blog/projectiles-are-two-problems Tue, 19 Aug 2025 00:00:00 GMT Projectile motion looks intimidating because the path is a curve. The trick that unlocks the entire topic is realising the curve is two straight-line problems that have nothing to do with each other. https://shivakumari.com/blog/factorising-is-pattern-spotting https://shivakumari.com/blog/factorising-is-pattern-spotting Tue, 08 Jul 2025 00:00:00 GMT Students who 'can't factorise' usually can — they just haven't been shown that there are only a handful of shapes to recognise. Name the shapes, drill the eye, and the panic goes away. https://shivakumari.com/blog/voltage-is-pressure https://shivakumari.com/blog/voltage-is-pressure Sun, 15 Jun 2025 00:00:00 GMT Electricity feels abstract because you can't see it. The water analogy makes it concrete — as long as you know exactly where it's telling the truth and where it quietly lies. https://shivakumari.com/blog/trig-identities-one-triangle https://shivakumari.com/blog/trig-identities-one-triangle Tue, 20 May 2025 00:00:00 GMT Students try to memorise a long list of trig identities and inevitably blank in the exam. Almost all of them fall out of two pictures you already know — so learn the pictures, not the list. https://shivakumari.com/blog/units-catch-mistakes https://shivakumari.com/blog/units-catch-mistakes Sun, 27 Apr 2025 00:00:00 GMT Students treat units as the boring thing you tack onto the end for a mark. Used properly, they're a free check that tells you a wrong answer is wrong before the examiner ever does. https://shivakumari.com/blog/friction-isnt-the-villain https://shivakumari.com/blog/friction-isnt-the-villain Wed, 02 Apr 2025 00:00:00 GMT Textbooks introduce friction as the force that slows things down and steals energy. That framing quietly teaches students to resent it — and to misread half the problems it appears in. https://shivakumari.com/blog/unit-circle-over-sohcahtoa https://shivakumari.com/blog/unit-circle-over-sohcahtoa Sun, 09 Mar 2025 00:00:00 GMT The mnemonic gets students through right-angled triangles and then abandons them the moment an angle goes past 90°. Here's the picture that actually carries trigonometry the rest of the way. https://shivakumari.com/blog/rereading-isnt-studying https://shivakumari.com/blog/rereading-isnt-studying Fri, 14 Feb 2025 00:00:00 GMT The most popular way to revise is also one of the least effective. Here's why re-reading fools you, and the slightly uncomfortable habit that actually moves marks. https://shivakumari.com/blog/the-minus-sign-problem https://shivakumari.com/blog/the-minus-sign-problem Tue, 21 Jan 2025 00:00:00 GMT I've marked thousands of algebra scripts, and the single most common lost mark isn't a misunderstood method — it's a dropped or mishandled minus sign. Here's where they hide and how I drill them out. https://shivakumari.com/blog/solving-for-x-is-undoing https://shivakumari.com/blog/solving-for-x-is-undoing Sun, 08 Dec 2024 00:00:00 GMT Most students treat solving an equation as a set of tricks to remember. It's actually one idea: whatever was done to x, undo it — last thing first, like taking off your shoes before your socks. https://shivakumari.com/blog/be-wrong-out-loud https://shivakumari.com/blog/be-wrong-out-loud Thu, 03 Oct 2024 00:00:00 GMT The quietest classroom is rarely the one learning the most. The habit I protect more than any other in young children is the willingness to say a wrong answer in front of everyone. https://shivakumari.com/blog/counting-on-fingers-is-fine https://shivakumari.com/blog/counting-on-fingers-is-fine Thu, 12 Sep 2024 00:00:00 GMT A worried parent asked me to break their daughter's habit of counting on her fingers. I asked them to leave it alone — and here's the longer answer I wish I'd had time to give.