Strategies for Teaching Mathematics

🗾The first time I saw how kids in Japan learn multiplication, I was stunned. They don’t start with memorized tables. They start with lines. Draw a few parallel lines for one number, cross them with lines for the other, and then simply count the intersections. Out comes the product. It looks more like art than math. 💡 Here’s the deeper insight: this method isn’t just a trick. It reveals a truth we often forget — math is not about numbers, it’s about representations. Change the representation, and suddenly what felt abstract becomes intuitive. And here’s what most people don’t know: Variations of this approach also exist in ancient Vedic math from India and in medieval Europe’s lattice multiplication. It works even with big numbers. You just add more lines, and patterns appear naturally. For children who are visual learners, it can unlock multiplication in a way rote memorization never could. Personally, it reminded me that innovation often comes not from inventing something new, but from seeing the old differently. 👉 My take: If kids can learn math by drawing, what could we re-learn in our own lives if we changed how we represent our problems? #Education #Learning #Innovation #Math

Numeracy does not stop at the school gate. If we want children to grow up confident with numbers, we also need to support adults. Too many people left formal education years ago with gaps in their confidence and competence around numbers. That affects their prospects at work, their ability to manage family finances and their confidence helping their children with maths. At The Richmond Project, our research found that less than half the UK public is proficient with everyday numbers, and almost six in ten score poorly on basic competence. The maths in question is not abstract or advanced. It's the maths of ordinary life. The good news is that the appetite to change is already there. 90% of respondents in our research recognised the importance of numeracy, and even many of those who struggle want to improve. The challenge is matching that appetite with support at every age and in every corner of the country. Today Lizzie Gaisman and I have written for The Telegraph on why improving numeracy means working with families, adults, employers and schools, and why this matters so much for social mobility. The UK House of Lords Numeracy for Life Committee, which we are giving evidence to today, is doing invaluable work exploring these issues. Improving our numeracy skills is not beyond us as a country. But if we want to crack social mobility, we have to crack numeracy. Read more here: https://lnkd.in/evPxQpaY

The Japanese multiplication method, often referred to as the lattice or line method, is a powerful and visually engaging way to understand the concept of multiplication beyond rote memorization. Instead of relying solely on the traditional algorithm, this technique uses intersecting lines to represent place values, allowing students to literally "see" how numbers interact. Each intersection creates a product, which is then organized and added along diagonals to form the final answer. What makes this method especially compelling is its ability to simplify large number multiplication by breaking it down into bite-sized visual components, fostering deeper comprehension rather than just mechanical calculation. For visual learners or those who struggle with abstract number manipulation, this method offers clarity, confidence, and even a bit of fun — transforming math into a creative puzzle. In classrooms across the globe, it serves not only as a computation tool but also as a bridge to deeper numerical literacy. Whether you're a curious student, a parent, or an educator, Japanese multiplication can change how you view numbers entirely. 👉 Follow Ravi Mishra for more such engaging and insightful educational content. 💫

Smart people sound dumb when they try to sound smart. (and a Nobel Prize winner proved it). Richard Feynman was a late talker. Didn't say a word until he was three. His teachers thought he was slow. He went on to win the Nobel Prize in Physics. But here's what made him different: He could explain quantum physics to a five-year-old. While other professors hid behind jargon, Feynman exposed the truth—complexity is often a mask for shallow understanding. The research backs this up. From lectures, we remember 5%. From reading, 10%. From teaching others? 90%. So Feynman built his learning method around teaching. I've used it to master everything from investing to psychology. Here's how it works: First, study deeply. Attack your topic from every angle. Books, videos, conversations. Fill pages with notes. Then teach it simply. Find someone who knows nothing about it. Explain using only simple words. No jargon. No acronyms. Just clarity. Next, find the gaps. Where did you stumble? Where did you reach for fancy words? Those are your knowledge holes. Go back and fill them. Finally, refine and repeat. Turn your explanation into a story. Share it. Improve it. Now you truly understand. I've watched billion-dollar founders explain their business in one sentence. I've also watched people use 47 slides to say nothing. Guess which ones succeed. This week: Pick one thing you want to master. Give yourself a week to study. Then teach it to someone. You'll be shocked how much deeper your understanding becomes when you're forced to simplify.

i built this prompt to make me proficient in any technical topic. it's been a godsend. it includes technical depth, but translates every piece of jargon into plain english with a real world example. feel free to steal it: 🧠 Deep Research Prompt Template (Extensible Version) Objective: Create a comprehensive research report on [INSERT TOPIC HERE]. The goal is to build a deep conceptual understanding of the topic — from its theoretical foundations to its real-world applications — so that I can use this as a launchpad for further exploration. Audience: A non-technical but intellectually fluent reader. I’m comfortable following complex discussions, but I’m not formally trained in this technical domain. Tone & Style: - Write in a clear, structured, and explanatory style. - Include technical depth, but translate every piece of jargon into plain English. - After each complex term, formula, or mechanism, provide: a) A plain-language translation (explain it like you’re teaching an intelligent layperson). b) A real-world, tangible example or analogy that makes the idea concrete. Content Requirements: 1) Foundations Section - Define the core principles, vocabulary, and historical context behind [TOPIC]. - Explain why this field exists, what problems it solves, and who pioneered it. - Use simple examples to show the basic mechanics at play. 2) Core Concepts & Mechanics Section - Dive into the key theories, processes, or frameworks that make up the topic. - Introduce any math, algorithms, or scientific models central to the field. - For each technical concept, pair the explanation with: a) A plain-language breakdown. b) A real-world illustration (e.g., from everyday life, business, nature, or technology). 3) Applications & Implications Section - Show how [TOPIC] is applied in real-world systems, industries, or technologies. - Include notable case studies or examples that demonstrate its impact. - Explain why understanding these concepts matters — what it enables or changes. 4) Integration & Broader Context Section - Connect this field to adjacent domains (e.g., how it interacts with math, physics, biology, economics, etc.). - If relevant, trace how the theory translates into practice (e.g., from code → circuits → behavior). - Highlight open questions or ongoing research frontiers. 5) Formatting & Accessibility Guidelines - Use clear headings, subheadings, and summaries at the end of major sections. - Define jargon inline, not in a glossary. - Use metaphors, analogies, or thought experiments liberally. - If helpful, include short “mental models” or “rules of thumb” to aid intuitive understanding. Output Goal: A research-style explainer (typically 3,000–5,000 words) that is educational, accessible, and intellectually rigorous — something that helps a curious but non-specialist reader gain a working, conceptual mastery of [TOPIC].

AI is making math MORE important for the next generation — not less. Do you calculate like this? There is a common misconception: “Why should kids learn math when AI can calculate everything?” I believe the opposite is true. As AI becomes increasingly powerful, mathematical thinking will become one of the most valuable human skills. AI can solve an equation in seconds. But can a child look at the answer and know whether it makes sense? AI can calculate a percentage. But does the child understand what that percentage actually means? AI can generate a sophisticated model. But can they challenge the assumptions behind it? That’s where education needs to evolve. Kids should become highly comfortable with: 🧮 Mental math — calculate simple numbers quickly and confidently 📊 Percentages & ratios — understand money, business and data 📈 Statistics & probability — distinguish signal from noise 🧠 Problem solving — break complex problems into logical steps ⚡ Estimation — know when an AI answer is simply unrealistic 🤖 AI literacy — use AI as a powerful tool, while challenging its output We shouldn't teach children mathematics because they will need to compete with calculators. We should teach mathematics because they will increasingly work WITH AI. The stronger their mathematical foundation, the better they can: Ask AI better questions → understand the answer → challenge the answer → build something better. The future isn't: Human vs. AI. It is: Human intelligence + AI capability. And mathematics may be one of the most important foundations connecting the two. Teach kids to use AI. But first, teach them how to think. #AI #Education #Mathematics #FutureOfWork #AIEducation #STEM #ArtificialIntelligence

🎲 Why are we still pushing teens to 𝗰𝗮𝗹𝗰𝘂𝗹𝘂𝘀 when they're 𝗯𝗲𝗶𝗻𝗴 𝘁𝗮𝗿𝗴𝗲𝘁𝗲𝗱 𝗯𝘆 𝗴𝗮𝗺𝗯𝗹𝗶𝗻𝗴 𝗮𝗽𝗽𝘀? Our math education system has backward priorities: We treat probability and statistics as optional while pushing students toward "fancy math" most will never use. Meanwhile, young people are making real-world decisions about risk every day without the mathematical tools to understand them. The math that actually matters isn't about calculating derivatives—it's about detecting misleading claims, understanding financial risks, and seeing through the false promises of sports betting apps. This isn't about making math easier—it's about making it relevant. A teenager who understands basic probability can immediately see through predatory gambling tactics, interpret health claims about supplements, analyze their social media performance data, and make smarter consumer decisions. Read my full essay "Math That Matters" to see why others are advocating for this long-overdue shift in what we teach. I've also included a proposed a high level year-by-year curriculum roadmap from middle school through high school that could transform math education. #MathEducation #Probability #Education #CriticalThinking #statistics

The Architecture of Ambition: Why Math is the Language That Matters Srinivasa Ramanujan saw visions of the divine in his equations. Across the ocean, René Descartes sat inside a ceramic stove to escape the cold, emerging with the realization that the physical world could be mapped through coordinates. Two mathematicians, worlds apart, understood a fundamental truth: Math isn’t about calculation. It is architecture—the scaffolding of logic upon which our digital universe is built. Watching my daughters navigate their own relationship with math recently, I realize we often do a disservice to the next generation by framing it as a hurdle to be cleared. We need to shift from "What is the answer?" to "How is this built?" Rote vs. Reason In our classrooms, we have optimized for Rote—the ability to memorize and replicate. But Rote is a closed loop. Reason is an open frontier. AI is already faster and more accurate at "Rote" than any human. If we train our children to be experts at calculation, we are training them to compete with machines they cannot beat. However, AI cannot yet replicate the "Reason" behind the architecture. Math is the ultimate "low-code" language; it teaches a mind to deconstruct massive problems into solvable units. The real risk isn't that our children will find math "hard," but that they will find it "irrelevant." Let’s show them they are witnessing the legacy of Descartes and Ramanujan, and many other mathematicians, in every AI experience they have. In an AI world, the "correct answer" is cheap. The ability to ask the right logical question is priceless. It has always been priceless. #TheArchitectureOfAmbition #RoteVsReason #FutureOfLearning #STEMEducation

I’m not a maths person.” How many of us have said this… in front of our daughters? New research shows something uncomfortable but important: 👉 Maths anxiety is being passed from mums to daughters. By age 8, girls already feel less confident in maths than boys. By GCSE and beyond, they perform just as well — but are far less likely to choose maths. Not because of ability. Because of confidence. And confidence is shaped at home. Girls see us tense up at homework. They hear us say “ask your dad”. They absorb the message that maths is stressful, abstract, or “not for us”. Fast-forward and it looks like: • avoiding maths A-level • letting others “handle the bills” • opting out of opportunities that quietly require number confidence This isn’t about blame. It’s about breaking the cycle. You do not need to be good at maths to raise a child who feels good at maths. Here are some practical ways parents can counter maths anxiety (starting with ourselves): 1️⃣ Change the language Swap “I’m bad at maths” for ➡️ “I didn’t enjoy how it was taught to me.” That one sentence matters more than you think. 2️⃣ Make maths part of everyday life Cooking, shopping, travel, splitting bills, doubling recipes — call out the maths casually, not like a lesson. 3️⃣ Let them see you learning Say: “I’m not sure — let’s figure it out together.” Confidence grows from problem-solving, not instant answers. 4️⃣ Connect maths to what they love Art = symmetry Sport = stats Baking = ratios Gaming = logic & patterns Maths isn’t abstract — school just made it feel that way. 5️⃣ Build usage, not perfection Maths is a muscle. Use it more → fear reduces → confidence grows. If we want more girls choosing maths after GCSE, the work doesn’t start in Year 10. It starts at the kitchen table — and with the stories we tell about ourselves. I remember freezing in maths lessons and copying my best friend’s maths homework!! Ironically, it became my favourite subject to teach as a primary school teacher. I loved teaching it because I knew how hard it can feel. Of all the subjects, maths is the most likely to have this all-or-nothing feeling that you either can or can't do it. That myth is the real problem. What shaped your attitude and mindset towards maths? 💬 Curious: what maths phrase did you grow up hearing at home? *************** ♻️ Repost for someone in your network who needs to see this. 🔔Follow me, Rachel Vecht 🌞🏡 for more on working parenthood & raising children to thrive.

My best tip for learning Financial Modeling? 👇 𝗠𝗼𝗱𝗲𝗹 𝘆𝗼𝘂𝗿 𝗼𝘄𝗻 𝗹𝗶𝗳𝗲. In business modeling there's always a learning curve... ▪️ Manufacturing? gotta learn it ▪️ SaaS? gotta learn that too ▪️ Insurance? you get the idea With your life, there's no learning curve (hopefully). So open a spreadsheet... Put some months along the top. And some line items down the left side like: ▪️ Paycheck ▪️ Rent ▪️ Utilities ▪️ Groceries ▪️ Travel ▪️ Discretionary (having fun) Can you fill out something for each month? ✔️ Congrats! You've built a 𝗕𝘂𝗱𝗴𝗲𝘁. Now, check it again next month (or next week)... Are the numbers different than what you guessed? If so, update them — how did things change? ✔️ Congrats! You've built a 𝗥𝗼𝗹𝗹𝗶𝗻𝗴 𝗙𝗼𝗿𝗲𝗰𝗮𝘀𝘁. Now what about cash? When is Rent due, and when is your Paycheck coming in? Open another tab, but this time put weeks (or days) on the top. Put the same line items down the left side. Put "Beginning Cash" at the top and "Ending Cash" at the bottom. Punch in 𝘦𝘹𝘢𝘤𝘵𝘭𝘺 when your Paycheck comes in and your bills go out. Do you have enough cash to cover your costs (in the short term)? ✔️ Congrats! You've built a 𝗖𝗮𝘀𝗵 𝗙𝗹𝗼𝘄 𝗙𝗼𝗿𝗲𝗰𝗮𝘀𝘁. (p.s., here's a free template 👉 https://lnkd.in/edmwgYCv) Last thing, if you could only open your file for 2 minutes... What key things would you NEED to see? ▪️ Estimated savings this month? ▪️ Estimated savings this year? ▪️ Maybe a graph of your estimated cash balance? ✔️ Congrats! You've just built a 𝗗𝗮𝘀𝗵𝗯𝗼𝗮𝗿𝗱. 🟢 𝗕𝗲𝘀𝘁 𝗖𝗮𝘀𝗲? ▪️ Better understanding of your personal finances ▪️ Improved Financial Modeling skills 🔴 𝗪𝗼𝗿𝘀𝘁 𝗖𝗮𝘀𝗲? ▪️ Great modeling practice ▪️ Exposure to business concepts understood at a personal level In fact, I learned most of my Excel skills building a personal finance model. Because I didn't need to spend time on the "learning curve." I just found the fastest way to present relevant info to myself. (And I still use that budget every week) So — give it a try! It's some of the best free education you can give yourself. ~~~ 👋 Hey, I'm Chris Reilly, and I teach Financial Modeling based on real Private Equity and FP&A experience. 📌 See Financial Modeling Courses 👉 https://lnkd.in/eG_uVhsE