Strategies for Teaching Mathematics

Great teachers often stumble over the same invisible hurdle. As a coach who’s worked with educators, I’ve repeatedly seen brilliant teachers unknowingly short-circuit student growth. Not because they lack expertise—but because they rely too heavily on giving answers, missing opportunities for students to find their own. The best teachers aren’t those who tell—they’re the ones who guide discovery. At 𝐂𝐨𝐚𝐜𝐡𝐔𝐏8, I’ll unpack three simple yet transformative shifts that help teachers ignite student curiosity and deepen learning. These shifts aren't complicated—they’re subtle changes in how teachers engage: 📝 Move from providing answers to provoking thoughtful questions. 📝 Shift from passive hearing to truly understanding what students express—and don’t express. 📝 Transform challenges into opportunities by changing the perspective students hold. These subtle shifts are game-changers during tough classroom moments: the disengaged student staring blankly, the persistent conflicts that disrupt lessons, or the hesitant learner stuck in a cycle of self-doubt. Teaching transforms when the teacher stops rescuing and starts empowering. Consider your own teaching practice: Where might you be unintentionally limiting student discovery by stepping in too soon? --- 📌 Want more content like this? Follow me Andrew Calvert, PCC Follow Serendipity Engine

The TAPPLE Method – Keep Every Student Engaged. T-A-P-P-L-E 💡 “The best classrooms aren’t quiet—they’re buzzing with thinking, sharing, and accountability.” Definition of the TAPPLE Method A structured engagement cycle that blends classroom management with formative assessment to keep students active, alert, and accountable. 🔑 The Steps of TAPPLE T – Teach First → Present the concept clearly and briefly. A – Ask a Question → Pose a question about what was just taught. P – Pair-Share → Students discuss with a partner. P – Pick a Non-Volunteer → Call on a student who didn’t raise their hand. L – Listen → Pay attention to the response. E – Effective Feedback → Reinforce correct answers or guide gently to the right one. 📘 Classroom Example: Photosynthesis 1. Teach → “Plants need sunlight, water, carbon dioxide.” 2. Ask → “What do plants need?” 3. Pair-Share → Students discuss with partners. 4. Pick → Teacher calls on a random student. 5. Listen → Student responds. 6. Effective Feedback → Teacher praises & reinforces. ✅ Why Use TAPPLE? • Promotes equity → every student gets a chance • Encourages collaboration → builds confidence • Provides real-time formative assessment • Reduces behavior issues by keeping students engaged • Creates a positive, accountable classroom culture 💡 Quick Tip Use TAPPLE every 5–7 minutes in your lesson to keep energy high and learning active. How do you keep all your students engaged and accountable during lessons? 👇 Share your strategies in the comments! #TeachingStrategies #ClassroomManagement #FormativeAssessment #TeacherTips #WholeBrainTeaching #EngagedLearning #Cognia #BritishCouncil

🤯 𝗦𝘁𝘂𝗰𝗸 𝗶𝗻 𝘁𝗵𝗲 ‘𝗪𝗵𝘆’ 𝗼𝗳 𝗠𝗮𝘁𝗵𝘀? 𝗟𝗲𝘁’𝘀 𝗖𝗵𝗮𝗻𝗴𝗲 𝗧𝗵𝗮𝘁! 𝗪𝗵𝗲𝗿𝗲 𝗺𝗮𝗻𝘆 𝘀𝘁𝘂𝗱𝗲𝗻𝘁𝘀 𝗮𝗿𝗲: Sitting with a complex maths problem, staring at the paper, feeling frustrated. They’ve memorized formulas, but when it comes to breaking down a tricky question – they freeze. ❄️ 𝗧𝗵𝗲𝗶𝗿 𝗱𝗿𝗲𝗮𝗺 𝗼𝘂𝘁𝗰𝗼𝗺𝗲? They want to approach any problem with confidence. To see complexity and think, “I’ve got this.” To understand every step—not just apply it. 𝗪𝗵𝘆 𝗗𝗼 𝗠𝗼𝘀𝘁 𝗦𝘁𝘂𝗱𝗲𝗻𝘁𝘀 𝗦𝘁𝗿𝘂𝗴𝗴𝗹𝗲? Most students fail because they focus on what to do, not why they’re doing it. They memorize steps but miss the logic. So, when they face an unfamiliar problem, they get lost.  • They don’t question the question.  • They skip the ‘why.’ 𝗧𝗵𝗲 𝗦𝗼𝗹𝘂𝘁𝗶𝗼𝗻: 𝗕𝗿𝗲𝗮𝗸 𝗗𝗼𝘄𝗻 𝗣𝗿𝗼𝗯𝗹𝗲𝗺𝘀 𝘄𝗶𝘁𝗵 ‘𝗪𝗵𝘆’ 𝗧𝗵𝗶𝗻𝗸𝗶𝗻𝗴 🧐 Teaching students to ask “why” at each step transforms their understanding. Here’s how it works: 1️⃣ 𝗦𝘁𝗮𝗿𝘁 𝘄𝗶𝘁𝗵 𝘁𝗵𝗲 𝗣𝗿𝗼𝗯𝗹𝗲𝗺, 𝗡𝗼𝘁 𝘁𝗵𝗲 𝗦𝗼𝗹𝘂𝘁𝗶𝗼𝗻: Instead of rushing to plug in formulas, encourage them to ask: • “What is this problem actually asking?” • “What information do I have?” • “What do I need to find?” 🧠 𝗧𝗶𝗽: Break the question into smaller parts. Each part should be a mini-problem to solve. 2️⃣ 𝗤𝘂𝗲𝘀𝘁𝗶𝗼𝗻 𝗘𝗮𝗰𝗵 𝗦𝘁𝗲𝗽: When they apply a formula or make a calculation, they should ask: • “Why am I doing this step?” • “How does this help me get closer to the solution?” 🔍 𝗘𝘅𝗮𝗺𝗽𝗹𝗲: Solving an equation? • Why do we move variables to one side? • Why do we simplify terms first? 3️⃣ 𝗥𝗲𝗳𝗹𝗲𝗰𝘁 𝗔𝗳𝘁𝗲𝗿 𝗦𝗼𝗹𝘃𝗶𝗻𝗴: Once they reach an answer, teach them to look back and ask: • “Did every step make sense?” • “Why did this method work?” • “Could I explain this to someone else?” This reflection cements learning 𝗧𝗵𝗲 𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗮𝘁𝗶𝗼𝗻 🌟 When students adopt ‘why thinking,’ they gain confidence, reduce mistakes, and develop deeper mastery of concepts. This approach shifts them from memorizing to truly understanding, paving the way to top grades. Let’s help them question the question. The answers will follow! 👍 Like | 💬 Comment | 🔁 Repost | 👤 Follow me, Faisal Naqvi #MathsMastery #GrowthMindset #QEDTuitions #CriticalThinking #ProblemSolving #WhyThinking #ConfidentLearners

🎯 One size never fits all in the classroom. That’s why differentiated instruction isn’t just a buzzword, it’s the reality of teaching today. This framework breaks it down into four simple levers: 1. Content → What students learn 2. Process → How students learn 3. Product → How students show learning 4. Environment → Where students learn When we adjust these, even slightly, we shift classrooms from “delivering lessons” to designing learning experiences. Some highlights I love from this chart: 📚 Tiered assignments & choice boards (student ownership in content) 🧩 Jigsaw method & gallery walks (collaboration in process) 🎭 Performance tasks & digital portfolios (creativity in product) 🪑 Flexible seating & movement breaks (agency in environment) It’s not about doing everything at once. It’s about finding the one small change that unlocks engagement for more students. 👉 Teachers, which of these strategies do you already use and which one are you curious to try next? #Education #TeachingStrategies #DifferentiatedInstruction #EdTech #ActiveLearning

Are your students forgetting fast? Struggling to transfer what they learn from situation to the next? The missing link? Schema: the mental architecture that organizes, connects, and deepens understanding. Schema is the mental structure that helps us organize and make sense of information. It’s how experts see connections and patterns instead of isolated facts. But students don’t build schema just by hearing information. They need intentional opportunities to physically and mentally organize concepts. Here’s one simple strategy: → Write the key concepts (nouns from your standards) on index cards. → Ask students to articulate how those concepts interact, moving them around to show a hierarchy, cycle, system or other structure that communicates relationships. → Put into sentences: Write or explain how the concepts interact, using factual evidence from specific contexts to ground their answers. This shifts students from memorizing terms to building meaningful networks of understanding. When students physically move ideas around and explain their thinking, they’re actively constructing schema. That’s what leads to long-term retention and flexible application of knowledge. Bigger picture, do this every single unit of study: 1) Identify 5–7 core concepts in a unit. 2) Build in time for students to organize and re-organize those ideas throughout the unit. 3) Use those concept maps as the basis for deeper writing, projects, or problem solving. This small shift changes the game from teaching content to building thinkers. Sources listed at the end of this piece I wrote in EdWeek: https://lnkd.in/eHks9XK4

The moment a student says "This is too hard!" most teachers rush to rescue. But here's what years in the classroom taught me: The magic happens in the struggle—if we scaffold it right. I watched a 7th grader spend 20 minutes on a single algebra problem. She erased her work three times, groaned twice, and almost gave up once. Then she solved it. The smile that spread across her face? That's what real learning looks like. According to ASCD research, productive struggle builds perseverance, problem-solving skills, and self-efficacy—but only when students work within their Zone of Proximal Development (ZPD): that sweet spot between "too easy" and "impossible." Here's my scaffolding formula: • Start with a challenge just 10% beyond their comfort zone • Offer hints, not answers ("What pattern do you notice?") • Use peer collaboration before teacher intervention • Celebrate the struggle, not just the solution • Gradually fade support as confidence builds What changes when we embrace productive struggle: • Students stop asking "Is this right?" and start asking "Does this make sense?" • Mistakes become data points, not defeats • The quiet kids suddenly have something to prove • Math anxiety drops as struggle becomes normalized The hardest part? Resisting the urge to save them too soon. I've learned to count to 20 before offering help. To ask "What have you tried?" before showing the way. To celebrate effort phrases like "I'm figuring it out" over "I don't get it." Because students don't need us to remove every obstacle. They need us to teach them how to climb. What's your go-to strategy for scaffolding struggle in your classroom? #Education #Teaching #ProductiveStruggle #Scaffolding #MathEducation #PedagogyThatWorks #TeacherLife #LearningScience

#ThursdayThought "Why is it always about you?" my daughter interrupted me, her voice loud. Just five minutes earlier, she had been venting about her overwhelming homework load and the pressures of club fundraising. I had responded with what I thought was a supportive anecdote: "I had even more homework in high school back in China. It's all about time management. If you manage your time effectively, you can get everything done." I believed I was being encouraging, sharing my experiences to help her. But in that moment of her outburst, I realized something crucial: once again, I had made it about me. To her, my response felt like I was the hero of the story, and she was left feeling small and unheard. This happened a few years ago, but the lesson remains fresh in my mind. I had failed to listen actively. As a mentor and coach, I've since learned the vital importance of active listening, a lesson my daughter taught me. Here are three key insights I've gained from that experience: 1. Empathy Over Solutions: Often, people don't want solutions right away. They want empathy. Their emotions need to be validated. 2. Ask, Don't Tell: Instead of jumping in with answers, asking thoughtful questions can help the other person find their own solutions. This empowers them and shows that you value their perspective. 3. Offer Suggestions Sparingly: Suggestions can be helpful, but only after the person has had the chance to explore their own ideas. Uninvited advice is not welcome. As a leader, I often want to jump in to help my team members when they face obstacles managing their projects. I've applied these active listening skills in coaching them—using the same formula. First, I show empathy. Second, I give them space and ask open-ended questions to help them find their own solutions. Lastly, I add some of my own suggestions only after they have exhausted their own ideas. In this way, they develop their problem-solving skills and feel proud of their achievements. And as their coach, I share in that pride. =========================== Lucy Chen, award-winning author and human potential coach (I specialize in guiding individuals to build resilience and achieve success—reach out through DMs to explore collaborative opportunities on your transformative journey.) (To order my book, https://lnkd.in/gmb4_WrA) #BuildResilience #BookWriting #GiftedCoaching #ActiveListening #Empathy #Leadership

We’re facing a math achievement crisis, and we’ve gotten one big thing wrong. We’ve assumed that harder means better. That if kids are struggling, they’re learning. That pushing through frustration is proof of progress. But here’s the reality: If students are lost, they’re not retaining more. If they don’t have fluency with basic operations, they can’t engage with higher-order math. If we skip foundational understanding, we’re setting them up for failure later. The best math classrooms don’t just push harder concepts. They prepare students to handle them. Fluency comes first. Before students tackle multi-step problems, they need automaticity with basic operations. Not just memorization, but real understanding of patterns and relationships. Strong modeling matters. A great math teacher doesn’t just explain. They show their thinking in a way that makes sense and sticks. They ask students to process what they've seen modeled. Engagement drives retention. Kids learn best when they’re active participants, talking through problems, synthesizing what they've seen modeled, and having an opportunity to ask questions. Rigorous math isn’t about throwing kids into the deep end. It’s about making sure they have the skills to swim. Struggle doesn’t always equal success. If we want better results, we need to focus on fluency, modeling, and engagement first. If you're not training your teachers and leaders on all three of those, what's the plan to get started?

In working with schools, I've learned that one of the most powerful ways to accelerate achievement is to help teachers make the shift from technical preparation to intellectual preparation. The technical part is clear and necessary: Are all the student materials copied and ready? Check. What activities will I do in what order? Check? Teacher PowerPoint made? Check. The challenge is that if the teacher hasn't intellectually prepared, lessons (even using HQIM) can feel like a series of activities with the goal of attempting or completing (or worse, copying) all the work in the curriculum. Intellectual preparation helps teachers support students to transition from surface-level work to deeper thinking ... from completing work to doing their very best work. It starts with something simple yet profound: The teacher should do ALL the work they ask of students -- from the do now to the exit ticket and all the annotation, data collection, and problem-solving in between. When teachers do that, they figure out if a question is oddly worded, the level of thinking students will need to complete tasks, and what misconceptions might hold students back. In other words, unless the teacher can do an A+ job on the student work, the teacher can't support students in doing an A+ job on their work. Doing the student work isn't the full process for intellectual preparation, but it's the first and most important step. (Determining the meatiest parts of the lesson, time stamping to ensure adequate time is spent on the meat, and creating criteria for success for student work and misconception/response plans are other critical components.) My experience is that most teachers teach lessons "flying blind" because while they know the technical flow of the lesson, they don't know exactly the level of thinking / quality of work they will expect -- and demand -- from students.