Overcoming Math Misconceptions in Students

Imagine the impact for students and teachers if more corrective math was occurring in classrooms as part of tier one instruction.

𝗠𝗼𝘀𝘁 𝗺𝗮𝘁𝗵 𝗺𝗶𝘀𝗰𝗼𝗻𝗰𝗲𝗽𝘁𝗶𝗼𝗻𝘀 𝗮𝗿𝗲 𝘁𝗿𝗲𝗮𝘁𝗲𝗱 𝘁𝗵𝗲 𝘀𝗮𝗺𝗲. 𝗧𝗵𝗮𝘁’𝘀 𝗮 𝗽𝗿𝗼𝗯𝗹𝗲𝗺, 𝗮𝗻𝗱 𝗵𝗲𝗿𝗲 𝗶𝘀 𝘄𝗵𝗮𝘁 𝘁𝗼 𝗱𝗼: Not all misconceptions come from the same place and if we don’t diagnose them correctly, we address the wrong thing. After coaching across multiple classrooms, here are 3 common types of misconceptions, and what to do to address it: 𝟭. 𝗖𝗼𝗻𝗰𝗲𝗽𝘁𝘂𝗮𝗹 𝗠𝗶𝘀𝗰𝗼𝗻𝗰𝗲𝗽𝘁𝗶𝗼𝗻𝘀 Students don’t fully understand the why behind the math. ➡️ Example: Believing a larger denominator means a larger fraction. What to do: 🧱 Rebuild understanding using visual models (number lines, area models) 📈Use the CRA progression (concrete → representational → abstract) ❓Ask: “Why does this make sense?” 𝟮. 𝗣𝗿𝗼𝗰𝗲𝗱𝘂𝗿𝗮𝗹 𝗠𝗶𝘀𝗰𝗼𝗻𝗰𝗲𝗽𝘁𝗶𝗼𝗻𝘀 Students misapply or incorrectly execute a process. ➡️ Example: Adding denominators when adding fractions. What to do: 🎯Identify the exact step where the error occurs 🗣️Model the correct process with think-alouds 📍Give targeted practice at the point of breakdown (not the whole problem) 𝟯. 𝗟𝗮𝗻𝗴𝘂𝗮𝗴𝗲-𝗕𝗮𝘀𝗲𝗱 𝗠𝗶𝘀𝗰𝗼𝗻𝗰𝗲𝗽𝘁𝗶𝗼𝗻𝘀 Students misunderstand the math because of vocabulary or phrasing. ➡️ Example: Misinterpreting words like “of,” “per,” or “difference.” What to do: 🔃 Pre-teach and revisit key vocabulary in context ✍🏿 Incorporate math writing and discussion routines 💡 Ask students to explain their thinking in their own words Strong instruction doesn’t just fix mistakes. It identifies the type of misconception and responds with precision. Because when we get clearer about the problem our instruction gets sharper. And student learning accelerates. ______ ♻️ Repost if this is a conversation your math team needs to have ➕ Follow for more on math instruction, coaching, and leadership systems 📬 Join my newsletter The 3-1-4 3 insights. 1 strategy. In 4 minutes. For leaders committed to strengthening math instruction and student outcomes. Link in comments ——— Hi, I’m Dwight Williams. I help schools and districts strengthen math instruction through coaching, curriculum support, and data-informed systems that drive student confidence and achievement.

Why do some students “study harder” but remember less? 🤔 As educators, we often focus on what we teach, but neuroscience reminds us that how students learn matters just as much. In mathematics especially, I’ve noticed that students retain concepts more deeply when they: ✅ Retrieve information instead of rereading ✅ Revisit concepts over time ✅ Explain their thinking aloud ✅ Experience productive struggle rather than immediate answers ✅ Learn from mistakes One thing I’ve learned through my journey as a Mathematics Coordinator is that strong learning does not happen through memorization alone—it happens when students are given opportunities to think, question, connect, and reflect. The goal is not simply to help students get the right answer today, but to help them still remember and apply the learning weeks, months, and years later. Which strategy has made the biggest impact in your classroom? 👇 #Education #Mathematics #Teaching #Learning #Neuroscience #EdLeadership #MathEducation #StudentLearning #Teachers #EducationLeadership

𝗠𝗮𝗻𝘆 𝘀𝘁𝘂𝗱𝗲𝗻𝘁𝘀 𝗰𝗮𝗻 𝗱𝗼 𝘁𝗵𝗲 𝗺𝗮𝘁𝗵 𝗼𝗻 𝗙𝗿𝗶𝗱𝗮𝘆… 𝗮𝗻𝗱 𝗳𝗼𝗿𝗴𝗲𝘁 𝗶𝘁 𝗯𝘆 𝗠𝗼𝗻𝗱𝗮𝘆. Not because they are “bad at math.” But because doing math once is not the same as truly learning it. Neuroscience tells us the brain remembers things better when students: 🗣️ talk about ideas 💡 explain their thinking ⏳ practice over time 🔗 connect learning to what they already know 🧩 struggle through problems before getting help But too many math classrooms still focus on: ❌ Memorizing steps ❌ Copying notes ❌ Fast answers ❌ “Watch me do it” teaching ❌ One-and-done lessons That may help students pass a test… but it often does not help them remember the math later. The brain builds stronger connections when students actively think about the learning. That’s why students remember math more when they: ✅ explain their reasoning ✅ compare strategies ✅ discuss mistakes ✅ revisit concepts often ✅ solve challenging problems ✅ make sense of the math instead of just copying steps This is why strong Tier 1 instruction matters so much. If students only learn math as: “follow these steps and get the answer,” they may finish the assignment… without really understanding the concept. The goal should not only be: “Can students do the problem today?” It should also be: “Will students still understand it next month?” That shift requires classrooms that value: 𝗖𝗼𝗴𝗻𝗶𝘁𝗶𝗼𝗻 > 𝗖𝗼𝗺𝗽𝗹𝗶𝗮𝗻𝗰𝗲 Because students are more likely to remember math they deeply think about. _____  📫 Join my bi-weekly newsletter, The 3-1-4. https://lnkd.in/eksSbCJs 3 insights, 1 strategy, in 4 minutes focused on math leadership, instructional coaching, and building cognitive-driven math classrooms. 👥 Follow me, Dwight S. Williams, for insights on math leadership, coaching, and instructional systems. ♻️ Repost if this changed how you think about learning math. _____ Hi, I’m Dwight Williams. I help school and district leaders move math instruction from compliance to cognition through coaching, systems, and instructional leadership — so classrooms drive stronger student thinking, confidence, and achievement. 👍🏿 Like | 🔔 Follow | 💬 Comment | ♻️ Repost

To ensure students experience deep thinking, clear reasoning, and sense-making in math across all classrooms, I would consider this process: 1. Shared Vision and Goals: * Establish a school-wide or district-wide vision for math instruction. This should emphasize problem-solving, critical thinking, and understanding mathematical concepts rather than just memorization. * Define clear, measurable goals for student learning that align with this vision. 2. Collaborative Planning and Curriculum Development: * Provide opportunities for teachers to collaborate on lesson planning and curriculum development. * Develop common units of study that focus on key mathematical concepts and skills. 3. Professional Development: * Offer ongoing professional development that focuses on effective teaching strategies. * Provide training on how to facilitate rich mathematical discussions and problem-solving activities. 4. Common Assessments and Data Analysis: * Implement common assessments that measure students' understanding of key concepts and skills. * Analyze assessment data to identify areas where students are struggling and adjust instruction accordingly. 5. Classroom Observations and Feedback: * Conduct regular classroom observations to assess the quality of instruction. * Provide teachers with constructive feedback and support to help them improve their practice. 6. Student Voice and Feedback: * Collect feedback from students about their experiences in math class. * Use student feedback to inform instructional decisions and improve the learning environment. By implementing these steps, schools can create a more consistent and effective math learning experience for all students.

𝗦𝗰𝗵𝗼𝗼𝗹𝘀 𝘀𝗮𝘆 𝘁𝗵𝗲𝘆 𝘄𝗮𝗻𝘁 𝗰𝗼𝗻𝘀𝗶𝘀𝘁𝗲𝗻𝗰𝘆 𝗶𝗻 𝗺𝗮𝘁𝗵. 𝗙𝗲𝘄 𝗸𝗻𝗼𝘄 𝘄𝗵𝗮𝘁 𝗶𝘁 𝗹𝗼𝗼𝗸𝘀 𝗹𝗶𝗸𝗲. Consistency is not: ❌ Every classroom doing the exact same thing at the exact same time ❌ Every teacher using the same strategy the same way ❌ No variation in instruction, regardless of student needs That’s not consistency. That’s compliance. Real consistency looks like this: ✅ A shared vision of strong math instruction ✅ The same instructional priorities showing up across classrooms ✅ Coaching that builds over time, not restarting every week ✅ Systems that turn student thinking into next-day instructional moves Some lessons will land. Some won’t. That’s normal. Consistency is what happens next. It’s: ⚙️ Adjusting based on what students actually did and said 💡 Learning from misconceptions, not ignoring them 🔂 Coming back the next day with a clearer plan Over and over. Because strong math systems aren’t built on perfect teaching. They’re built on: 𝗖𝗹𝗮𝗿𝗶𝘁𝘆. 𝗖𝗼𝗵𝗲𝗿𝗲𝗻𝗰𝗲. 𝗖𝗼𝗻𝘀𝗶𝘀𝘁𝗲𝗻𝗰𝘆. If your school can stay committed through imperfect lessons… That’s where real student learning accelerates. ⸻ ♻️ Repost if you believe consistency is about alignment—not sameness. ➕ Follow for more on math instruction, coaching, and leadership systems 📩 Join my newsletter The 3-1-4 for practical strategies on math instruction, coaching, and leadership. Link in the comments. ⸻ Hi, I'm Dwight Williams. A proud first-gen everything, and I help schools and districts strengthen math instruction through coaching, curriculum support, and data-informed systems that drive student confidence and achievement. 👍🏿 Like | 🔔 Follow | 💬 Comment | ♻️ Repost

𝗖𝗼𝗺𝗺𝘂𝗻𝗶𝗰𝗮𝘁𝗶𝗼𝗻 𝗶𝘀 𝗻𝗼𝘁 𝗮 𝗯𝘆𝗽𝗿𝗼𝗱𝘂𝗰𝘁 𝗼𝗳 𝗺𝗮𝘁𝗵 𝗹𝗲𝗮𝗿𝗻𝗶𝗻𝗴. 𝗜𝘁 𝗶𝘀 𝗽𝗮𝗿𝘁 𝗼𝗳 𝗺𝗮𝘁𝗵 𝗹𝗲𝗮𝗿𝗻𝗶𝗻𝗴. Students can’t explain their thinking if math classrooms never require them to. Too often, students are asked to: ▶️Get the answer ▶️Show the steps ▶️Finish the assignment But not necessarily: 💭 Explain their reasoning 🗣 Defend their thinking ❓ Ask questions 🔄 Build on another student’s idea ✍️ Communicate mathematical understanding And then we wonder why students struggle to talk about math. 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗮𝗹 𝗰𝗼𝗺𝗺𝘂𝗻𝗶𝗰𝗮𝘁𝗶𝗼𝗻 𝗶𝘀 𝗮 𝘀𝗸𝗶𝗹𝗹. Like any skill, it has to be intentionally developed through consistent opportunities to think, speak, write, and reason. That means classrooms should regularly include: ✅Turn-and-talks ✅Sentence stems ✅Writing in math ✅Student discourse routines ✅Opportunities to justify reasoning ✅Multiple strategies and representations ✅Questions that go beyond “What answer did you get?” Strong math classrooms are not just places where students solve problems. They are places where students make sense of mathematics out loud. That shift matters because students often deepen their understanding when they are required to communicate and defend their thinking. School leaders and math coaches should look for evidence of student reasoning and discourse during walkthroughs, not just task completion and teacher explanations. A classroom full of completed work does not always mean students are thinking deeply about mathematics. _______  ♻️ Repost if you believe math classrooms should prioritize reasoning, discourse, and student thinking. 👥 Follow me, Dwight S. Williams, for insights on math leadership, coaching, and instructional systems. 📫 Join the 3-1-4, my bi-weekly newsletter.  3 insights, 1 strategy, in 4 minutes focused on math leadership, instructional coaching, and strengthening thinking-driven math classrooms. Link in the comments.  _______  Hi, I’m Dwight Williams. I help school and district leaders move math instruction from compliance to cognition through coaching, systems, and instructional leadership — so classrooms drive stronger student thinking, confidence, and achievement. 👍🏿 Like | 🔔 Follow | 💬 Comment | ♻️ Repost

What if student success had less to do with talent and more to do with belief and access? In this conversation, I sit down with James ONeal, Jr., M.Ed.'Neal, founder of Mastery For All, to explore how mindset shapes math instruction and why every student needs opportunities to win. We explore: - How teacher beliefs create (or block) student mastery - Why "notice and wonder" activities build ownership and confidence - The role of joy, belonging, and student voice in engagement - How leaders can support math instruction without being content experts - Practical strategies from his upcoming book, The Engaged Classroom One powerful reminder: When students stop winning, they start believing they can't. Perfect for math teachers, instructional coaches, and school leaders who want to create classrooms where mastery is possible for all. 🎧 Listen now: https://lnkd.in/gappqr9P #AspireToLead #MathInstruction #EducationalEquity #StudentEngagement #MathMastery #SchoolLeadership #InstructionalCoaching #EdLeadership

𝗙𝗮𝗿 𝘁𝗼𝗼 𝗺𝗮𝗻𝘆 𝗰𝗹𝗮𝘀𝘀𝗿𝗼𝗼𝗺 𝘄𝗮𝗹𝗸𝘁𝗵𝗿𝗼𝘂𝗴𝘀 𝗳𝗼𝗰𝘂𝘀 𝗼𝗻 𝘁𝗵𝗲 𝘄𝗿𝗼𝗻𝗴 𝘁𝗵𝗶𝗻𝗴. 𝗖𝗼𝗺𝗽𝗹𝗶𝗮𝗻𝗰𝗲. Leaders ask: ❓ Are students on task? ❓ Is the room quiet? ❓ Is the teacher following the plan? But none of that guarantees students are actually thinking. If you’re a school leader, here’s a set of look-fors you can use immediately: 𝗠𝗮𝘁𝗵 𝗖𝗹𝗮𝘀𝘀𝗿𝗼𝗼𝗺 𝗟𝗼𝗼𝗸-𝗙𝗼𝗿𝘀: 𝗖𝗼𝗺𝗽𝗹𝗶𝗮𝗻𝗰𝗲 𝘃𝘀. 𝗧𝗵𝗶𝗻𝗸𝗶𝗻𝗴 What School Leaders Should Look For to Identify the Difference 𝗦𝘁𝘂𝗱𝗲𝗻𝘁 𝗥𝗼𝗹𝗲 🔴 Compliance: Follow steps 🟢 Thinking: Make sense of the math 𝗧𝗲𝗮𝗰𝗵𝗲𝗿 𝗥𝗼𝗹𝗲 🔴 Compliance: Demonstrates and directs 🟢 Thinking: Facilitates and probes 𝗦𝘁𝘂𝗱𝗲𝗻𝘁 𝗧𝗮𝗹𝗸 🔴 Compliance: Minimal or scripted 🟢 Thinking: Explaining, debating, justifying 𝗦𝘁𝘂𝗱𝗲𝗻𝘁 𝗪𝗼𝗿𝗸 🔴 Compliance: Answers only 🟢 Thinking: Reasoning, models, multiple representations 𝗦𝘁𝗿𝗮𝘁𝗲𝗴𝗶𝗲𝘀 🔴 Compliance: One “right way” 🟢 Thinking: Multiple pathways explored and compared 𝗣𝗮𝗰𝗶𝗻𝗴 🔴 Compliance: Fast to “cover” content 🟢 Thinking: Slower to ensure understanding 𝗣𝗿𝗼𝗱𝘂𝗰𝘁𝗶𝘃𝗲 𝗦𝘁𝗿𝘂𝗴𝗴𝗹𝗲 🔴 Compliance: Avoided or rescued quickly 🟢 Thinking: Expected and supported 𝗤𝘂𝗲𝘀𝘁𝗶𝗼𝗻𝘀 𝗔𝘀𝗸𝗲𝗱 🔴 Compliance: “What’s the answer?” 🟢 Thinking: “Why does that make sense?” 𝗦𝘂𝗰𝗰𝗲𝘀𝘀 𝗖𝗿𝗶𝘁𝗲𝗿𝗶𝗮 🔴 Compliance: Getting it right 🟢 Thinking: Explaining and justifying 𝗖𝗹𝗮𝘀𝘀𝗿𝗼𝗼𝗺 𝗙𝗲𝗲𝗹 🔴 Compliance: Quiet, controlled 🟢 Thinking: Engaged, productive, sometimes messy You can walk into a quiet classroom, see students completing work.. and still observe very little learning. 𝗧𝗵𝗶𝗻𝗸𝗶𝗻𝗴 𝗶𝘀 𝗱𝗶𝗳𝗳𝗲𝗿𝗲𝗻𝘁. It’s visible. It’s audible. And once you know what to look for you can’t unsee it. And more importantly 𝘆𝗼𝘂 𝗰𝗮𝗻 𝗰𝗼𝗮𝗰𝗵 𝘁𝗼 𝗶𝘁. 𝗧𝗵𝗮𝘁’𝘀 𝗵𝗼𝘄 𝘄𝗲 𝗮𝗰𝗰𝗲𝗹𝗲𝗿𝗮𝘁𝗲 𝘀𝘁𝘂𝗱𝗲𝗻𝘁 𝗹𝗲𝗮𝗿𝗻𝗶𝗻𝗴 𝗶𝗻 𝗺𝗮𝘁𝗵. __________ ♻️ Repost if you’re committed to moving math instruction from compliance to thinking ➕ Follow for more on math instruction, coaching, and leadership systems 📬 Join my newsletter The 3-1-4 3 insights. 1 strategy. In 4 minutes. For leaders committed to strengthening math instruction and student outcomes. Link in comments __________ Hi, I’m Dwight Williams. I help schools and districts strengthen math instruction through coaching, curriculum support, and data-informed systems that drive student confidence and achievement.

Especially in the Age of AI when the computer can do so much of it for the student, the thinking side is critical to education.