Mathematics, often seen as a challenging or abstract subject, is an essential part of education. It builds critical thinking skills, enhances problem-solving abilities, and is fundamental to many fields, including science, engineering, technology, and even art. However, despite its importance, maths and Mathematical Thinking can sometimes feel quite separate from students’ daily lives, especially in an online learning environment.
For those of us that work in online education like Sophia High School does, one of the biggest challenges educators face is how to make abstract mathematical concepts engaging and accessible. With the rise of digital learning platforms, educators have an opportunity to integrate interactive, fun, and creative ways to help students develop a love for math. We need effective strategies to engage online school learners in mathematical thinking and provide a selection of websites and tools that can make learning math more exciting.
Specialist IGCSE Maths Teacher at Sophia High School
The Power of Mathematical Thinking
Mathematical thinking involves much more than simply memorizing formulas or solving equations. It is about developing a mindset that emphasizes logic, reasoning, and problem-solving. Mathematical thinking includes:
- Pattern recognition: Identifying patterns in numbers, shapes, and data.
- Logical reasoning: Using deductive reasoning to draw conclusions from assumptions or given information.
- Problem-solving: Using creative strategies and critical thinking to solve complex problems.
- Abstract thinking: Understanding and manipulating symbols and numbers to represent real-world situations.
In an online classroom, the challenge is to create a virtual environment where students can practice these skills, apply them in various contexts, and see the value of math in the world around them.
Strategies for Engaging Students in Online Mathematical Thinking
1. Interactive Learning Platforms and Gamification
One of the most effective ways to engage students in mathematical thinking is through the use of interactive tools and games. Gamification in online education is a powerful approach that can turn learning into an enjoyable, competition-based activity. Platforms that offer interactive problems, levels to conquer, and rewards for success can be highly motivating for students.
Some Examples of Interactive Mathematical Thinking Websites (great for use over the holidays!):
This is one of the most popular educational platforms, providing free online courses on various math topics. It offers personalized learning dashboards and practice exercises that help students master mathematical concepts at their own pace. The platform also uses rewards and badges to motivate learners, turning math practice into an interactive game.
A math-focused game where students embark on a fantasy adventure, solving math problems to unlock new features. Prodigy adapts to each student’s skill level, ensuring that the challenges are always appropriate to their learning pace. With its fun, engaging format, Prodigy has made learning math exciting for younger audiences.
Sumdog:
Sumdog combines math practice with games to make learning enjoyable. Students can compete against others in online math challenges or practice at their own pace. The platform provides personalized learning, which can help students master essential skills, from basic arithmetic to advanced concepts like algebra and geometry.
2. Real-World Connections
Mathematics is everywhere, as the wonderful mathematician Eddie Woo suggests. It is embedded in architecture, engineering, economics and art. By demonstrating the real-world relevance of mathematical concepts, educators can help students understand that math is not just a set of abstract rules but a powerful tool for understanding and solving real-life problems.
Strategies:
Project-based learning:
This is a strong area of focus at our school: it involves projects in which students must use math to solve real-world problems. For example, they could design a small building using geometric principles or analyze the best value for products using ratios and percentages. This type of learning helps students connect mathematical theories to practical applications.
Math in the real world:
Show how professionals like engineers, data scientists, and architects use mathematics in their daily work. You can create virtual guest sessions or interviews with professionals who use math, demonstrating its application in fields like space exploration, technology development, or environmental sustainability.
3. Incorporating Visual Tools for Mathematical Thinking
Mathematics often involves abstract thinking, which can be hard for students to grasp. Visual tools can help students make sense of complex problems by turning them into images or graphs. These tools not only help to simplify math concepts but also appeal to students who are visual learners.
Websites for Visualizing Math:
A dynamic mathematics software tool that allows students to explore geometry, algebra, calculus, and statistics interactively. GeoGebra provides both visualizations and simulations to help students see mathematical concepts come to life, making abstract concepts more accessible and intuitive.
Desmos offers a free graphing calculator and a variety of interactive tools for exploring functions, graphs, and other mathematical concepts. It allows students to visually manipulate graphs and explore mathematical relationships in real-time. We often use this in IGCSE lessons.
Created by the University of Colorado Boulder, PhET provides free, interactive math and science simulations. These tools help students explore math concepts such as probability, geometry, and algebra through interactive models and real-world scenarios. This has been great for helping students build their own interactive electrical circuits, for example.
4. Collaborative Learning and Peer Engagement
Mathematics often feels like a solitary endeavor, but collaboration and peer interaction can play an essential role in boosting engagement and understanding. Creating opportunities for students to work together, even in an online environment, can help foster a sense of community and enable peer-to-peer learning.
Strategies for Collaboration:
Group problem-solving activities:
Organize virtual group activities where students work together to solve math challenges, using breakout rooms in Google Classroom, for example.
Peer tutoring:
Encourage stronger students to assist their peers. Peer tutoring can be a powerful tool for reinforcing the tutor’s own learning while helping others. Platforms like Socratic (available as an app) can allow students to discuss math problems and get feedback from others in the class.
Math forums and communities:
Online math communities or discussion forums (such as those found on Reddit’s r/learnmath) can provide students with a platform to ask questions, share solutions, and engage with fellow learners outside of class time.
5. Incorporating Mathematical Thinking into Popular Culture
Engage students by showing how mathematics intersects with the world of popular culture, including sports, music, art, and even social media. Relating math to their interests can spark enthusiasm and demonstrate that math is more than just a subject in school—it’s a tool for making sense of the world around them.
Ideas for Making Mathematical Thinking More Relatable:
Math in Music:
Show how math is used in music, such as patterns in rhythms, scales, and harmonies. Use musical examples that illustrate fractions, ratios, and symmetry.
Math and Sports:
Bring in the use of statistics in sports, such as calculating batting averages in baseball or player efficiency ratings in basketball. Websites like Sports Reference can be used to analyze player statistics and demonstrate how math plays a key role in sports analysis.
6. Flipped Classroom Model
The flipped classroom model turns the traditional approach to teaching on its head. Instead of students passively listening to lectures, they engage with instructional materials (like video lessons or interactive tasks) before class and use class time for active mathematical thinking learning through discussion, problem-solving, and application of concepts.
How to Use the Flipped Classroom for Math:
Pre-recorded video lessons:
Provide students with access to video lessons that introduce new concepts. Encourage them to review these videos at home before engaging in class activities.
Interactive home learning:
Use tools like Edpuzzle to assign interactive video lessons where students can answer questions during the video to ensure they understand the material.
Problem-solving sessions:
Use class time for collaborative problem-solving, discussions, and the application of newly learned concepts. Tools like Padlet can facilitate real-time problem-solving and discussions among students.
Websites and Apps to Boost Engagement in Math
Here are a few more specific resources that can aid in making math more exciting and interactive:
Brilliant is an interactive learning platform that covers math, science, and computer science. It offers engaging problem-solving challenges and courses designed to help students develop deep mathematical thinking and problem-solving skills. Brilliant is ideal for older students or advanced learners.
This app allows students to solve math problems and understand step-by-step solutions. While it should be used carefully to avoid over-reliance, it’s a great tool for helping students understand complex problems and build confidence.
A powerful computational engine, WolframAlpha allows students to enter math problems and get instant solutions. It can help students visualize solutions, explore different approaches, and better understand mathematical concepts.
Conclusion: Inspiring a Love for Math in an Online School
Engaging students in mathematical thinking, particularly in an online learning environment as Sophia High School, requires creativity, effort, and the right tools. By using interactive platforms, connecting math to real-world applications, incorporating visual aids, and fostering collaboration, educators can transform the way students experience math. These strategies not only make math more exciting but also help students develop the critical thinking skills that are essential for success in both academic and real-life scenarios.
With a wide variety of tools and websites available, the opportunities to make mathematics more engaging and accessible have never been greater. By leveraging the power of technology, educators can inspire students to develop a lasting love for math and become confident, independent learners.
