For nine years, I taught mathematics to an array of students from various ages, backgrounds, and abilities. My teaching experience ranged from middle school mathematics, remedial algebra, to AP Calculus. I taught in suburban Texas, the New York City public school system, and a private international school in South America, all with students of varying socioeconomic backgrounds.
Despite the incredibly diverse students I’ve worked with across my teaching career, I’ve found several similarities and strategies that have been remarkably effective at not only helping students better understand math, but to truly engage and connect with the material in a way that is relevant and relatable. In general, I found the best practices in mathematics education include:
- Incorporating different representations of mathematics (e.g. verbal, pictorial, symbolic)
- Providing a variety of opportunities for students to engage with mathematical concepts and ideas
- Encouraging students to explain their thinking and reasoning
- Promoting collaboration and communication among students
- Encouraging students to persevere when faced with challenging tasks
- Helping students to develop a positive attitude towards mathematics
In this article, I’ll share some more details on each of these practices and how they might look in classrooms.
What is Meant by Verbal, Pictorial, Symbolic in Mathematics Education?
Verbal, pictorial, and symbolic are all ways of representing mathematical ideas. Verbal representations use words to describe mathematical concepts, pictorial representations use pictures and diagrams to illustrate mathematical ideas, and symbolic representations use mathematical symbols to represent mathematical concepts. Each type of representation has its own strengths and weaknesses. Using multiple representations can help students see mathematical concepts in different ways and deepen their understanding.
Singapore Math is a curriculum that is used in Singapore and other countries. It is based on the philosophy that less is more, and that students should be able to understand concepts rather than just memorize facts. Singapore Math emphasizes pictorial and symbolic representations. One way Singapore Math uses pictorial representations is through the use of bar models. Bar models are a way of representing information pictorially, using bars and blocks. This can be helpful in solving word problems, as it provides a visual way to see the relationships between different quantities. Another way Singapore Math uses symbolic representations is through the use of algebra. Algebra is a branch of mathematics that uses symbols to represent quantities and relationships. This can be helpful in solving problems that require the use of variables, as it allows for a more abstract way of thinking about the problem.
How can we Provide a Variety of Opportunities to Engage with Mathematical Concepts and Ideas?
Mathematics is often viewed as a complicated and intimidating subject. For many students, it can be hard to make the connection between mathematics and the real world, leaving them feeling unmotivated or discouraged. That’s why it’s important to make mathematics more relatable for students. Here are several ways to make mathematics more relatable for students:
- Connect mathematics to real-world experiences. One of the easiest ways to make math more relatable is to connect it to real-world experiences. For example, you could use the example of budgeting to explain the concept of percentages or the example of a home renovation project to explain the concept of measurement and angles.
- Use visuals to show how mathematics is used. Many of our students are visual learners, and visuals can be a great way to show students how mathematics is used in everyday life. For example, you could show a visual of how a formula is used to calculate the area of a room or how a graph is used to track data.
- Incorporate technology into the classroom. Incorporating technology into the classroom can make mathematics more engaging for students. For example, you could assign students to create a presentation using a program or use interactive apps to help reinforce or connect theoretical concepts to real-life situations.
Encouraging students to explain their thinking and reasoning
As educators, it is of the utmost importance that we foster an environment of learning in the classroom. One of the best ways to do this is to encourage students to explain their thinking and reasoning. By having students explain their thought process, we can assess their level of understanding and provide guidance for further learning. Explaining one’s reasoning and thinking is beneficial for both the student and the teacher. It allows the student to articulate what they have learned and how they arrived at their conclusion. It also allows the teacher to better understand the student’s thought process and provide further instruction or guidance. So how can teachers encourage students to explain their thinking and reasoning? Here are a few ways:
- Ask open-ended questions. Instead of asking “What is the answer?”, ask “How did you come to this conclusion?” or “Walk me through your thought process.”
- Provide positive reinforcement. Praise and reward students when they explain their thought process.
- Model the behavior. Show students how to explain their thinking and reasoning by doing it yourself.
- Make it a habit. Incorporate activities and discussions into your lessons that require students to explain their thinking.
Explaining one’s thinking and reasoning is an important skill that students need to learn. It not only helps them better understand the material, but it also helps them become better communicators and problem solvers. By providing students with the tools and encouragement to explain their thinking, we can help them develop these skills and reach their full potential.
How can we promote more collaboration and communication among students?
As students, we know how important it is to work together and communicate in order to achieve our academic goals. But in today’s competitive world, it can be difficult to find the time and energy to foster collaboration and communication among students. Fortunately, there are several ways to promote more collaboration and communication among students. Here are a few tips for getting started:
- Encourage open discussion. Encourage students to have open conversations about their classes and studies. This can include talking about their struggles, successes, and any study tips they have learned.
- Create study groups. Studying with other students can help you stay focused and motivated. Plus, it gives you an opportunity to collaborate and discuss ideas with peers.
- Utilize technology. Technology can be a great way to promote collaboration and communication among students. Utilizing online tools like video conferencing, group chats, and message boards can make it easier for students to connect with each other.
- Participate in activities together. Participating in activities together can be a great way to promote collaboration and communication among students. This could include anything from attending lectures and studying together to taking part in club activities or sports.
By following these tips, you can help to promote more collaboration and communication among students. This will not only help to foster a more positive learning environment, but it can also help students to stay motivated and engaged in their studies.
How can we help students develop a positive attitude towards mathematics?
One way to help students develop a positive attitude towards mathematics is to focus on the enjoyment and beauty of mathematics. This can be done by incorporating puzzles and games into the classroom, showing students how mathematics is used in the real world, and highlighting the aesthetic aspects of mathematics. It is also important to create a positive classroom environment where students feel safe to make mistakes and are encouraged to ask questions. A mathematics lesson that incorporates real life examples might discuss how to figure out a tip at a restaurant, or how to calculate the cost of a trip based on the cost of gas.
It is also important to give students frequent feedback and recognition. This will help them to understand what they are doing right and what they can improve upon. Additionally, by recognizing their efforts and accomplishments, it will help to build their confidence in mathematics.
Finally, work on building resilience with your students. Continued resilience will result in a positive attitude and success towards mathematics. Specific ways you can build resilience include focusing on the process rather than the outcome – when students focus on the process rather than the outcome, they can learn to appreciate the journey rather than the destination. This can help them to stay motivated and to continue to work hard even when they make mistakes. As their teacher, you can also help students to set realistic goals, which can help them stay challenged yet feel success and a sense of accomplishment as they make progress.
Go Forward and Teach!
This article discusses best practices in mathematics education, focusing on the use of different representations of mathematics, providing students with opportunities to engage with mathematical concepts, encouraging students to explain their thinking and reasoning, promoting collaboration and communication among students, and helping students to develop a positive attitude towards mathematics. Through the use of real-world examples, visuals, technology, and activities, educators can provide relatable, engaging, and effective mathematics instruction that can help students understand and connect with the material. By encouraging students to explain their thinking and reasoning, promoting collaboration and communication among students, and helping students to develop a positive attitude towards mathematics, teachers can help foster an environment of learning and help students reach their full potential.