The ultimate goals of mathematics teachers are students understanding the material presented, applying the maths skills, and recalling the concepts in the future. There’s little benefit in students recalling a formula or procedure to prepare for an assessment tomorrow only to forget the core concept by next week. It’s imperative for teachers as well as maths tutors and tuitions centers alike to focus on making sure that the students understand the material and not just memorize the procedures.
Here are six ways to teach maths for understanding in the mathematics classroom:
The first five minutes of the class period set the tone for the entire lesson. Ideally, teachers would start by sharing the agenda for the class period so that students will know the expectations for what will be occurring. Next, teachers could post and articulate the learning objective or essential question to the class so that students know the purpose and, at the end of the lesson, can self-assess whether the objective has been met for them. Finally, the opener might include one or more warm-up problems as a way to review and assess students’ prior knowledge in preparation for exposure to the new material.
The more types of representations that you can present to students addressing their different learning styles, the more likely they will truly understand the new maths concept being presented. Different representations could include using manipulatives, showing a picture, drawing out the problem, and offering a symbolic representation. For example, when presenting linear relationships with one unknown, illustrate to students the same problem as an equation, on a number line, in words, and with pictures. Students who are exposed to and can recognize the same relationship posed in the different representational modes are more likely to have conceptual understanding of the relationship and perform better on assessments (PDF).
In the best classroom environment, the teacher is able to show different ways to solve the same problem and encourage the students to come up with their own creative ways to solve them. The more strategies and approaches that students are exposed to, the deeper their conceptual understanding of the topic becomes. Empowering students to create their own problem-solving methods can make the teacher nervous. What if we don’t follow their logic? What if they’re incorrect? However, it’s worth the risk to have them explore. After an individual, pair, or small group of students finish solving the class problem using a single method, encourage them to look for alternate ways to come up with the same correct solution. Having students develop their own methods and then share the correct steps with the class is a very powerful learning experience. The video below shows how a teacher encourages students more than one way to solve the same problem on rectangular prisms.
In a perfect world, we would always be able to demonstrate how every concept can be applied to the real world — and when that’s possible, it helps improve the students’ understanding. When a concept cannot be applied in that manner, we can still share how it might be applied within mathematics or another subject area. Another option is showing how the concept was developed through the history of math. Consider taking a minute out of each lesson to show your students where or how the math can be seen or used in life outside of the classroom.
Students need to explain their reasoning when solving maths problems. In order for a teacher to determine if every student truly understands the objective for the class period, it’s necessary for each student to communicate both orally and in writing. By giving the class ten minutes to discuss their reasoning with each other while exploring multiple ways of solving the problems, you’ll promote excellent engagement and learning. It’s not always easy to get students talking in class, but there are ways to encourage them (PDF).
Everyone can get lost in the class period, and it’s easy to lose track of time until the bell rings and class is over. The final seven minutes might be the most critical in making sure that students have understood the day’s learning objective. You can use this time to accomplish three very important things:
These are just some of the activities for the close of a lesson. At tutoring club, our math tutors work with students to ensure higher scores on math tests whether it is gcse maths, IB maths or k12 maths, tutoring club in dubai can help.