There are many ways in which you can help students understand math. For instance, by presenting several examples, encouraging alternative solutions, and framing the teaching methodology with a clear agenda and efficient summary.

The ultimate objectives of mathematics instruction are students applying the skills, understanding the material presented and recalling the concepts in the future. There is very little benefit in students remembering a procedure or formula to prepare for an assessment for the next day only to forget the main concept by next week. It is imperative for teachers and trainers to focus on ensuring that the students understand the concepts and not just memorise the procedures.

Here are six methods for teachers to teach for understanding in the mathematics subject:

1. Create a class opener

The first ten minutes of the class period set the vibes and tone for the entire lesson. Teachers would ideally start by sharing the planning for the class period so that everyone knows the expectations for what will be happening. Next, teachers should post and elaborate on the learning goal to the class so that everyone knows the purpose. At the end of the lesson, everyone should be able to self-assess whether the goal has been met for them. Eventually, the opener may include one or two warm-up math problems as a way to review and assess each person's prior knowledge in preparation for exposure to the new material.

2. Display the topics using multiple representations

The more kinds of representations you can present to students addressing their learning styles, the more likely they will properly understand the concept being presented. Multiple representations may include using manipulatives, drawing out the problem, showing a picture and offering a symbolic representation. For instance, when displaying linear relationships with one unknown, present to students the same problem as an equation, in words, on a number line, and with images. Students who are exposed and can recognize the same connection posed in the different representational modes are much more likely to have a deep understanding of the relationship and perform better on exams.

3. Multiple ways to solve a problem

In an ideal classroom environment, the teacher is able to teach several ways to solve the same problem and should encourage his/her students to come up with their own ways to solve them. The more approaches that students are exposed to, the deeper their understanding of the topic will become. Empowering them to develop their own problem-solving methods could also make the teacher nervous: What if I can’t follow their logic? What if they are incorrect? But it is absolutely worth the risk to have them explore. When an individual, pair, or small group of students have finished solving the class problem using one method, encourage them to find alternate ways to come up with the same correct solution. Let them use a regular casio calculator as it will make them feel more comfortable while solving the problem and it will also speed up the process. Having students create their own methods and then explaining the correct steps to the class is a powerful learning experience.

4. Explain the application

In an ideal world, we will always be able to demonstrate how every single concept can be applied in the real world. This is because when this is actually possible, it helps enhance the students' understanding. When a concept can’t be applied in this way, we can still see how it may be applied within maths or another subject. Another alternative is showing how the concept was created through the history of math. Consider taking one minute out of each lesson to explain to your students how or where the math can be used or seen in life outside of the classroom.

5. Students should explain their reasoning

Students need to communicate their reasoning when solving a problem. In order for a math teacher to determine if every student really understands the goal for the class period, each student must communicate it both orally and in writing. By giving the class five minutes to discuss their reasoning with each other while looking for multiple ways of solving the problems, you will be promoting excellent engagement and real learning. It is not always very easy to get students talking in class, however there are ways to encourage them.

6. End the class with a summary

Everyone can (and will) get lost in the class period, and it is relatively easy to lose track of time until the bell rings and the class is over. The final ten minutes may be the most important in ensuring that students have comprehended the day's learning goal. You can use this time to achieve 3 very important things:

• A swift formative assessment to establish how much was learned, such as students self-rating their comfort with the concepts on a scale 1 to 10.
• Reviewing the goal for the class period and a short discussion as to where the lesson will go next class .
• Previewing the homework all together to avoid confusions .