How to excel in Mathematics?

Mathematics is considered to be a rather challenging subject to many students. For the majority in this group,studying mathematics is time consuming and frustrating.


However, there are those who love mathematics, they know that once you are familiar with the patterns in the questioning techniques, solving mathematics problems gives them a sense of satisfaction. Some said that you are either born to do mathematics, or not. I tend to disagree.


To be good in mathematics, you need to have the conceptual understanding, the strategy and the discipline to practice. Think of mathematics to be like a competitive sports like football. Firstly, you need to understand the rules of game. Then you need to have a strategy on how to win in this game. Lastly, you need to practice regularly in order to execute your strategy with precision.


Mathematics is not a passive subject. You can’t just read about it. You need to tackle and solve those problem sums regularly, in order to get real expertise and excel in this subject. Once you understand these principles, you will begin to see the beauty of this subject. As Bertrand Russell, the great philosopher and mathematician,once said, "Mathematics posses not only truth, but also supreme beauty".


Lastly, if you aspire to be at the top of the game, you need to have that passion for learning and desire to excel. Using football as an analogy again, the top footballers are able to achieve success because they have a passion for the sports. They truly believe that they can make a difference in the game. If you have such passion, you are on your way to success. If you are still struggling, fear not. You can always look for a mentor, someone who is able to guide you in your journey to excellence.

Challenging PSLE Math Question 2/2012

24 more girls than boys signed up for a holiday camp. 
3/4 of the girls and 2/3 of the boys turned up for the camp. 
20 did not turn up. 
How many children signed up for the holiday camp?

Challenging PSLE Math Problem with Video Solution

Challenging Math Problem (PSLE) with solution

•88 children took part in a swimming competition.

•1/3 of the boys and 3/7 of the girls wore swimming goggles.

•Altogether 34 children wore swimming goggles.

•How many girls wore swimming goggles on that day?


Solution below:

Role of the Teacher in Mathematical Discourse

Teachers play an important part in orchestrating mathematical discourse in the classroom. In designing math lessons that promote discourse, the following should be considered:

1.    Problematising the content – By turning content into problems, it creates opportunities for students to discuss and present possible solutions. Instead of offering standard solutions, the teacher can facilitate learning by posing questions to elicit and challenge students’ thinking. Through appropriate questioning technique by the teacher, students would be actively engage in clarifying and justifying their ideas, either orally or in writing.

2.    Scaffolding – To support the students, teachers have to decide when to provide information, when to clarify an issue, when to model, when to lead, and when to let a student struggle with a difficulty. When misconceptions are surfaced during their discussion, teachers should seize the opportunity to turn it into a teachable moment to explain a certain concept with more details.

3.    Feedback – Providing timely feedback to students on their performance will enhance their learning. Teachers could also create opportunities for students to provide constructive feedback to their peers. Giving peer critique involves higher order thinking skills such as analysing and evaluating, which are desirable outcomes of education.

4.    Monitoring- During learning activities in the classroom, teachers should monitor students’ participation and decide when and how to encourage each student to participate. It is also a good practice to reflect after the lesson to identify what students have achieved, where they make errors, when they have misconceptions, when they are not engaged - in this way, teaching and learning can be synchronised and powerful.

With students taking more responsibility of learning, teachers would have to consider adjusting their role in the classroom to complement the change in teaching approach. From delivering instruction in the past, teachers have to assume the position of a facilitator, who will provide appropriate scaffolding and feedback to guide the students in the right direction.

What is Mathematical Discourse?

Mathematical discourse is a teaching approach that engages students in discussion about math in a manner that articulate their understanding of concepts. Through the lesson activities, students also sharpen their skills in mathematical reasoning and debate. This approach to teaching mathematics is a more constructivist and student-centered approach that involves teachers asking probing questions; think “Socratic Questioning”, to make student thinking visible by eliciting from them the steps needed to arrive at the solution and why a certain strategy was used. Through strategically designed learning activities, students are given opportunities to critique their own and others’ idea and uncover efficient solutions to mathematical problems. 

The Theory 
Classroom discourse is based on the theory of constructivism, which states that learning happens when the students interact with the environment. Through these interactions, knowledge is created. This is also aligned with the social-cultural views on learning which advocates that learning is a social process whereby students working collaboratively are able to reach new understanding that otherwise could not be achieved by working alone.

Make Thinking Visible Through Flip Classroom Model

What is the flipped classroom?

An innovative teaching model that delivers instructional content outside class through interactive, teacher-created resoruces (eg. Podcast, online digital videos, power-point presentation, etc) and interaction with the content – skill development, practice and related learning activities – is done in class. Moving lectures outside of the classroom allows teachers to spend more 1:1 time with each student. Students have the opportunity to ask questions and work through problems with the guidance of their teachers and the support of their peers - creating a collaborative learning environment.

In a flipped class, instructional activities like explanation and lecture are done at home, while homework activities like math problem sets or writing practice activities are done in class. Thus homework becomes classwork and vice versa.

What are some benefits of this method?

·   Allow teachers to spend more time to faciliate students’ learning

·   Foster stronger student/teacher relationships

·   Offers a way for teachers to share teaching resources with other teachers, students and parents easily

·   Enable students to “rewind” lessons and master topics at their own pace

·   Creates a conducive environment in the classroom that promotes collaborative learning