With the implementation of the new primary Mathematics syllabus this year, much emphasis is placed on developing problem-solving skills. Although there is a myriad of procedures and processes in the whole field of Mathematics, there must still be a focus on conceptual understanding and problem-solving in which strategic thinking and coherent reasoning are vital. This simply means that students have to know the ‘why’, on top of the ‘what’ and ‘how’. An appreciation of this relational understanding is highly beneficial to all students as it helps them to apply strategies in a more effective way.
The new syllabus focuses on ‘big ideas’ – a concept that seeks to bring connection and coherence between various topics. In fact, it is common to find questions in Mathematics free test papers that test across a few chapters. Teachers are tasked with helping students view and establish connections among mathematical ideas within a topic, or between topics across levels. Concepts from different topics which can exemplify the big idea can be identified and developed by teachers. By explaining the connections between the topics or by directing students to uncover these connections for themselves, a deeper and more meaningful understanding of Mathematics will develop. Students will learn to regard these big ideas in a manner that will facilitate the mastering of advanced topics in future.
In the area of problem-solving, students have to accept the fact that not all mathematical problems in life will be familiar and routine. Therefore, there must be opportunities for them to learn to solve new and non-routine problems. In fact, some Primary 6 Maths questions in exams are so novel – hence challenging – that they garner the attention of the media. Students must also learn to approach such problems in a systematic manner using specific strategies. In top school papers, we often come across particular types of problems that require specific heuristics such as listing, working backwards, guess and check etc. to solve them. Students should be familiar with each of these techniques as they progress through the levels.
Mathematical concepts are, at times, abstract and hard to grasp for younger children. Thus, it is important to begin from concrete examples, objects and experiences that they can relate to. This applies to the subject of Science as well. By careful observation of the world around them, students can better relate the concepts in textbooks to their real-life experiences. There are many Singapore PSLE Science questions that assess a student’s ability to explain observations using scientific theories. It is hence important for educators to use relevant examples to reinforce concepts.
Finally, it is crucial to instill the right attitude in learning Mathematics. Students will be confident and motivated to learn if they experience success and feel capable of learning. There must be opportunities for students to reflect on their learning and then explain the process to one another. Teachers can post non-routine problems which are within the ability of the students to encourage them to think. This can allow students to develop metacognition. In addition, they will also value Mathematics as a life-long essential skill if they can see its relevance to the real world and in their everyday life.