When it comes to Mathematics, the most commonly heard piece of advice is perhaps the familiar phrase “Practice Makes Perfect”.
While these are wise words to live by, and is generally true for Mathematics at Primary and Secondary levels, the game changes when students progress to Junior College, where the complexity of the subject increases substantially. Due to the increased difficulty, purely attempting as many practice questions as possible is often not enough to assure students of a good exam grade where higher-level Mathematics is concerned.
Another technique commonly relied upon by students is going through past-year exam papers in an attempt to spot patterns and trends, and revising accordingly. As we know, all predictive techniques come with some measure of risk, and question-spotting, being a gamble by its very nature, will not guarantee students good exam grades.
Contrary to popular belief, the key to scoring consistently high grades in Mathematics at Junior College level is neither lots of practice, nor question-spotting or analyzing how examiners set questions.
The most foolproof method of achieving consistently high marks for tests and exams is for students to develop an in-depth understanding of each topic, as well as the versatility in applying this understanding to solve the different types of questions they may encounter.
The most common problem Junior College students face while attempting to complete their tutorials is that they often get stuck very early on, leaving them frustrated and discouraged. The reason this problem arises is in part due to the heavy assignment workload students are given, as well as their tight academic schedule. Feeling the pressure to complete their assignments on time, students tend to jump straight into doing their tutorial assignments after just a cursory reading of their lecture notes, often having to revisit and consult their notes when they realize that they are out of their depth.
This disorganized and unfocused approach often leads to students developing an incomplete and in come cases, an incorrect understanding of the topic.
As a result, students often find themselves having to relearn key concepts, and this vicious cycle places a further drain on their already limited resources of time and energy.
The solution to this problem is counterintuitive and not always easy – ideally, students should spend as much time as possible to reading and understanding their lecture notes before they sit down to attempt tutorial questions. In other words, there has to be a re-proportioning of the time students allocate to reading lecture notes and to doing questions, with the focus being on gaining a thorough understanding of each topic rather than on merely completing assignments and tutorials.
Consistent and good grades can be accomplished in a three-step process, namely:
1. Concept Understanding
2. Topical Outlining
As we touched on earlier, firstly, students should take their time to reading their notes closely and carefully instead of rushing through them, the optimal proportion of time devoted to theoretical understanding and practice being 50% each. The next step would then be to form a logical framework of the topic, noting and highlighting what the key points are. The goal is to reduce each topic into a condensed outline of key information, such that students can tell at a glance what is important and what is not. Lastly, students should put their understanding to the test by attempting practice questions, refining their logical frameworks along the way.
The above approach will help students to achieve consistent results via a thorough and complete understanding of the concepts, which in turn enables them to answer effectively any kind of question they encounter during their tests and exams.