Mathematics is a subject that many students find challenging and stressful. It requires not only computational skills, but also logical thinking and problem-solving abilities. Many students struggle to do well in mathematics, finish their papers on time, or understand particular questions. They may feel frustrated, confused, or even hopeless.
The root cause of all of these problems is that they lack complete concept clarity. Concept clarity means that you have a deep and thorough understanding of the mathematical concepts, principles, and methods that you are learning. It also means that you can apply them to different situations and contexts, and explain them in your own words.
But why is concept clarity important? When taking your papers, you must be able to answer your questions confidently and quickly. This comes from immediate pattern recognition, which is only possible with complete concept clarity. If you have concept clarity, you can easily identify the type of question, the concept involved, and the best approach to solve it. You can also avoid common mistakes, errors, and misconceptions.
Pre-requisite information
If you really think about it (as discussed here), most math papers in the IB DP have a common breakdown. They consist of three types of questions:
- 50% easy: These are questions that test your basic knowledge and skills. They are usually straightforward and similar to the ones you have practiced before. They require minimal thinking and calculation.
- 25% challenging: These are questions that test your higher-order thinking and reasoning. They are usually more complex and involve multiple steps or concepts. They require more thinking and calculation.
- 25% ambiguous: These are questions that test your creativity and adaptability. They are usually unfamiliar and have more than one possible approach or solution. They require the most thinking and calculation.
Which means that if you really study in a manner that adheres to this breakdown, you can score really well. This article will show you how to use this understanding to change your study plan, and provide tips on how and where you can get the correct resources in order to succeed in this plan.
Change your study routine
The first step to gaining concept clarity in mathematics is to change your study routine and your approach to which you study. Many students make the mistake of studying math in a passive and superficial way. They rely on memorizing formulas, copying solutions, or following procedures without understanding why they work. This may help them pass the easy questions, but it will not help them with the challenging or ambiguous ones.
Instead, you need to study math in an active and deep way. You need to engage with the concepts, explore their connections, and discover their applications. You need to practice solving a variety of challenging problems, explaining your reasoning, and checking your answers. This will help you develop concept clarity, as well as confidence and competence.
You can change your study routine by following the next three steps when learning new techniques or concepts in mathematics, in order.
Start by familiarizing yourself with the concept
The second step to gaining concept clarity in mathematics is to start by familiarizing yourself with the concept. Before you attempt any questions, you need to have a clear idea of what the concept is, what it means, and how it works. You need to learn the definitions, properties, formulas, and examples of the concept.
There are many ways to familiarize yourself with the concept. You can watch videos, have your teachers solve questions for you, read and check out the textbook, or do whatever is most comfortable for you. The key is to use multiple sources and methods, and to pay attention to the details and explanations.
Then, practice with IBDP past paper questions
The third step to gaining concept clarity in mathematics is to practice with IBDP past paper questions. This will help you understand how to answer the 50% of the exam paper that consists of easy questions. These questions are often regurgitated from previous years with small differences in a similar format. They test your basic knowledge and skills, and they are usually straightforward and simple.
For this part, I cannot stress this enough. Approach topics in math not as topics, but rather as a set of types of questions. For each topic, identify the common types of questions that appear in the past papers, and master each and every one of them. For example, when doing the unit on functions, break it down into sketching, inverse, domain and range, etc. And then, break each of those down further into sketching linear graphs, sketching exponential graphs, sketching graphs with oblique asymptotes, etc.
The best way to practice with IBDP past paper questions is to use a timer and simulate the exam conditions. Try to solve the questions without looking at the solutions, and check your answers afterwards. If you make any mistakes, analyze where you went wrong and how you can improve. Repeat this process until you can solve the questions correctly and quickly.
Finally, explore other exam boards and types of questions
The fourth and final step to gaining concept clarity in mathematics is to explore other exam boards and types of questions. This will help you prepare for the 25% of the exam paper that consists of challenging or ambiguous questions. These questions are often unexpected and have more than one possible approach or solution. They test your higher-order thinking and reasoning, and they are usually more complex and difficult.
To explore other exam boards and types of questions, you need to look beyond the IB DP curriculum and syllabus. You need to expose yourself to a wide new range of questions that may have different formats, styles, or levels of difficulty. You need to challenge yourself to solve problems that you have never seen before, and to find creative and efficient ways to do so.
One of the best resources to get these kinds of questions is exammate. Exammate is a website that breaks down questions topic-wise and has questions from a wide range of curriculums, from A levels, IB DP, etc. This is your one-stop resource for math, and being able to study in this method. You can use exammate to find questions that match your topic and level, and to practice solving them with feedback and solutions.
Conclusion
Mathematics is a subject that can be mastered by anyone, as long as they have concept clarity. Concept clarity means that you have a deep and thorough understanding of the mathematical concepts, principles, and methods that you are learning. It also means that you can apply them to different situations and contexts, and explain them in your own words.
To gain concept clarity in mathematics, you need to change your study routine, familiarize yourself with the concept, practice with IBDP past paper questions, and explore other exam boards and types of questions. By following these steps, you will be able to improve your performance, confidence, and enjoyment in mathematics. You will be able to ace the IB DP math exam, and any other math exam that you may encounter in the future.