To be a successful Maths student, you need to focus on improving five areas of your study, starting right from the day you begin the course and keeping this up until the completion of your final exams and assignments. It is important that you spend enough time on the subject but also how, when and where you do your work is equally important. The five areas are:
Punctuality Punctuality is the ability to do something reliably and on time. Not only do you have to turn up for your lessons, but you need to be on time consistently. When studying at home or when you meet up with fellow students to do group study, you need to stick to the planned time. This also applies to submitting homework tasks and assignments by the due date and arriving for exams and SACs on time. Turning up late for lessons means that you miss out on the introduction or instructions which takes place at the start of a lesson. Since Maths teaching and learning is logically organised and teachers often do relate current learning to previous learning, in those crucial early few minutes, you miss out on understanding the topic fully. As a result of being late, you will need to work extra harder to understand the lesson, thus wasting valuable time. Commencing private and group study times as planned makes your day less stressful, allowing you to get a goodnight sleep and relax a bit before bedtime. Leaving your homework until late at night and rushing through the work can lead to making many careless errors and poor learning. When planning to meet friends for group study, aim to meet up on time so that everyone’s contributing to the study and you gain the full benefit of the sessions. Assignments come with a due date and often marks are deducted for late submission of assignments. It’s important to complete or at least attempt all homework tasks on time in order to benefit from classroom discussions. Arriving for SACs and exams late will lead to stress and you may not be able to focus on the tasks in a calm manner. The stress arising from late arrival, may lead to not being able to complete the questions you would have otherwise done well on. Preparation Preparation must happen at many levels in order to achieve success in Maths. On a day to day basis, you will have to prepare for your lessons and tutorials (if attending). Ensure that you allocate enough time to study for topic tests, exams and SACs. When you prepare well for your assignments and projects, the process of writing it becomes easier. Anticipating what you are going to learn in class helps with understanding and grasping concepts. Teachers often provide a unit or topic planner at the commencement of a topic. When you check this prior to your class, you will know what will be covered in that lesson. You can skim read your textbook on the topic beforehand. Some teachers may provide printed notes with spaces for you to fill in while listening to the teacher. Reading this beforehand helps you to be more attentive during the lessons and thus gain better understanding. If you work with a tutor, they may give some homework tasks to complete prior to each lesson. Often the tutor would have chosen a concept you may not have a good grasp on. Diligently completing these consolidating tasks will help with your progress and ensure that you understand the next lesson better. To do well in a topic test, you will generally need to prepare for about 2 to 3 days and to do well in exams and SACs, you many need about 2 to 3 weeks or longer in preparation time. When you are preparing for topic tests, you may need to ensure that you complete review questions, any extra revision questions given by your teacher and prepare a summary sheet if you are allowed to take one into your test. The summary sheet may include formulas, worked examples of challenging questions, calculator instructions or a checklist of possible errors. In exams and SACs, especially for Mathematical Methods and Specialist Mathematics, you will be required to bring together knowledge from different areas and apply them in familiar and unfamiliar situations. To answer the extended response questions well, make sure you practise a wide range of questions – first with the notes and then under exam conditions. Assignments and extended analysis tasks can be given as assessment tasks for students. It is important to make use of the whole time duration given for the task to work on it rather than rushing to complete it in the last minute. Reading the task carefully and making sure you understand what is required of you is the first step. The next step is to collect any necessary data and doing the calculations and/or necessary graphs or diagrams. Finally, you will need to check all your work and present the work neatly. Participation Actively listening, asking questions, contributing to class discussions and group study will help improve your understanding, consolidate learning and thus help gain better grades. Participating fully in class or tuition sessions may include: being attentive during the class, asking questions to help consolidate your understanding, seeking clarification when needed, contributing to class discussions or summarising what has been taught. A typical lesson might have an introductory or warm up activity (5 to 10 minutes), time for content to be covered (about 15 minutes), time to improve fluency and/or work on problems (15 to 20 minutes) and a summary of what has been taught. An introductory activity might involve a loop game where each student gets a card with an answer on the top of the card and a question at the bottom. Teacher might start off by asking a question and the student who has a card with the answer calls out the answer. They will then read out the question on the card for the next student to answer. The activity continues until all the students have time to answer questions. Alternatively, a teacher might ask a question and students think in pairs, jot down answers and offer possible answers before teacher instructions. During the period when content is covered, teachers often pause so that students can attempt the working out of a problem question. Teachers might also ask questions such as why some answers are not possible and may seek an explanation as to why this is the case. These are opportunities for students to contribute and learn and may provide important key ideas or concepts for the students’ notes. At this stage, students are encouraged to put their hands up and ask questions. This is a good time to ask questions if you don’t understand fully. You will generally be given time in class to complete work on your own, in pairs or in small groups. The teacher will often come around to check whether you are understanding the task, offer help if needed and make sure you are on track with the task. This is another opportunity to interact with your partner, group members and teacher. Make use of this time to discuss, clarify and understand your work. At the conclusion of the lesson, teachers may wrap up the lesson by asking students to summarize, talk about the answers or even tabulate results. Pay attention and contribute in order to maximize your learning. Practice You can’t become good at Maths by just reading the notes or attending the classes. You need to be able to do exam or SAC style questions by yourself under timed conditions. So how do you gain fluency, problem solving skills and the ability to communicate mathematically? The answer is to practice using a variety of questions in many stages right until the major assessments such as exams and SACs. The sooner you practice doing the set questions after learning, the easier it will be for you to remember how to do them when it comes to the exam. You can start working on the questions in class after your teacher has explained the concepts. The easiest ones to do first are the skill or fluency questions. A typical example might be differentiating a polynomial function using the rule. While you are completing these skill questions, think about where the rule came from (knowledge of limits) and how you are going to apply the skills (the worded questions on slopes). Once you complete these questions, check the answers at the back of the book and tick them off. Once you are comfortable with the skills, move on to doing the worded application questions. More time is needed to be spent on them as they are more challenging, requiring a multitude of skills. The other types of questions to practice are ‘prove’ or ‘show’ questions and multiple-choice questions (MCQ). In the extended response and MCQ, you may be allowed to use a calculator. Learning how to use the CAS calculator efficiently and practising with it regularly will make you proficient in using it and will save you time. This will help you gain better marks in your calculator allowed exams and SACs and all assessments in Further Mathematics. When you work on these questions, you may notice that you didn’t quite understand some concepts as well as you thought you did. It is important to note down these areas and clarify them with your teacher or Maths tutor. Something that happens very often is that students do well in topic tests but struggle when it comes to exams and SACs. In tests, only a small amount of content is tested, whereas in exams and SACs, a large amount of content learnt over two or more years is tested. In order to excel in exams, you not only need to focus on doing all different types of questions, but also when and how you do them. Allocate some time each study session to practice material covered weeks or even months ago in addition to what you are currently learning. Randomly practicing questions from different areas on a regular basis prepares you for the way exams questions are set. You can increase the difficulty of questions that you tackle over the course of your study while improving your confidence. When you are completing the questions, it is a good idea to think about what you will include in your summary notes and jotting them down as you go. It is better to have several small study sessions instead of one long one. It is important to practice Maths after each Maths lesson at school, completing required tasks, adding to your summary notes and practicing some material towards exam preparation. Studying in a quiet space without distractions and at a time you are most alert will maximise learning. When you complete your tasks, tick them off as this gives a sense of achievement. Perseverance When you embark on math studies, you will have to overcome obstacles many times. You may not understand the content the first time you learn it. When you try to do the set questions, you may not know how to start or will not know how to proceed in order to complete a question. You may not do well in the assessment you thought you would have done well in. Asking for help, seeking explanation from another source or sources, trying the same question using another method, and recognising your mistakes and learning from them are all examples of persevering with your studies. When you don’t understand a concept the first time it’s presented to you, try to understand again, either from another source such as a textbook, online tutorials or seeking the help of the tutor. A tutor who is able to explain the concept in a different way and at a pace which suits you might be an invaluable source of help in your Maths success. With the help of a tutor, you may realise that you may have missed out on or simply don’t understand a key concept which is integral to your current studies. This can easily be fixed, but will require perseverance and hard work. Again, when working on one on one or in a small group, a tutor will be able to work out your area of weakness and facilitate understanding. When you don’t know how to proceed with a question, reading a worked example from the textbook or class notes will often help you to work out how to do the problem. It could take more time and effort to solve some of the more challenging questions. If you read these questions at the start, you will have more time to think about how you might go about solving these questions. A diagram, table or modelling using a simpler concept could help solve this question. Try and record your efforts, attempt the question with your study partners and if not successful, seek help from your teacher or tutor. Tests, quizzes and assignments should all be treated as opportunities from which to learn. If you do not do well, you need to be prepared to find out where you lost marks and work on not making avoidable mistakes in the future. Teachers will often go over tests and exams in class and will often write comments on your assignments for you to help improve. Pay attention, take note of areas to improve and try to do better in the next assessment. A private tutor may be able to go over all the questions and find you similar questions to improve your confidence.