Understanding Effective Planning and Learning Who am I? Mark Grady Teaching Maths for 23 years Grew up in Sydney Worked at schools including APHS, BBHS, CHS Uni Coordinate LMC Some Tips From the Sydney Morning Herald Writers: Nikky Vanderhout has many years of experience in teaching mathematics to both metropolitan and country students in NSW. After beginning teaching in north-western NSW, she transferred to Sydney, teaching students in a co- educational comprehensive setting. An executive member of the Mathematical Association of NSW, Vanderhout contributes to a variety of activities which promote quality learning of mathematics. She has worked on a variety of projects with the Board of Studies in NSW Department of Education and is currently head teacher, Mathematics, at North Sydney Girls High School. Aiming for the finish line Preparing for the HSC Mathematics exams is much like training for a marathon race. In the final weeks before the event, the athlete commits to extra practice sessions to strengthen and improve running skills. Special care is taken to ensure that the route is known and race tactics are planned so that a personal best is achieved on the day. Mathematics students who aim for a personal best would do well to follow a similar pattern of preparation. Use past assessment tasks and practice questions to determine your strengths and weaknesses and then plan a strategy for improvement. Set aside a regular time and place for revision which includes opportunities to work through past papers under timed conditions so that you become familiar with concentrating for three hours at a time. Commit to extra practice sessions Use past assessment tasks and practice questions to determine your strengths and weaknesses Plan a strategy for improvement. Work on your weaknesses. Set aside a regular time and place for revision which includes opportunities to work through past papers under timed conditions so that you become familiar with concentrating for three hours at a time. Reward yourself! Useful revision techniques Give yourself a target mark for relevant sections and aim to achieve it in every exam practice. If you dont aim at anything, you are certain to miss! Sit the exam under exam conditions (as best you can). Include 5 min reading time. Underline the key words in every question Ensure you know when to differentiate and when to integrate Useful revision techniques Whatever the mind can conceive and believe it can achieve Stephanie Rice I wouldn't say anything is impossible. I think that everything is possible as long as you put your mind to it and put the work and time into it. My goal is one Olympic gold medal. Not many people in this world can say, 'I'm an Olympic gold medalist. Dont just go along with the crowd what are YOUR aspirations? (HSC, ATAR, Maths isnt the entire HSC) The best way to learn mathematics is to work through problems, correct them, analyse where any errors occurred and then work on similar problems again. Reading through notes and worked solutions is never as effective as working through a problem for yourself. A good source of questions is the NSW HSC Online website (hsc.csu.edu.au/maths). Follow the links to the course and topics you need.hsc.csu.edu.au/maths Useful revision techniques Making a mind-map or summary of an entire topic adding links to related topics. Writing formulae or ideas on cards and then memorising them. Talking problems over with others. Talking problems over with others. Mapping out a procedure for typical problems such as mathematical induction, drawing a graph using calculus etc Useful revision techniques Procedure for Mathematical Induction Test using the first allowable value of n often n=1) Assume true for n=k Show true for the next value in the problem (often n=k+1) Write a suitable conclusion. e.g. Hence if the result is true for n=k, then it is true for n=k+1. Since it is true for n=1, it must be true for n=2, n=3 etc for all positive integers n. Depends on the question Explain to someone what key words mean. E.g. continuity, parametric form, Newtons method to approximate roots etc Making appointments with your class teacher to work through areas which still cause concern. Useful revision techniques During the reading time go through each question making mental notes of where your favourite types of questions are located. Do what you know first. Work quickly and accurately. Time saved at the beginning will provide you with thinking time for possibly challenging questions at the end. When instructed to draw a diagram, make it at least 1/3 page in size and use pencil. Planning the tactics Skills to optimise responses Tracing the diagrams can also save you time. Write your solutions in pen, spacing out your work clearly, leaving lines after each answer to help when you go back to check your work. This will also assist the markers who read your solutions. (make the marker happy!) Time your examination. Do what you know first. You do not have to start at Q1, though this will usually be the easier part of the paper. Presenting your work well Don't use liquid paper but simply put a line through it so that the marker can read what you have written, for, at times, marks can be given for process. Avoid leaving the examination early but relax and think of something which makes you feel calm, for often a solution to a teasing problem can then come to mind. Map out the time between now and the exam and put together a study timetable. Dont think about schoolies! Useful sites Tutorials Assessment practice HSC guidelines Improve your exam score Know what markers expect and learn from others mistakes Extension 1 and Extension 2 students Mathematics (2U) students Be familiar with the glossary of terms, exam format Time your exam Show working!!!!!!! Cannot give part marks if no working is shown Round answers in the final step only Write justifications like the audience has no understanding of mathematics and needs each bit explained. Read your justification back to yourself. Does it make sense? Bring a ruler, calculator, geometry set for diagrams Set solutions out logically Draw large, clear, well labelled diagrams using a ruler Use the table of integrals! Relaxation Techniques It is important to be refreshed and alert before undertaking any challenge so plan to get a reasonable amount of sleep on the evening before the examination. Staying up late to cram can increase levels of anxiety and, although the added adrenalin caused by being a little on edge makes the mind more alert, too much will cause problems in logical thinking - never a good thing before a maths exam. Planning the tactics Hand up if you never get stressed. Do the rest of you ever feel..... Tired and exhausted Body tension, leading to headaches, migraines, upset stomach or increased heart rate Like there is just to much to do where do I start, deliberate avoidance Your mind is in a whirl; cant think straight, concentrate or work effectively You have sleep problems; either cant sleep or sleeping too much A loss of appetite or increased eating of comfort foods A feeling under pressure; no time; often in a panic Sometimes these symptoms can indicate a medical problem, and it is worth checking this out with your GP. But if you are looking for ways to manage your stress levels it is worth considering some of the things you can do. Relaxing the body Sit up and back in your chair, legs slightly apart, feet flat on the floor. Drop your shoulders while you take a deep breath, letting it out slowly. Close your eyes. Keep focused on your breathing and breathe in slowly to the count of four - hold to the count of four - breathe out to the count of four - pause to the count of four. Repeat in an even, comfortable rhythm Now slowly tense, hold and release the main muscle groups, working up through your body. Start with toes and feet; tense as much as possible, hold and release. Move on to calf muscles, thighs, bottom, stomach and upper body in the same way, paying particular attention to the upper back and shoulders, where we hold a lot of tension. Then work on your arms and hands. Finally, if you can (some places are just too public), screw up the muscles of your face and neck and release. After this, gently massage your neck and upper spine, then return to focusing on slow breathing and check back through your body for any remaining tension. Relaxing the mind There are many techniques for clearing the mind, and, again, no one method will suit all people. Some people benefit from developing an image of a familiar place which is associated with safety or tranquillity which they can call to mind when unwanted thoughts intrude. Another technique known to be useful is to allow any troublesome thoughts to be present in your mind without fighting them. Allocate a fixed time to deal with it (e.g. 10 minutes). Then, deal with it! Relaxing the mind and body Music x x x And one more thing Oh no no no no