BEING SUCCESSFUL AT MATHEMATICS

You are reading this page because you are interested in learning how to study for Mathematics B using MIC. There are many good ideas on this page, but they will be of no use unless you use them. To help you do this I will stop occasionally and ask you to do something. I will label these times ACTION so that you know that it is important for you to stop reading and for you to think and make decisions.

1. Have a goal or focus - if you don't know where you are going, it is impossible to get there.

2. Focus on understanding - it is important to not only be able to do the sums but to understand the mathematics behind what you are doing.

3. Check your understanding - once you think you understand the mathematics it is important to use the ideas to solve problems.

4. Revise regularly - you need to revise frequently otherwise you will forget.

5. Know how you are going - keeping a record of your progress, what you can do and what you are having difficulty with.

A goal is a target that you set for yourself. A goal can be anything from the personal standards you want to set yourself through to a tangible target like the career you wish to pursue. People often speak of the value of having short-term goals and long-term goals. Short-term goals are targets that can be met in the near future. Long-term goals are targets that often are a result of effort over a long period of time. Short-term goals can be considered to be the stepping stones that you have to cross to reach your long-term goals.

The value in having goals is that they help to keep you focussed at the times when it is easy to slacken off. It is a happy student who has both short-term and long-term goals. This is because the desire to reach your long-term goals helps you to focus on each of the small goals along the way.

MIC has been designed so that the long-term goal of mastering Mathematics B has been broken up into short-term targets called Key Concepts. At the beginning of each chapter there is a list of all the Key Concepts that need to be mastered in that chapter. These are also listed in the Progress Monitor.

Focus on understanding

In MIC you are usually introduced to the Key Concepts in Explorations, where you can work in or out of class, and by yourself or with others. If you use the right skills at this stage you will understand this new work. The skills you need are:

1. FOCUS - Start the Explorations in a frame of mind ready to listen, participate, and concentrate.

   Participate - In the Exploration make sure you get fully involved. Make sure you participate in class discussions and groupwork. Don't let others do all the work - they will get all the benefit.

   Listen - Be an active listener. As you listen ask yourself these questions:-
   "Is this new, or do I already know this?" "What is the new work here?"
   "Is this like something I already know?" "How is this different from what I already know?"
   "Is this common sense, or radically new?"

   Concentrate - Keep your goals in view. Ask yourself "How is this Exploration helping me to master the Key Concept?"

2. VERBALIZE - Understanding is greatly improved if you try to write or talk about what you are learning. Students who share their ideas and insights and listen to others, end up with better understanding. Ask questions. No serious question is ever "dumb". You may be asking a question that someone else would like answered. Teachers never think that your questions are dumb, they like to know you are listening and thinking about the lesson.

3. SUMMARIZE - Keep a "Mathematics Summary" book. It doesn't have to be fancy, just somewhere where you write down the main ideas, definitions, formulae etc. of each lesson. In MIC, you are given paragraphs to write as a summary at the beginning of each "Check your understanding". At the end of each Chapter you are asked to create a mind map for the chapter. This helps you to see the connections between the Key Concepts in the chapter. Some students use filing cards with a question on one side and its answer on the other, to record what they need to know.

Check your understanding

When you think that you understand the Key Concept, you then need to practise applying it. Practice will not only help you to understand and remember the Key Concept, it will also help you to become so familiar with it that you can easily do it at other times, like in exams. There are two main times to practise, during class and doing homework:

1. IN CLASS - In most mathematics lessons you will have time in class to check how well you understand the Key Concept. In the Check your understanding's you are given simple problems to do first which test if you have learnt the Key Concept. No one learns everything the first time, so don't be embarrassed if you need help, just make sure that you understand what to do before you leave the lesson. If you can't do any of the tasks set, you should follow the basic steps:

   • FOCUS on what it is that you are unclear about, where you are having trouble. Be SPECIFIC. Don't say "I can't do this", say "I can get the diagram, but I don't know what to do next".

   • See if you can work it out from the Conclusion discussion or WORKED EXAMPLES in the text.
   • Talk it over with a classmate. In explaining it to you he/she will understand it better - so both of you are helped.
   • See your teacher. Have a SPECIFIC question to ask which refers to your attempt and where you are having trouble. Do not rub out your incorrect attempt as your teacher will want to look at it.

2. HOMEWORK - Trying to do the tasks set as homework really gives you an idea how well you have understood the day's work. The tasks set are usually more complex than those done in class and may relate to other work learnt previously. Correct your work at home so that you can see if you need help the next lesson. It is a good idea to draw a circle around where you are having trouble and write out the question you want to ask, because you often forget before next lesson. Never skip your homework - it is vital to your understanding!

Revise regularly

Many students say, "I can do it in class, but when exam time comes I forget." Some blame it on nervousness in exams. Nearly always however, the reason students cannot do a task during exams is because either
(a) They did not really understand how to do it in the first place
or
(b) They did understand the task in class but have forgotten when it comes to exams.

Revision means going back over work you have already done, to make sure that you still understand and remember it. You do this by DOING PROBLEMS from the Key Concepts already covered so far in the semester. You need to have a set time put aside every week when you do just revision - not homework or assignments. You should revise in each of the following three ways:

1. EACH NIGHT - Just doing your homework is the first type of revision. This includes learning the work from the day's lesson including new definitions, formulae, procedures, etc.

2. EACH WEEK - Set yourself a minimum of 45 minutes per week. During this time you should do problems from earlier Key Concepts in the semester, to make sure that you still understand and remember how to do them. You should plan systematically so that you review each of the Key Concepts from each of the previous chapters covered. Keep your revision in a separate book. Your teacher may ask to see these when helping you with your problems. The chapter quizzes have been designed to give you ample questions to revise the knowledge an procedures of the course. They are self-correcting and should be used regularly to keep earlier work fresh in your memory.

3. BEFORE EXAMS - If you have been doing the weekly revision, you may not need to do a major study prior to the exams. You may only need to concentrate on those Key Concepts that have been causing you difficulty.

Know how you are going

At the beginning of each chapter there is the list of Key Concepts for the chapter. You will find these listed in the Progress Monitor. The Key Concepts list all the knowledge and procedures that you will need for exams. (There are many other skills that you are developing in this course as well as these such as how to effectively use technology, and work as a team etc). The Key Concepts in the Progress Monitor have some boxes to their right under the heading of "Progress". These boxes allow you to keep a record of how well you know the work for the exams. An example is given below:

There are three parts to the Progress Monitor:

1. CODE for the Key Concepts - this identifies which of the Key Concepts and Check your understandings is being revised.
2. DESCRIPTOR - this is a brief description of the Key Concept
3. PROGRESS - this is where you record how successful you have been with the tasks in the Key Concept.

When you have completed the Check your understanding for the Key Concept, make a decision about whether you feel confident with the Key Concept or whether you are still having difficulty. If you feel confident place a in the first box. If you aren't confident with the Key Concept place a in the first box.

Each week, in your revision over the semester, you should do more tasks to do with this Key Concept . The next time you revisit this Key Concept, you should do some of the earlier tasks in the Check your understanding and some questions from the chapter quizzes. When you do, place a or a in the second box, depending on your success. The next time you revisit this Key Concept, do some of the latter tasks, and mark the third box. Your Progress Monitor becomes a record of how you are progressing through the course.

Code	Descriptor	Progress
KC1.1	identify the real numbers and represent them on the number line.

The 's and 's begin to show you where you need to concentrate your study. If you have all 's then you probably know the work relating to the Key Concept; if there are a lot of 's it means that you are still having difficulty and should seek help.

When you approach your teacher for assistance, you should show him/her your Progress Monitor. Your teacher will be able to use it to help you with your difficulties.

I wish you good luck with your Mathematics B studies and finish with this final word: