HOW TO UNDERSTAND MATHEMATICS FORMULAS ----- BY. MWL. JAPHET MASATU.

HOW    TO  UNDERSTAND  MATHEMATICS   FORMULAS. INTRODUCTION.

In a recent IntMath Poll, many readers reported that they find math difficult because they have trouble learning math formulas and an almost equal number have trouble understanding math formulas.
I wrote some tips on learning math formulas here: How to learn math formulas.
Now for some suggestions on how to understand math formulas. These should be read together with the “learning” tips because they are closely related.
a. Understanding math is like understanding a foreign language: Say you are a native English speaker and you come across a Japanese newspaper for the first time. All the squiggles look very strange and you find you don’t understand anything.
If you want to learn to read Japanese, you need to learn new symbols, new words and new grammar. You will only start to understand Japanese newspapers (or manga comics ^_^) once you have committed to memory a few hundred symbols & several hundred words, and you have a reasonable understanding of Japanese grammar.
When it comes to math, you also need to learn new symbols (like π, θ, Σ), new words (math formulas & math terms like “function” and “derivative”) and new grammar (writing equations in a logical and consistent manner).
So before you can understand math formulas you need to learn what each of the symbols are and what they mean (including the letters). You also need to concentrate on the new vocabulary (look it up in a math dictionary for a second opinion). Also take note of the “math grammar” — the way that it is written and how one step follows another.
A little bit of effort on learning the basics will produce huge benefits.
b. Learn the formulas you already understand: All math requires earlier math. That is, all the new things you are learning now depend on what you learned last week, last semester, last year and all the way back to the numbers you learned as a little kid.
If you learn formulas as you go, it will help you to understand what’s going on in the new stuff you are studying. You will better recognize formulas, especially when the letters or the notation are changed in small ways.
Don’t always rely on formula sheets. Commit as many formulas as you can to memory — you’ll be amazed how much more confident you become and how much better you’ll understand each new concept.
c. Always learn what the formula will give you and the conditions: I notice that a lot of students write the quadratic formula as

But this is NOT the quadratic formula! Well, it’s not the whole story. A lot of important stuff is missing — the bits which help you to understand it and apply it. We need to have all of the following when writing the quadratic formula:

The solution for the quadratic equation
ax² + bx + c = 0
is given by

A lot of students miss out the “x =” and have no idea what the formula is doing for them. Also, if you miss out the following bit, you won’t know how and when to apply the formula:
ax² + bx + c = 0
Learning the full situation (the complete formula and its conditions) is vital for understanding.
d. Keep a chart of the formulas you need to know: Repetition is key to learning. If the only time you see your math formulas is when you open your textbook, there is a good chance they will be unfamiliar and you will need to start from scratch each time.
Write the formulas down and write them often. Use Post-It notes or a big piece of paper and put the formulas around your bedroom, the kitchen and the bathroom. Include the conditions for each formula and a description (in words, or a graph, or a picture).
The more familiar they are, the more chance you will recognize them and the better you will understand them as you are using them.
e. Math is often written in different ways — but with the same meaning: A lot of confusion occurs in math because of the way it is written. It often happens that you think you know and understand a formula and then you’ll see it written in another way — and panic.
A simple example is the fraction “half”. It can be written as 1/2, and also diagonally, as ½ and in a vertical arrangement like a normal fraction. We can even have it as a ratio, where the ratio of the 2 (equal) parts would be written 1:1.
Another example where the same concept can be written in different ways is angles, which can be written as capital letters (A), or maybe in the form ∠BAC, as Greek letters (like θ) or as lower case letters (x). When you are familiar with all the different ways of writing formulas and concepts, you will be able to understand them better.
Every time your teacher starts a new topic, take particular note of the way the formula is presented and the alternatives that are possible.

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Do you have any tips to add? How do you figure out your math formulas? Which formulas are hardest to understand?
Good luck with understanding math formulas!

How to learn math formulas

In a recent IntMath Poll, readers indicated that the hardest thing about math was learning the formulas.
Here are 10 things you can do to improve your memory for math formulas.

1. Read ahead

Read over tomorrow’s math lesson today. Get a general idea about the new formulas in advance, before your teacher covers them in class.
As you read ahead, you will recognize some of it, and other parts will be brand new. That’s OK – when your teacher is explaining them you already have a “hook” to hang this new knowledge on and it will make more sense — and it will be easier to memorize the formulas later.
This technique also gives you an overview of the diagrams, graphs and vocabulary in the new section. Look up any new words in a dictionary so you reduce this stumbling block in class.
This step may only take 15 minutes or so before each class, but will make a huge difference to your understanding of the math you are studying.
I always used to read ahead when I was a student and I would be calm in class while all my friends were stressed out and confused about the new topic.

2. Meaning

All of us find it very difficult to learn meaningless lists of words, letters or numbers. Our brain cannot see the connections between the words and so they are quickly forgotten.
Don’t just try to learn formulas by themselves — it’s just like learning that meaningless list.
When you need to learn formulas, also learn the conditions for each formula (it might be something like “if x > 0″).
Also draw a relevant diagram or graph each time you write the formula (it might be a parabola, or perhaps a circle). You will begin to associate the picture with the formula and then later when you need to recall that formula, the associated image will help you to remember it (and its meaning, and its conditions).
During exams, many of my students would try to answer a question with the wrong formula! I could see that they successfully learned the formula, but they had no idea how to apply it. Diagrams, graphs and pictures always help.
Most of us find it difficult to learn things in a vacuum, so make sure you learn the formulas in their right context.
When you create your summary list of formulas, include conditions and relevant pictures, graphs and diagrams.

3. Practice

You know, math teachers don’t give you homework because they are nasty creatures. They do it because they know repetition is a very important aspect of learning. If you practice a new skill, the connections between neurons in your brain are strengthened. But if you don’t practice, then the weak bonds are broken.
If you try to learn formulas without doing the practice first, then you are just making it more difficult for yourself.

4. Keep a list of symbols

Most math formulas involve some Greek letters, or perhaps some strange symbols like ^ or perhaps a letter with a bar over the top.
When we learn a foreign language, it’s good to keep a list of the new vocabulary as we come across it. As it gets more complicated, we can go back to the list to remind us of the words we learned recently but are hazy about. Learning mathematics symbols should be like this, too.
Keep a list of symbols and paste them up somewhere in your room, so that you can update it easily and can refer to it when needed. Write out the symbol in words, for example: ∑ is “sum”; ∫ is the “integration” symbol and Φ is “capital phi”, the Greek letter.
Just like when learning whole formulas, include a small diagram or graph to remind you of where each symbol came from.
Another way of keeping your list is via flash cards. Make use of dead time on the bus and learn a few formulas each day.

5. Absorb the formulas via different channels

I’ve already talked about writing and visual aids for learning formulas. Also process and learn each one by hearing it and speaking it.
An example here is the formula for the derivative of a fraction involving x terms on the top and bottom (known as the “Quotient Rule”). Then in words, the derivative is:
dy/dx = bottom times derivative of top minus top times derivative of bottom all over bottom squared.
The formula is actually as follows, if we let u = numerator and v = denominator of the fraction, then:

6. Use memory techniques

Most people are capable of learning lists of unrelated numbers or words, as long as they use the right techniques. Such techniques can be applied to the learning of formulas as well.
One of these techniques is to create a story around the thing you need to learn. The crazier the story, the better it is because it is easier to remember. If the story is set in some striking physical location, it also helps to remember it later.

7. Know why

In many examinations, they give you a math formula sheet so why do you still need to learn formulas? As mentioned earlier, if students don’t know what they are doing, they will choose a formula randomly, plug in the values and hope for the best. This usually has bad outcomes and zero marks.
I encourage you to learn the formulas, even if they are given to you in the exam. The process of learning the conditions for how to use the formula and the associated graphs or diagrams, means that you are more likely to use the correct formula and use it correctly when answering the question. This is also good for future learning, because you have a much better grasp of the basics.

8. Sleep on it

Don’t under-estimate the importance of sleep when it comes to remembering things. Deep sleep is a phase during the night where we process what we thought about during the day and this is when more permanent memories are laid down. During REM (rapid eye movement) sleep, we rehearse the new skills and consolidate them.
Avoid cramming your math formulas the night before an exam until late. Have a plan for what you are going to learn and spread it out so that it is not overwhelming.

9. Healthy body, efficient brain

The healthier you are, the less you need to worry about sickness distracting from your learning. Spend time exercising and getting the oxygen flowing in your brain. This is essential for learning.

10. Remove distractions

This one is a problem for those of us that love being on the Internet, or listening to music, or talking to our friends. There are just so many things that distract us from learning what we need to learn.
Turn off all those distractions for a set time each day. You won’t die without them. Concentrate on the formulas you need to learn and use all the above techniques.
When you are done, reward yourself with some media time — but only after you have really accomplished something.

UNDERSTANDING MATHEMATICS LEARNING PROBLEMS --- BY. MWL. JAPHET MASATU

UNDERSTANDING   MATHEMATICS   PROBLEMS.

What Are They?

Students who experience significant problems learning and applying mathematics manifest their math learning problems in a variety of ways. Research indicates that there are a number of reasons these students experience difficulty learning mathematics (Mercer, Jordan, & Miller, 1996; Mercer, Lane, Jordan, Allsopp, & Eisele, 1996; Mercer & Mercer, 1998; Miller & Mercer, 1997.) The following list includes these research-based math disability characteristics.

Characteristics of Students Who Have Learning Problems

Learned Helplessness - Students who experience continuous failure in math expect to fail. Their lack of confidence compels them to rely on assistance from others to complete tasks such as worksheets. Assistance that only helps the student "get through" the current set of problems or tasks and does not include re-teaching the concept/skill, only reinforces the student's belief that he cannot learn math.

Passive Learners - Students who have learning problems often are not "active" learners. They do not actively make connections between what they already know and what they are presently learning. When presented with a problem-solving situation, they do not employ strategies or activate prior knowledge to solve the problem. For example, students may learn that 8 x 4 = 32, but when presented with 8 x 5 = ___, they do not actively connect the process of multiplication to that of repeated addition. They do not think to add eight more to thirty-two in order to solve the problem. Students that have learning problems often believe that students who are successful in math just know the answers. They do not understand that students who are successful in math are good at employing strategies to solve problems.

Memory Problems - Memory deficits play a significant role in these students' math learning problems. Memory problems are most evident when students demonstrate difficulty remembering their basic addition, subtraction, multiplication, & division facts. Memory deficits also play a significant role when students are solving multi-step problems and when problem-solving situations require the use of particular problem solving strategies. A common misconception about the memory problems of these students is that it is an information storage problem; that somehow, these students just never get it stored properly. This belief probably arises because one day the student can do a math task but then the next day they can't. Teachers then re-teach the skill only to have the same experience repeated. In contrast to an information storage problem, these memory deficits are often a result of an information retrieval problem. For these students, instruction should include teaching students strategies for accessing and retrieving the information they have stored.

Attention Problems - Math requires a great deal of attention, particularly when multiple steps are involved in the problem solving process. During instruction, students who have attention problems often "miss" important pieces of information. Without these important pieces of information, students have difficulty trying to implement the problem solving process they have just learned. For example, when learning long division, students may miss the "subtract" step in the "divide, multiply, subtract, bring down" long division process. Without subtracting in the proper place, the student will be unable to solve long division problems accurately. Additionally, these students may be unable to focus on the important features that make a mathematical concept distinct. For example, when teaching geometric shapes, these students may attend to features not relevant to identifying shapes. Instead of counting the number of sides to distinguish triangles from rectangles, the student may focus on size or color. Using visual, auditory, tactile (touch), and kinesthetic (movement) cues to highlight the relevant features of a concept is helpful for these students.

Cognitive/Metacognitive Thinking Deficits - Metacognition has to do with students' ability to monitor their learning: 1.) Evaluating whether they are learning; 2.) Employing strategies when needed; 3.) Knowing whether a strategy is successful; and, 4.) Making changes when needed. These are essential skills for any problem solving situation. Because math is problem solving, students who are not metacognitively adept will have great difficulty being successful with mathematics. These students need to be explicitly taught how to be metacognitive learners. Teachers who model this process, who teach students problem solving strategies, who reinforce students' use of these strategies, and who teach students to organize themselves so they can access strategies, will help students who have metacognitive deficits become metacognitive learners.

Low Level of Academic Achievement - Students who experience math failure often lack basic math skills. Because it takes students with math disabilities a longer time to process visual and auditory information than typical learners, they often never have enough time or opportunity to master the foundational concepts/skills that make learning higher level mathematics possible. Providing these students many opportunities to respond to math tasks and providing these practice opportunities in a variety of ways is essential if these students are to ever master the math concepts/skills we teach. Additionally, teachers need to plan periodic review and practice of concepts/skills that students have previously mastered.

Math Anxiety - These students often approach math with trepidation. Because math is difficult for them, "math time" is often an anxiety-ridden experience. The best cure for math anxiety is success. Providing success starts first with the teacher. By understanding why students are having the difficulties they are having, we are less inclined to place "blame" on the students for their lack of math success. These students already feel they are not capable. The attitude with which we approach these students can be a crucial first step in rectifying the math problems they are having. Providing these students with non-threatening, risk-free opportunities to learn and practice math skills is greatly encouraged. Celebrating both small and great advances is also important. Last, if we provide instruction that is effective for these students, we will help them learn math, thereby helping them to experience the success they deserve.

Math Instruction Issues That Impact Students Who Have Math Learning Problems

Although it is very important to understand the learning characteristics of students with math learning problems, it is also important to understand how math instruction/curriculum issues negatively affect these students (Mercer, Jordan, & Miller, 1996; Mercer, Lane, Jordan, Allsopp, & Eisele, 1996; Mercer & Mercer, 1998; Miller & Mercer, 1997). The following list includes these instruction/curriculum issues as well as how they impact the students described above.

Spiraling Curriculum - Within a spiraling curriculum, students are exposed to a number of important math concepts the first year. The next year, students return to those math concepts, expanding on the foundation established the year before. This cycle continues with each successive year. While the purpose of this approach is logical and may be appropriate for students who are average to above average achievers, the spiraling curriculum can be a significant impediment for students who have math learning problems. The primary problem for these students is the limited time that is devoted to each concept. Students who have math learning problems are never able to truly master the concept/skill being taught. For these students, "exposure" to foundational skills is not enough. Without an appropriate number of practice opportunities, these students will only partially acquire the skill. When the concept/skill is revisited the next year, the student is at a great disadvantage because the foundation they are expected to have is incomplete. After several years, the student has not only "not mastered" basic skills, but has also not been able to make the important connections between those basic skills and the higher level math skills being taught as the students moves through the elementary, middle, & secondary grades.

Teaching Understanding/Algorithm Driven Instruction - Although the National Council on Teaching Mathematics (NCTM) strongly encourages teaching mathematical understanding and reasoning, the reality for students with math learning problems is that they spend most of their math time learning and practicing computation procedures. Because of their memory problems, attention problems, and metacognitive deficits, these students have difficulty accurately performing multi-step computations. Therefore, instructional emphasis for these students is often placed on procedural accuracy rather than on conceptual understanding. This emphasis on algorithm (procedure) proficiency supersedes emphasis on conceptual understanding. An example of this is the process of multiplication. Students who only are taught the procedure of multiplication through drill and practice often do not really understand what the process represents. For example, consider the relationship of the following two multiplication problems: 2 x 4 = 8 and ½ x ¼ = 1/8. When students are asked why the answer in the first problem is greater than its multipliers but the answer to the second problem is less than each of its multipliers, the students are unable to answer why. They have never really understood that the multiplication sign really means "of" and that "2 x 4 = 8" means two groups of fours objects, while " ½ x ¼ = 1/8" means one-half of one-fourth. Teaching understanding of the math processes as well as teaching the algorithms (procedures) for computing solutions is critical for students with math learning problems.

Teaching to Mastery - As described under "Spiraling Curriculum," students with learning problems need many opportunities to respond to specific math tasks in order to master them. Teaching to mastery requires that both the teacher and the student monitor the student's learning progress on a daily basis. Mastery is indicated only when the student is able to perform a math task at 100% accuracy for at least three consecutive days. In situations where student progress is assessed only by unit tests, it is very difficult to determine whether a student has really mastered the skills covered in that unit. Even if the student performs well on the unit test, a teacher cannot be certain that the student actually has reached mastery. Because of the learning characteristics common for these students, it is possible that the student would not score as well if given the same test the next day. Mastery can only be inferred when the student demonstrates consistent mastery performance over time. Such continuous assessment is rare in math classrooms. When evaluation of student progress occurs only by unit tests and the students with learning problems do not perform well, the teacher is left with a difficult dilemma. Does the teacher take additional class time to re-teach the skill, thereby falling behind the mandated curriculum's instructional pace? Conversely, does the teacher instead move on to new material, knowing that these students have not mastered the preceding skills, making it less likely the student will have the prerequisite skills to learn the new information? This no-win situation can be avoided if continuous daily assessment is implemented for these students. It is easier and more time efficient to re-teach an individual math skill the same day of initial instruction, or on the following day. Attempting to re-teach multiple math skills many days after initial instruction is much more difficult and time consuming. Due to the hierarchical nature of mathematics, if students do not master prerequisite skills, it is likely that they will not master future skills.

Reforms That Are Cyclical in Nature - The cyclical nature of mathematics curriculum/instruction reforms creates changing instructional practices that confuse students with learning problems. Like reforms for reading instruction, math instruction swings from primarily skills-based emphasis to primarily meaning-based emphasis dependent on the philosophical and political trends of the day. Most students experience at least one of these shifts as they move through grades K to 12. While students who are average to above average achievers are able to manage these changes in instruction, students who have learning problems do not adjust well to such change.

Application of Effective Teaching Practices for Students who have Learning Problems - Research has identified math instructional practices that are effective for students who have learning problems, but these instructional practices are not always implemented in our schools. These instructional practices are described and modeled in this CD-ROM program. Descriptions also include how the particular characteristics of each instructional strategy complement the learning characteristics of students with learning problems. Guidance is also provided which will help you implement these instructional practices in an organized and systematic way.

How Does This Information Help Me?

Teachers who understand the learning needs of their students are more empowered to provide the kind of instruction their students need. Knowing why a student is struggling to learn math provides a basis for understanding why particular instructional strategies/approaches are effective for him/her. Each of the instructional strategies included in this program has unique characteristics that positively impact the learning characteristics of students who have math learning problems. As you learn about each strategy, you are encouraged to refer often to the learner characteristics described in this section. While reading about each instructional strategy and then watching a teacher model the strategy, note how the specific instructional characteristics of the strategy complement or "match" the learning characteristics of students with math learning problems. The text descriptions for each instructional strategy found in this manual clarify these relationships. The elaborated video clips in the CD-ROM also emphasize how the specific characteristics for each instructional strategy positively impact students who have math learning problems.

HOW TO SYUDY FOR A MATH EXAM ----- BY. MWL. JAPHET MASATU.

HOW    TO  STUDY    FOR    A   MATH    EXAM.

INTRODUCTION.

Many people try to study for math in the same way they would study for a history exam: by simply memorizing formulas and equations the way they would memorize facts and dates. While knowing formulas and equations is important, the best way to learn them is by using them. That's the great thing about math - you can do math. You can't simply "do history."

Steps

1. 
   1
   Attend class every day. Listen and pay attention to the material. Math is typically more visual than other subjects due to the equations and problem solving.
   • Jot down any example problems from the session/class. When you review your notes later on, you will have a better knowledge of the specific lesson that was taught, rather than relying on your textbook.
   • Ask your teacher any questions that you might have before the day of the exam. The teacher might not tell you specifically what is going to be on the exam, but he or she may give you helpful guidance if you don't understand. Not only will they show you how to do the problem, but a teacher who has seen you before and knows who you are will be more willing to help you in the future (or maybe even cut you a little slack if your grade is borderline).
2. 
   2
   Read the text. Make sure you read all of the text and not just the examples. Textbooks often include proofs of the formulas that they expect you to know; this is useful for truly understanding the material and why it works.
3. 
   3
   Do homework problems. Most classes have assigned, or at least suggested, problems that the teacher feels are most useful. A lot of exam problems are extremely similar to homework problems; sometimes they are even exactly the same.
   • Try to find other problems that are similar to those that were assigned for homework. Take this opportunity to finish off an entire page if the assigned homework was a portion of that (for example, if the homework was to do the odd-numbered problems, do the even ones too).
   • Do as many problems as you can so that you can get as much practice as possible and become familiar with the different problem set ups. #Try to find out various ways to tackle a certain problem. For example, with systems of equations, you can solve them by either substitution, elimination, or graphing. Graphing is best used when you can utilize a calculator (e.g TI-84+ or TI-83) as you are more likely to get the correct answer. However, if you can't use one, then either use substitution or elimination based on the question (some are solved easier by x method than y), or determine which way is easier for you to do. This is better than becoming adept at one method, which may let you down when the time comes to take a test.
4. 
   4
   Join a study group. Different people see concepts in different ways. Something that you have difficulty understanding may come easily to a study partner. Having his/her perspective on a concept may help you to comprehend it.
5. 
   5
   Have someone make up problems for you to work out. Get them to draw out similar examples from your textbook or ideas from online sources and reveal the answers to you if you're finished or seriously stuck on them. Don't try to create your own study sheet since you're not challenging yourself enough.
6. 
   6
   Know that teachers will go back into the past. Even if you're studying for a chapter or two, they may "polish" your skills and come up with math problems that you studied a while back or at the beginning of the term.
7. 
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   Finished.
8. 8
   Try to buy workbooks of maths and try the questions it will give you extra knowledge. And you may face that problem next day.        

Tips

• It is often useful to understand how a formula is derived rather than just memorizing it. Things will make more sense, and it is often easier to remember just a few simple formulas and how to derive more complicated ones from them.
• Solve problems. In this way, you have the tendency to understand and realize the formulas and the given problems. You can solve the problems that have been given to you. Solve some problems even if you don't know the answer and let someone check it for you.
• If math is something you find boring and not worth studying for, speak to your family and decide on a reward if you get over a certain percentage in the exam. That way you have an incentive to do well.
• Make sure that when you are understanding the math problems, you aren't just doing them. You have to understand them and if you have the slightest doubt, you should ask a teacher or an advisor.
• Study all day before the test after homework.
• If you find math boring, give yourself incentives to finish problems. For example, promise yourself you'll treat yourself to some cookies, half an hour of your favourite programme etc after you finish 20 sums. You could also race your friends in finishing the sums if you can manage group studying.
• Start studying 2 months before the exam and do not wait till the last minute. As for the day before the exam, do not be stressed and just relax. Clear your mind when you sleep and you will definitely do well.
• Just calm down and think positive, be confident that you can do it.
• Sleep for 7-9 hours to keep your mind fresh and perform calculations mentally.
• Ask your teacher if your math book has an online website. Sometimes online texbooks can help by providing quizzes and additional instructional material.

• Start studying while you still have time to go to a professor or teacher for answers if you need to. If you start studying too late, you leave yourself with no options or opportunities to study.
• If you need help ask your teacher or a classmate.
• Do not rely on your teacher to make you understand a concept or a problem. You will never get it and you might feel that the teacher is being rude by not bringing down the question to your level of understanding. Instead, do it all by yourself, start to finish. Some questions are so tricky, they almost always have to be memorized, so mark them and revise them again and again before an exam so that it is well set in your mind.
• In all math tests, the toughest questions that you encounter while preparing are the ones asked in the test, prepare by reviewing study guides, other tests, homework, and other papers regarding the things covered before the test
• Try to enjoy math. Feel happy and satisfied when you manage to finish a problem and then proceed to the next sum.
• Relax and start by doing the easiest problems first, that way you can have more time focussing on the harder problems.
• Make sure to drink lots of water and have a small snack before you study. This will stimulate your brain and will help you memorize and work on your math concepts.
• Just play and enjoy! Don't be scared of someone like tutor, etc. At the last day of preparation study more and more. But don't be stressed at the exam day or you will be fail.
• Form a creative study group based on education and a bit of social discussion.

Warnings

• Do not do all of your studying at one time. Be sure to take breaks and let the information sink in a little before going back to studying.
• Don't be tempted to use a calculator when solving problems. In fact, you should practice the basics - addition, subtraction, multiplication, and division. Practice them as often as possible with random numbers. However, once you get to harder things, a calculator probably will be required to do your homework.
• Don't look up the answer as soon as you get stuck on a problem. Struggling with it for some time will be much more beneficial, because you may find a new way to understand the problem. Even if in the end you need to look up the answer anyway.
• Do not just try to find example problems that emulate homework problems. Try to understand why certain steps are taken. If the professor likes to be tricky (many do), knowing the example problems will not be very helpful, but truly understanding the material will. There are a few clues in the question and you have to solve the question with the given materials.

HOW TO STUDY FOR AN APPROACHING EXAM ---- BY. MWL. JAPHET MASATU.

HOW   TO  STUDY   FOR  AN   APPROACHING   EXAM.

INTRODUCTION.

Nothing instills fear and anxiety in the minds of students like a big test. Wanting to study is one thing, but it can be difficult to without the proper guidance. It's important to build good study skills early in your schooling career--skills which will carry you throughout. Fortunately, studying is an issue faced at all levels of school by all students, so you can find help. Read below the jump to get started.

Steps

1. 
   1
   Calm down. Keep in mind that if you have a decent attendance rate, and did a reasonable job doing your assignments, you actually have a lot of knowledge already. This main knowledge will help you throughout your test.
   • Don't panic. Panic will only make your situation worse. You will be focusing on the horror, and not the upcoming test. Many times, panic can even deter your chances of doing well on the exam. If you panic, take deep breaths (try not to hyperventilate), and think that you can do this.
   • You're smart enough to realize you need to study days in advance. While some people study the day before, and some people always study this way, realize that last-minute cramming is not the ideal way to study, especially not for the sake of long-term retention of the subject matter. Also make sure not to study too much! Take some breaks for about 5-10 minutes.
2. 
   2
   Determine what material needs to be covered. Most exams cover specific subjects and material, and it's important to know which material or components you need to study. Otherwise, you may be using your precious remaining study time incorrectly. Ask your teacher about the subjects you'll be tested on and which chapters you need to cover. For example: What period in African history? Are diagrams important? Ask your teacher if you're unclear, as they want you to succeed.
   • Study the most important topics first. Exams usually cover a few core ideas, concepts, or skills. When pinched for time, focus your energies on the very important bits you'll be tested on, rather than scattering your studies everywhere. Review sheets, the highlighted topics in textbooks, and the parts your teacher stressed repeatedly are all clues as to what the most important topics or components are.
   • Find out how the test will be presented. What types of questions will be on it (multiple choice, essay, word problem, etc.)? Find out how much each section is worth. If you do not know, ask the teacher. This will help you know what the most important sections will be, and how the exam will be presented.
3. 
   3
   Make a study plan. It may seem like a basic and simple task, but people who make a detailed study plan often have an easier time with studying and they find they have more time to relax and chill. When making a study plan, build in the amount of time you have left before the exam date. Is the exam in a month? Did the teacher spring the test on you suddenly? Is it a mid year exam that has been building since the start of the year? Depending on the time frame, make your study plan long or short.
   • Determine what subjects you don't know as much about and include more study sessions on these topics. The aspects you know more about still need reviewing, but they will come easier, so try to focus on the more challenging topics.
   • Plan your time. It's tempting to put everything off until the night before the test. Instead, figure out how much time you will put aside each day for study. Remember to account for breaks. A good rule is: study for a half-hour, have a break for ten minutes.
4. 
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   Figure out your study methods. Study methods include using colors, pictures and brainstorm or mind map pages. Some people learn and remember things better if they're in certain colors whereas other people may remember diagrams and pictures more easily. Use the method that works for you; as long as it's effective, it doesn't matter what it is. It's no use reading a ton of text if your study method is diagrams. Remember, everyone has different methods to study, what works for your best friend may not work for you.
   • Use tools that will help you to study. Tools like flash cards may be boring, but really help memorize important things. If flash cards don't seem to help, typing out an outline of your notes may work.
   • Tape flash cards in random places to quiz yourself. This is a good way to sneak in study time, as discussed below.
   • Remember to study smarter, not harder.
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   Take notes and ask questions. It's never too late, and the sessions before the exam are usually for review, which is just what you need. If you're studying and happen to come across a part you can't understand, write it down. Ask your teacher either during class or during office hours. And don't worry – you aren't dumb if you ask questions. Questions mean that you're actively paying attention, and you're learning. Besides, a question ahead of time could mean a better grade on the exam.
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   Find your resources. Your textbook, notes, online sources, classmates, teachers, and possibly your family members can all be of use. Old assignments are especially good, as some exams have questions directly off homework.
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   Ask for help. You don't get bonus points for doing it alone. Classmates can be helpful in studying, but choose someone who will really help you, not the friend you tend to goof off with. Ask help from your parents or siblings; they may really appreciate being asked. Younger siblings especially like "quizzing" older brothers or sisters!
   • Form a study group. Not only do you have additional help, you also have the advantage of studying with people you know well. However, avoid accepting those that will be of no help, and only distract your whole group from studying. Don't be rude and reject everyone whom you don't like, but do be cautious about who you add to your study group!
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   Memorize as much as possible. The key to top performance is the ability to memorize all relevant materials. There are tricks for helping to memorize, otherwise called mnemonics. These can include, for instance, poetic or rhyming mnemonics for the auditory learner, visual imagery and fantasy for the visual learner, dance or movement for the kinesthetic learner (as muscles have memory), or some combination. Repetition is another form of memorization that is most commonly used. It allows for high recall if practiced in regular intervals. Practice it even beyond the point at which your memory recall is instantaneous, because this serves as a form of reinforcement.
   • A common mnemonic is HOMES for the Great Lakes. Another one is drawing stick figures to represent vocabulary words (like a good reason for drawing cartoons!). Create your own mnemonics that suit your needs.
   • Try rewriting down your notes to study. This is an effective way to memorize.
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   Sneak in study time. Short, repeated periods of study are often more effective than long periods of study. Go over your flash cards while waiting for the bus. Look over a diagram of the spleen while waiting for your breakfast. Read an important quote from "Macbeth" while brushing your teeth. Review the information during study halls or extra time at lunch.
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    Reward yourself. It can help to have a reward to strive for in meeting your goal. Have rewards in place for study milestones and for achieved results, in increasing value to you.
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    Organize yourself for the test. Be sure you have what you need for the test the night before. If you need a No. 2 pencil, a calculator, a German dictionary, or any other supplies, you must have them. The more put-together you are, the calmer you will be, and the more likely you will do well. Be sure your alarm clock is set, so you won't oversleep.
    • If you're allowed to take food in, take some jelly babies for a sugary hit, but it's best to stick to healthy fruit and vegetables. Apple or carrots make an easy snack that will help replenish your brain power.
    • Take a bottle of water with no stickers or labels (these could raise suspicions that you're hiding answers on them).
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    Eat properly. Good nutrition is vital for optimal thinking. Try to stay away from high sugar and fatty foods such as ice-cream and cookies. Replace sweet sugary drinks with a cool glass of water or a fresh juice or milk.
    • Have a "brain" meal the night before. Fish makes a great meal the night before, as it is nutrition for your brain. Try eating some fresh vegetables and pasta with the fish.
    • Eat a good breakfast. It will keep your mind alert. An example of a good breakfast is a glass of juice, an egg, toast, and cheese. If you do have to eat a bowl of cold cereal, make sure it's wholesome and whole-grain, not a sugary brand, or you may experience a 'crash' during the test.
    • Avoid drinking coffee, as this will only keep you up and provide you a sugar rush. Once the caffeine has worn out, you won't be able to keep your eyes open. Taking a test while you're drowsy is a no-no, so avoid intake of caffeine or any other foods too close to bedtime. All that digesting will keep you awake at night.
    • Be careful about making any abrupt eating changes; eat what you would normally eat on a regular school day in order to not disrupt your digestive patterns.
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    Get enough sleep before the big day. This step is extremely important and cannot be skipped. Without sleep, your chances of doing well on the test quickly lower, because your brain can't focus on what it needs to.
    • If you can't get to sleep, try some warm milk or tea, but be sure there is no caffeine in your drink!
    • Do not alter your sleeping patterns. Go to sleep at your regular time in order to keep your sleeping patterns regular.
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    Turn up ready for the test. Set your alarm clock in the morning; arrive on time or even a few minutes early. If it's a test that requires registration, fees, identification and the like, schedule extra time for that.
    • Keep a positive attitude! Studying lots, but thinking you can't really ace that exam, will reduce your chances of succeeding. See yourself as acing it, relying on all the preparation and attention you've given your studies to this point. Confidence is the key!
    • Aim high. Don't just aim to pass the test (if passing the test is quite easy), aim to get an A+. This way, you get a better grade. Plus, if you don't do as well on the next test, your A+ will still keep your overall grade high enough.

Tips

• If you were absent a day, and missed notes, diagrams, maps, etc., don't wait until the day before or even the test day to get these. Get the information in the time you have!
• If the teacher writes certain points on the board, this is usually an important indicator of what will be tested, and you should write it down as well.
• Study in a neat, tidy area, not a cluttered, papers-flying-around place. Have everything in order. Sharpen your pencils and get your erasers, pens, rulers, math-set etc.
• Avoid listening to music while trying to fall asleep, as this will only keep your mind active and prevent you from going to sleep!
• Sucking on a peppermint while studying will stimulate your mind, making it easier for you to remember the facts you need to know.
• Friends are not always a reliable source for notes. Get the notes from the teacher instead. The point of notes are to take down what you think will be important. Your friend and you may have a very different idea of what is important from the information.
• Don't keep looking at a phone, iPod etc! It is just a distraction when you are revising; you will definitely be tempted to text friends, listen to music, play games etc.
• When revising, try looking at past papers. Although it is unlikely that the same question will be asked, it allows you to test your knowledge, work on exam techniques and most importantly your timing!
• Some study guides the teacher gives you will not give you questions that will be in the test, but rather aspects that will be in the test, which you should have notes on. If you don't have notes on something, ask the teacher! Don't wait around wondering.
• Sometimes, listening to music while studying may help, but be cautious of the types of songs you choose. While classical music is an excellent choice, loud rock or songs that contain lyrics in them will not only distract you, but also prevent you from remembering the answers you need to know!

• It is sometimes assumed you just know how to study, but it's a learned skill. Ask your teacher, guidance counselor, and parents for these services if you think you may need extra help. If you feel lost about it, remember that you are not the only one.
• If you find that you still have trouble falling asleep, be sure you have eliminated all possible sources of light. Close all curtains and switch off any appliances that will produce light. Nightlights are not recommended for those that have trouble falling asleep with light.
• You mustn't procrastinate. You will not do your best on the exam if you do, and procrastination is a serious problem for some.
• Keep in your mind that you are smart and no one is better then you. Be confident. If you study well as recommended, you'll achieve your goals.

Warnings

• In some cases, friends may not always be the best with studying. If you miss questions on an assignment which you can use to study for the test, your best bet is to ask a teacher about the question you missed. Studying the wrong answer is one of the worst things you can do to study for the test.
• As for procrastination, do not use the "I'm going to study after..." because this is simply procrastination in poor disguise.
• Avoid cramming; it's not a good study habit. Next time, study consistently over the school year.
• Don't study so hard that by the time you see the answers your mind blanks out because you studied too hard before the exams and you're too stressed out to function. "Studying hard" doesn't mean studying to the point of utter exhaustion.
• Don't stay up too late studying. When faced with lack of time, study the main details only that sum up the information. If you stayed up all night and learned the material, you can still do poorly as a result of lack of sleep.
• Commercial notes like "Cliff Notes" may be appropriate study aids, but realize they're not substitutes for your own notes.
• Study groups can turn into a social event rather than academic discipline. It can help to have an adult monitor your studying, even if it's a helpful parent.
• Never cheat on a test no matter how desperate you are. Listen to your conscience. It can be worse to be caught cheating on a test than failing a class. You won't feel as good as you should if you pass the test. Aim to walk out of that classroom with pride, knowing you did your best. This is far better than false pride, and having to shove aside the thought that you cheated.
• Never say "I will study". When you say this, at that moment you'll only start studying.

Things You'll Need

• Materials to study with
• A good study area
• A fresh mind to start studying

HOW TO GET HIGHER MARKS IN EXAMS BY. MWL. JAPHET MASATU

HOW   TO  GET  HIGHER   MARKS  IN   MARKS  IN  EXAMS.

INTRODUCTION.

Absorbing Knowledge EfficientlyStudying Like a ProPreparing Your BodyAcing the Test

Have you got an important test coming up that you really want to ace? Do you generally want to improve your grades? There are a number of tricks and practices which can significantly improve your chances of scoring high on a test. This article will help you in studying, analyzing and solving exam questions, so read on!

Method 1 of 4: Absorbing Knowledge Efficiently

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   Pay attention in your classes. The best thing you can do to raise your test scores is to pay attention when you're supposed to be learning the material: in class! Letting your mind wander or not showing up at all are both likely to make you miss out on key information that will later appear on tests.
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2. 
   2
   Take good notes. This is important if you want to have an easier time studying later. Not only will writing the information down as you learn it help you in absorbing the information and paying attention, but you'll have a reference for when you go to study later.
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   Do your homework. Homework, such as assignments and at-home reading are where you will find the rest of the information that will be on tests, so doing this homework is important. Schedule time and set aside a quiet place just for homework to help beat the procrastination blues.
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   Use mnemonics and other tricks. Various memory tricks really can be useful for remembering certain things like numbers, categories, and lists. Just make sure that you learn them correctly and don't mix them up!
   • Mnemonics are phrases which can help you remember the order of certain things. For example, "Katy Perry Came Over For Great Songs" is a great way to remember the biological classifications (Kingdom, Phylum, Class, Order, Family, Genus, Species).
   • Another memory trick is if you have to remember a string of numbers. Instead of trying to remember 2537610925, for example, break it up like a phone number: 253-761-0925. You can break up dates this way too. 14 Oct 1066 (the Battle of Hastings) can become a locker combination: 14-10-66.
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   Do practice tests. Ask your teacher or go online and print a few practice tests. Taking a practice test will help you figure out how much information you actually know vs how much information you think you know. Knowing your weak spots before a test is crucial!

Method 2 of 4: Studying Like a Pro

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   1
   Study frequently. Studying hard for only a few hours the night before the test isn't going to help ensure perfect scores. If you really want to ace those exams, study old and new material every day, or at least several times a week. This will make test-taking a breeze.
   • Take study breaks. When you study, make sure you take a 5-10 minute break after every 30 minutes of study. This will help keep your brain from getting overloaded and give it more time to absorb the information.
   • On study breaks, try not to fill your brain with more information, even if that information is more about your favourite celebrity's latest concert rather than Winston Churchill's foreign policy.
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   2
   Study according to your learning style. You may know that different people have different learning styles. Some people are visual learners, some people prefer sound, some need physical motion, and so on. Know how you learn best and work that into how you study.
   • For example, if you learn better by physically doing things, try walking around while you study. If you learn better with sounds associated with the information, listen to music while you study. If you're a visual learner, make a chart of the information you have to know.
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   Take advantage of sense memory. Your brain is pretty good at associating smells or sounds with ideas or memories. You should take advantage of this! While you're studying, wear some unusual cologne or perfume (with a smell you don't usually encounter) and then expose yourself to that smell again right before or during a test.
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   Listen to music. Your teacher probably won't let you have headphones during a test, but you should at least listen to music, specifically classical music, right before taking a test.^[1] Studies have proven that exposure to certain types of music right before rigorous mental activity can really help, by waking up your brain and increasing your awareness.

Method 3 of 4: Preparing Your Body

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   1
   Eat right. The most important thing is to eat, full stop. Being hungry during a test will distract you and make you tired. Don't eat too soon before a test though, as some foods can make you tired. Instead, make sure you get a meal filled with lean protein before you have to take a test.
   • Eating healthy will generally boost brain performance too, so make sure you're always eating a healthy diet to help you learn all through school.
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   Sleep well. If you don't sleep you won't be able to focus when the pressure's on! Make sure to go to bed early the night before a test, rather than staying up all night to study. Your brain won't be able to hold on to all that crammed information anyway.
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   Have all the necessary supplies. Go to your test with all of the calculators, pens, pencils, blank paper, and other supplies you might need. Not having these things could mean you'll have a much harder time!
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   Drink lots of water. Getting dehydrated during a test can be distracting and reduce your ability to think clearly. Stay hydrated before your test and bring a bottle of water with you to the test as well.
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   Don't do anything different. If you aren't used to drinking coffee, now is a bad time to start. Try not to do anything different in your basic routine the day of or the night before the test. This can really throw you off.

Method 4 of 4: Acing the Test

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   Write important things down first. As soon as the test starts, write down all formulas or other important information on some scratch paper before you start going through the questions. This will help keep you from blanking when you need that information later.
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   Do the problems you know first. Always do the fast, easy problems to which you know the answer first. This will help make sure that you get as much of the test done as possible. If you get stuck, just move on to the next problem that you can answer quickly.
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   Cross out the wrong answers. Once you've answered the questions you know, move on to the ones you're not sure about. When you're dealing with multiple choice questions, eliminating answers that you know are impossible or silly will help you better decide between the possible options.
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   Look for clues in the other questions. Sometimes the answer to a question can be contained within or hinted at in another question on the test. Look at other answers or questions to help jog your memory.
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   Never leave questions blank. Unless you're docked for incorrect answers, never just leave a question blank. Especially if it's multiple choice; you'll at least have a 25% chance of getting the right answer.
   • As mentioned above, this is where eliminating wrong answers will come in handy.
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   Pace yourself. This is important! Always keep track of how much time you have and try to use your time wisely. You can always go back to check or improve your answers later!
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Tips

• Never fret over lost marks in previous exams and get depressed. Instead, take a deep breath whenever you think about it, be optimistic and study well for upcoming exams. This will help you to do well in your exams.
• A good timetable will help you. You may organize it in such a way that a long/hard subject takes more space than a short/easy subject. Remember, however, that all subjects should be studied.
• Studying while containing fear inside yourself is a waste. Get rid of fear and any other possible bad feelings before studying.
• Make notes while studying. Write a synopsis for your subject if you are studying it for the first time/ in the beginning of the school year. This will help you in the future examinations by allowing you to remember the contents of your subjects.
• Studying while having something in mind that you want to do is a waste of time. Do everything you want first then study; as your brain will not beg you to stop studying. However, if you have nothing in mind, then don't play (for example) before studying - finish your job towards school and then enjoy in the rest of the day.
• Don't be disappointed with bad previous results.
• Study in a silent place, so that your mind won't be distracted from what you're studying.
• There is no shortcut to success. This is the first thing you should remember. For this reason, you have to make a great deal of effort.
• Focus. When studying for your exam, be somewhere where there are no distractions. Also, make sure you have eaten and have had plenty of sleep, otherwise you could become tired and unfocused easily. Have no distracting things around you, unless they can be used as inspiration for helping you study (such as a cork board full of notes made throughout the year).
• Make a list of all the things you need to do to study for each subject, and how long you think it will take you. Use this information to make up a study timetable. Be certain that you have given yourself all the time you think you need, plus a little extra per subject, in your study plan. Also make sure your study plan has enough space in it, so if something comes up one day, you can shuffle around your plan so that you don't lose study time.

• Get rid of any unnecessary 'time wasting mechanisms' while studying. This includes TV, computer (only if you need Internet access), mobile phones, tablet, or even your siblings!
• When you are preparing for a test or exam- forget about the actual test or a exam and just know that what you are doing exactly.
• Attempt the questions which you find easy first and then the ones that seem harder.
• Write clearly and be direct to the point. Don't write any irrelevant information. Don't wrap the right answer in a wrong answer. Write in full sentences. Don't expect the examiner to link your sentences, fill in the space or any other thing. Think that the examiner is your little brother, and you are explaining to him. Will he understand anything by just telling him the keywords? No!
• Each subject has a unique way of preparing, studying and answering its questions. Some competitive exams (university exams, for example) need a long and complex preparation, while your school exams may need preparation of one or two weeks.
• Study in phases. Each phase should not exceed 40 minutes in time. Take a break after each phase (up to 20 minutes).

Warnings

• Never try to cheat. You are very likely to get caught, which would result in a zero. Be confident. Believe in yourself. If you have the attitude to do well, then you will!

HUMAN RIGHTS ----- CIVICS FORM ONE BY.