Useful Tips

How to learn math from scratch on your own?


The curriculum involves the study of mathematics, which is one of the main disciplines. The study of mathematics consists in the study of arithmetic, geometry, algebra, higher mathematics. Despite the fact that higher mathematics is a complex discipline, some elements and basic concepts are still studied in schools and lyceums in high school. Most face problems in mastering mathematics, as this is a complex discipline. Someone loves geometry, someone likes algebra, and someone cannot learn either. How to achieve efficiency in the study of algebra?

Effective study of algebra is the right approach to the learning process, which means that the learning process should be clear and interesting. In order to achieve this, you can use presentations on algebra, which will clearly explain the material and help you learn it. Presentations on algebra can be used by both teachers and students. In the event that the teacher does not explain the material clearly during the lesson, the presentations will do it for him. The basis for success in training begins with an understanding of the material, and for this you need to highlight the most important aspects, remember them and structure your knowledge.

Some can not boast of knowledge in the field of algebra, even after graduation. Algebra needs to be understood in order to be taught, and knowledge gaps need not be allowed. Difficulties in the study of algebra may arise due to the teaching methodology of the teacher. Often, success in mastering algebra is based on the quality of the textbook. Is it worth it to depend on one textbook when you really want to learn algebra? A very good solution is the use of other useful literature and resources on the network that will help to understand what could not be understood using a fixed program and a single textbook. Nobody says that the textbooks are bad, they just cannot take into account the individualities of each student, which is why useful thematic literature is useful.

Useful books on algebra:

- “Modern elementary algebra in problems and solutions”, S. B. Hashkov

- “Algebra: Textbook”, A.A. Nechaev, M.M. Glukhov, V.P. Elizarov

- “Lectures on Algebra”, A.A. Zykov

- “Introduction to General Algebra”, L.A. Kaluzhin

- “Basic concepts of algebra”, I.R. Shafarevich.

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Moral training

Before you begin to study mathematics, you should be mentally prepared. This is especially true for those to whom this subject was practically not given at school. After all, it happens that a person has not a mathematical, but a humanitarian mindset.

Below we will discuss what to do if you cannot figure out one of the topics. But in any case, you need to be prepared for a long study, because to quickly learn math is actually almost impossible.

Moral preparation is to:

  1. Try to make it clear that you can study any science if you wish. After all, somehow excellent students and good guys are well-versed in discipline. Moreover, if the teacher says that this is an easy topic, then it is worth believing.
  2. For a while, postpone entertainment, chatting with friends and various activities that are not so important in order to enhance knowledge of the queen of all sciences. Let the bulk of the time be devoted to the study of obscure topics.
  3. Before class, give yourself a good rest. For example, take a walk in the fresh air in the park, perform several physical exercises or urgent tasks. For it is very important that no worries and requests from the outside are distracting.
  4. Tune in to training your memory in order to remember the rules and formulas. They are actually not as complicated as they seem.
  5. To understand that mathematics for the most part requires logical thinking and ingenuity from a person.
  6. To take science not as something for granted, but as a puzzle game in which you need to go through specific stages and check the "backup option" for the correct solution to the problem.
  7. Convince yourself that memorization training is good for the brain.
  8. To understand that the solution of many problems and examples, the construction of figures and graphs, as well as various geometric proofs, is an exciting process that can be put into practice.

Let these recommendations become helpers for you every time you want to leave the study of complex topics. It turns out that it’s not so difficult to learn math from scratch.

Assessment of your knowledge

It is very important to be able to evaluate your knowledge. For example, you are a student of grade 9, or at the moment it’s summer, and the goal is to get a good look at the topics that were missed and not understood before. In this case, we do this: open the textbook of the 5th grade, find any complex problem and solve it. If the answer is correct, then we can easily proceed to the tasks for the 6th grade and check ourselves against them. It is advisable to solve a couple of tasks from each topic.

Now let’s figure out how to quickly learn the rules of mathematics.

There will certainly be a problem that you find it difficult to solve. For example, the topic is related to quadratic equations, but the example is given in the form of two works with brackets that need to be expanded. And you forgot the rules for opening brackets, as a result of which the answer is incorrect, the verification solution does not converge. In this case, it is worth noting in a separate sheet-plan that you need to figure out in which case the “+” sign is put, and in which “-” when opening the brackets. Other topics should also be considered.

A bit of geometry

As for geometry, it should also be studied first, in order to understand what figures, theorems, and how to work in this discipline in general.

But how to learn math in a short time, if almost all topics are incomprehensible or unfamiliar, and is this possible? Here are some suggestions.

If a lot is lost

Is it worth saying that it is best to disassemble math from scratch with a tutor or relative, a classmate? It is quite difficult to study this subject yourself, especially in comparison with history or geography. Nevertheless, if there is a lot of free time, you can try to solve the examples yourself. For this, it may be necessary to study in more detail simpler topics, which are mainly included in the 5th grade program.

Now we will make a plan of our actions:

  1. Get textbooks and solvers for all high school classes. The program should be consistent with what you study in school.
  2. Make a list of all the topics that are available.
  3. Prepare a blank notebook for solving problems. It is not recommended to solve examples on pieces of paper, let all the actions taken be before your eyes, even if they are blots and mistakes.
  4. If you still have notes with lessons learned and examples solved in the class, be sure to work through them. Write down the task in the notebook, then close the abstract, start solving it yourself. As you finish, check what you did right and what is wrong.
  5. Learn the rule and formulas for the current topic. Remember that mathematics does not “like” to cram, it “likes” to understand the definition.

This approach will help you learn math on your own. How to remember everything at once? In fact, this is not necessary.

Best way to remember

As mentioned above, ordinary memorization will not help. Need to figure it out. Suppose you have a topic related to finding the definition of the volume of shapes in geometry. These formulas are quite simple and easy to remember. But in order to better learn the lesson, it is advisable, following the formula, to solve the problem. At the same time, you will notice the sequence: what depends on what and how it is displayed. For example, an elementary finding of the area of ​​a rectangle: we multiply the lengths of two sides that do not lie in parallel. And that’s it, the problem is solved. It is much more difficult to determine the area of ​​a circle or the volume of a cylinder, but if you remember the formulas, then this will not be difficult.

And how to learn mathematical rules if they are not connected with formulas? Everything is pretty simple. For example, the same parentheses. You just need to remember that "multiplying minus by minus gives plus, and multiplying minus by plus (and vice versa) always gives minus." And that’s all. In the future, to solve even the most complex tasks for opening the brackets will turn out one-two!

Successful development

The knowledge gained should always be reinforced. Do you remember the discriminant formula or memorized the sequence of finding the unknown through the construction of graphs. Be sure to solve various examples on this topic again and again, so that everything is stored in memory.

Teachers, and tutors, recommend from time to time to return to the topic to test yourself. It actually takes a few minutes. Surely you have noticed that those who are in time in mathematics are capable of passing the work, which is designed for half an hour, in 15-20 minutes. What is so surprising here? It’s just that the topic was mastered quite well and there was no need to rack one's brains for a long time, remember formulas or try to ask a neighbor.

How to learn math 5 minutes before the control, and is it possible? Of course, if the previous sections are mastered well, and the current has not been studied for some reason, then you can go over the rules and formulas. But success will be only if the topic logically continues the previously studied ones.

It’s not given and that's it

Unfortunately, most students cannot understand science either in the classroom or on their own. It is necessary that the topic is explained separately. Often you have to resort to the help of a tutor.

But there is an opportunity to learn math from scratch on your own and for free. Naturally, with the help of the ubiquitous Internet:

  • YouTube video tutorials
  • orientation courses on math sites,
  • online tutor.

Thus, you can find a way to understand the topic without unnecessary costs. There are many video tutorials on individual topics that are easy to learn by looking at how to correctly and in what sequence the tasks are solved. It is advisable to repeat the lesson by yourself.

If the topic is very complicated

There are a lot of complex topics in mathematics, especially in grades 9, 10 and 11. Often, the help of knowledgeable people can not do. Therefore, it is worth listening carefully to the lesson so that there are no problems in the future.

After all, even the most complex topic lends itself to explanation and understanding. You just need to train your perseverance, patience and desire to learn. Indeed, for a reason this word means "teach yourself." Many students closer to the final exams ask how to learn math so that the score is high. It's simple: you should prepare in advance (work through all the topics and solve the proposed problems).

Necessary tools for work

Many teachers insist that students memorize the multiplication table, learn to count in the mind, and do without calculators as much as possible. Indeed, did mathematics exist somehow without electronic computers? There were scores, but they only developed thinking. And modern gadgets, on the contrary, weaken mental activity and impair memorization. Therefore, it is better for a modern student to take care in advance about how to learn mathematics, or rather arithmetic, so that in the future it would be easier to solve any problems without the help of a calculator.

As you can see, mathematics is a complex science that requires perseverance. You won’t be able to quickly learn it. Therefore, it is advisable to carefully study each topic from the elementary grades.