The article describes effective strategies for learning the concepts of higher mathematics, which will be useful for those who teach mathematics independently.
We’d all like a better understanding of math. Many of the tips below will be useful for those who teach math and more.
These rules should be treated with respect, because they were developed for a long time by the best minds. Your mind must be open to it: blind memorization will not yield results. Memorization of mathematical facts by those who teach mathematics usually occurs naturally in the course of repeated use of the previously learned fundamentals.
Don’t worry if you don’t understand some concept of mathematics on the move. It’s proven that the brain evolves even when you make mistakes. You don’t have to worry if somebody’s problem solving is easier. More often than not, it’s just a matter of experience and discipline in the mind. Our books and courses will help you wake up your math.
Many of those who have taught or are still teaching maths have faced this situation. What is not interesting at a particular point in the current stage of learning becomes clear and even fascinating later after passing the curious nowadays topics. Interest can develop from the need for a certain type of knowledge. If you are passionate about artificial intelligence, you immediately understand where linear algebra, probability theory, etc. will be useful.
Try to focus on only one topic within the allotted time interval. It is better to switch between global areas rather than adjacent mathematical concepts.
If you need reference material, such as a collection of formulas, use topic guides. This includes short ones – the same cheat sheets that are easily found on request “[topic of study] cheat sheets”.
If the task cannot be solved for a long time, leave it and start again later. Go back to it until you solve it, but don’t spend too much time at once. At some point, the brain will learn enough on other tasks to solve a more complex one.
If you feel you have reached a dead end, do not hesitate to ask for help, including on the Internet – from those who are still learning math or already an expert. If you see the situation with different eyes, you will discover previously unknown sources of solutions.
It is crucial to warm up. Nutrition to brain tissue carries blood, and if blood flow is difficult, learning is harder. Make it a rule to warm up every 45-50 minutes: walk around the room, squat, do exercises. So that the blood can be saturated with oxygen, exercise in well-ventilated rooms.
A change of scenery is also important. After half a day of exercise, take a walk or work out, do your homework. After a week of study, go to the countryside for a rest. The change of scenery gives a feeling of freshness, gives a new perspective on the tasks at hand.
Do not neglect the food. It has to be balanced. Thinking processes are among the most energy consuming tasks solved by the human body. You can “motivate” the brain with small snacks after solving a predetermined number of tasks, evenly dividing meals according to the number and difficulty of tasks. Eat more polyunsaturated omega-3 fatty acids – they directly affect thinking concentration and brain activity. Drink enough water.
Avoid stress. One of the most common types of stress for the body is lack of sleep. Sleep deprivation is a catastrophic decrease in mental performance. It helps to recover not only at night, but also a short sleep during the day.
Analogy, Diagram, Example, Explanation, Term. At the beginning, ask yourself the question: Have I ever seen anything like this before? For example, the concept of electrical resistance is similar to that of fluid movement in a pipe. Connect the knowledge you are getting with the knowledge you know before, include it in an existing picture of the world. Remembering by association is more effective, while the isolated knowledge is removed first by our internal “garbage cleaning” system.
Diagram. Visualize the concept. A concrete image should appear before your eyes, on which you can rely for further reasoning. It can be a drawing, a list of elements, a table, mindmap, etc.
An example. Consider a concrete example of using the concept, try to solve the problem, get the first experience in using the material.
Description. Describe the concept in your own words: what it consists of and what is needed for.
The term. Finally, give a strict technical definition linking the concept to other terms. This formalizes the understanding and allows communication with specialists in the same language. How fast prep for gre math?
Write and draw when writing a synopsis, but do not print it. The use of motor skills stimulates our creativity and allows the brain to absorb the material better. If you are afraid of losing records, scan them.
When taking a rest break, do not try to come to the logical conclusion of the topic. Make full use of the specific time you decide to spend on the class, but once it has expired, take a break immediately. Ideally, go to the peak of the topic. This advice is based on several psychological prerequisites.
First, the lessons in this form have a strictly outlined framework. You will not wear yourself out and will not spend extra time. And, therefore, you will treat the lessons more enthusiastically. Check out workbooks for 4th grade.
Secondly, it will be easier for you to enter the working rhythm starting the next class. By slightly refreshing your knowledge, you can quickly adjust your brain to new activities. When the start of a new topic coincides with the start of the activity itself, extra effort is required to get into it. This is the most difficult place to take from acceleration.
Third, when you get used to thinking about mathematical abstractions regularly, this approach will allow you to develop mathematical intuition. Despite the fact that you have interrupted the class, the brain will continue to work and build a logical chain of reflection on its own, without the support of educational material.
At the very least, you can be the listener yourself. Explain the topic to your imaginary student from start to finish. You will see that from this angle you have been able to understand it more deeply. This approach obliges you to understand all the obscure places.