What do you want to optimise with our study tips?
Completing a successful university career is not easy, especially since all students mostly have school subjects in which they can learn better, but also always those in which it is difficult for them to be interested in the subject and to remember important definitions, technical terms, connections, vocabulary, exercises etc. However, with ExamPrep we have developed an optimal learning system that contains many useful learning technique tips.
Here you can already look for yourself what you would like to improve with our learning technique tips:
1. Learn with index cards and query systems
2. Better timing
3. Formulate aims correctly
4. Write good summaries
5. Read faster, memorise more
6. Emergency programme: short-term exam preparation
7. Mind Maps – skillfully used
How do you learn math?
Learning math works only by doing math.
However, this can be quite frustrating when you e.g. can’t do a single homework even though you were in class. What to do if you just have the feeling “I can’t do math”?
What are possible difficulties?
The statement “I cannot solve this task” can mean many things:
- I do not know some of the terms used in the task text.
- I get stuck somewhere, get no solution, or my solution is wrong.
- I do not know what to do.
It is important to ask yourself which of these three points is the problem for a specific task or topic (e.g. exam preparation).
If you do not know terms, it is necessary to look up the definitions. In mathematics terms are used very specifically, often you can only solve a problem if you know exactly what is meant by a particular term. The task also indirectly asks e.g. “Do you know what properties a right triangle has?”
So ask yourself: “What are the terms that are used over and over in class at the moment? Can I imagine something under these terms, have I seen how they are used? Did we even write down a precise definition? “
If you don’t know what to do with a task, it can e.g. the reason is that one does not read the task text exactly. Mathematical tasks have to be read slowly enough, sometimes a single word decides what is actually meant.
There is also a widespread misconception that a math problem has to be solved in a very specific way, and if you don’t know the trick or the appropriate method, you cannot solve the problem. Even the simplest equation can be transformed in different ways and lead to the correct solution, but of course some procedures are much easier than others. Of course, it’s worth remembering the most useful tricks and the simpler methods, but it doesn’t mean that you have to learn a new method for each new task.
Don’t think so much about “cooking recipes” that you have to learn by heart, but rather about “tools” whose use you should practice until you can use them quickly and safely.
So ask yourself: “What methods of solving problems on this topic did I learn in class? Which methods are used again and again, which of them make sense to me, which ones have I already been able to use? “
If you cannot complete a task or the result is incorrect, it is an important opportunity to learn something. If you solve tasks for hours before an exam, but can’t do anything, the time is of course not used very well!
If you have a solution to the task available (e.g. an example from class or in a theory book), or you can ask someone, the question should be:
“What information from the task text did I forget or did I not notice? What is wrong with my approach so that the result is wrong? At which point did I not think of a necessary step myself and how exactly does it work? “
It is very important, when the task has been completed, to pause briefly and not simply to start the next task, because otherwise the learning effect will not be as great as it could be. At this very moment, you have to reassess yourself why you couldn’t do the task alone. So not just “Now I know how to do it”, but “I have confused this term or overlooked it in the task”, “I have used this procedure incorrectly, but I now know when to use it and when not to use it” or maybe “I always forget that one could also exclude in this situation”.
Maybe you want to write down such places on a separate, special sheet, on which you also write down the questions that you still want to ask in the classroom and where you can also write down the answers.
The best thing to do after a moment like this is to try to solve the same task again without looking at the previous notes: Is it now possible to go without looking up?
The general rule is: unfortunately you don’t learn to solve math problems by watching someone solve them or simply by reading a pre-solved example. Only when you try it yourself will you see what is clear and where you are still stuck.
What exactly do I want to learn?
Make sure you exactly what you want to learn. Mostly it is about being able to solve problems better in exam situations. But it can also be the case that you don’t get along in the class and feel that you don’t understand enough about the theory behind the tasks.
Learn to solve problems better:
It is very important to learn to differentiate between different requirements in math tasks. Otherwise you get a general feeling of “I can’t do it” and don’t even know where to start. There are several levels of requirements, and they can and must be practiced in very different ways:
Notation and transformation rules:
Of course, you have to know how the mathematical symbols are defined and which rules apply to dealing with them. Sometimes it can be confusing that certain transformations are “allowed” for certain operations, but others are “prohibited”.
The “algebraic craft” such as exclusion, factorization, adding fractions etc. especially requires practice. Of course there are rules on how these transformations work, and all of these rules can be understood, but unfortunately it doesn’t help much if you have understood all the rules (especially if you have noticed where there are pure definitions, i.e. conventions, hidden, which you don’t understand at all, but can only take note of), because you have to be able to make these transformations quickly and safely. Since an exam has to be solved with a time limit (but also the homework should be able to be done within a reasonable time), it is imperative to reach a minimum level here, otherwise you will get stuck at this hurdle in all difficult tasks. Unfortunately, it is of little use if you can correctly transform a word problem into an equation, but then you cannot solve it correctly because you do a simple transformation incorrectly.
Establishing equations, algebraic formulations of word problems
“Translating” linguistically formulated tasks into mathematical equations is tricky and is the main difficulty with such types of tasks. The approaches required for this cannot simply be memorized, but must be practiced again and again using many different examples. As already mentioned, it is necessary to read the task carefully and slowly, and to ask yourself:
“What is in demand?”, “Are you looking for a (or more) specific size?”, “Are relationships between the size sought and the given sizes formulated?”
Theory for this type of task
Dealing with notation and algebraic transformation rules and establishing equations alone are not sufficient for all types of tasks. Depending on the field of mathematics, you need “some theory”. For example, it is necessary to know certain relationships, called “mathematical laws” (keywords such as Pythagorean theorem, solution formula of the quadratic equation, vector product, integral, etc.) Can the task be assigned to a specific topic? Are it e.g. Exercises for an exam on a specific topic? Then of course the question is:
“What laws on these sizes have we covered in class?”
But be careful: Not every task that deals with a figure can be easily solved with geometric means, and not every pure text problem has to be solved with an equation. As soon as you have the feeling that you have found a usable solution to the problem, ask yourself: “Could the problem be solved differently, perhaps even more simply?”
When do I study?
Do I have to understand the theory to be able to write an exam? Unfortunately, understanding is not a guarantee of being able to solve a task, but it is also not a prerequisite. You can learn to solve a task of a certain type without understanding why the procedure works, and you cannot solve a task, even if you understand the whole theory behind it, if you do not master the tricks for this type of task.
That is why it is important to keep taking turns. When defining new terms, simple questions about those terms can help you apply them correctly and make sure you understand them. When solving tasks on a particular topic, you may discover that you have not yet fully understood the theory behind the topic.
How do you best proceed? What can you start with?
- Shortly before the exam: If the whole theory is not yet understood, you still concentrate on the tasks. As I said, you can also solve tasks if you have not understood everything. While this is not ideal and undesirable, it is of no use if you have not practiced enough for the exam because you are still stuck in theory.
- Enough time: As just described, you alternate cheerfully. Too much theory tired in one go, too many tasks to understand terms that don’t mean anything to you also frustrate.
- In class: It is unbelievable how much more you can benefit from attending classes if you do not simply listen to how questions are answered that you did not ask yourself. Therefore: Before each lesson, ask yourself questions like:
“What is the current topic, which terms are used frequently at the moment?”, “What did I write down last hour?”, “What were the tasks for today and what problems did I have?”, “What specific question would I have on the topic would like to get an answer today? “
This focuses your attention, you can follow the lessons much better and if you have terms that are still difficult for you, you may even be able to ask a question yourself.