Introduction
Proofs always seem to be a hard concept for many (it's probably that we're too lazy to word out our reasonings for a mathematical problem). A proof is meant to help you understand what you're doing at an advanced level ,it can also give your answer some type of crediblity meaning that you actually have the work down by theorems or basic rules.
So how do proofs really help us?
Proofs are the problems we see that seem hard but really aren't. To many it's just a waste of time but if you ever want to correctly check your work a proof is the way to go. When you create a proof you get this credibility to your math problem even if your work is wrong you can easily fix it just by checking what you did wrong on the table.
How was the first proof ever like?
The firsts proofs were long and very wordy (no reason why we should complain now). One of the first proofs was put in the Euclid's Elements that also happens to be one of the oldest written proof. 
What are some of the main components of a proof?
Geometric proofs can be written in one of two ways: two columns, or a paragraph. A paragraph proof is only a two-column proof written in sentences.
Task
When creating a proof you must first know the basic steps to solving your problem.
1. You must start with the given in every mathematical problem you're given.
2. After you have put in the given you must find the next step similar to the given.
3. When finding all of the statements be sure never to forget to also find a corresponding reason!
Is there a limit on how big your proof can be?
It always depends on how complicated your problem is, but in many cases you can always use theorems or rules to make a proof shorter than it should be. So if you have a problem that seems to be really long I would try to find ways around that long path such as looking for certain math rules or focusing on getting straight to the prove.
Why should you always start from the given?
Starting with the given gives you an easy access to solving the prove. Usually the given helps you determine the rest of the statements meaning that if you have x=3 as the given and you must prove that 4x=12 then your answer would be the given because in the given you get the answer.
Why is it important to have a structured proof?
When you have a structured proof it narrows down the steps without even noticing. Creating one can help you determine the errors you could possible have when trying to find a reason for the prove.
Process
History of proofs:
Proofs can sometimes be in paragraph form but are most commonly used as a two column method.
5th century BCE in Greece where philosophers developed a way of convincing each other of the truth of particular mathematical statements.
The word "proof" comes from the Latin probare meaning "to test".
And, the purpose of proving a theorem is to establish its mathematical certainty. ’A proof confirms truth for a mathematician the way experiment or observation does for the natural scientistâ? [Griffiths, 2000, p. 2]
If you have a conjecture, the only way that you can safely be
sure that it is true, is by presenting a valid mathematical proof
What does the word proof mean and from what language?
Proof means to test and it comes from the Latin language
In what way do proofs give our work a valid understanding?
If we have the correct information on the proof it shows that we both know hwo to solve it and correctly explain what we're doing by using the correct formulas .
What was the first recorded form of a proof?
The first recorded form of a proof was in the Euclid's Elements.
Evaluation
Importance of a proof:
There's two types of proofs known as:
-Indirect Proof: Indirect proof means that we try to find a way of obtaining a result in some "round about" way. One way is by supposing that if the result we are looking for is not true, then the starting point cannot be true.
-Direct Proof: Direct Proof is possible if we have agreed definitions to start from and an agreed method (a logical argument) that enables us to proceed logically step by step from what we know to what we do not know, but think is true.
"Davis and Hersh [1981] argue that it is probably impossible to define precisely what type of argument will be accepted as a valid proof by the mathematical community"
When you have a problem and you need to solve it using a proof gives you a way of credibility and if you are uncertained about something you can always look for the error right away to fix it.
Many of the times when you have a problem someone might try to correct you even though your reasonings may be correct you can always show them your statements. By examining a proof, a reader can understand why a certain statement is true.
Although proofs seem hard at times when you create them you start getting the hang of the geometry rules and theorems you also start developing different ways of explaining different problems.
What are some ways proofs can improve your mathematical way of solving a problem?
Proofs can help us remember different ways of solving a problem.
Are there different types of proofs?
As I searched up there's two types such as indirect and direct.
Why do we keep using proofs if they don't seem important?
Proofs are not only used to help us improve ourselves but to gives us a reason for having that answer.
Conclusion
Proofs may stress us out but in the long run it can help us dramatically. If you want to correctly know each step and reason on how you solved it then proofs will definitely help yo!
Level 0: Visualization. Students can recognize a geometric figure as an entity (e.g., a square), but cannot recognize properties of this figure (e.g., a right angle).
Level 1: Analysis. Students can recognize components and properties of a figure. However, students cannot see relationships between properties and figures, nor can they define a figure in terms of its properties. For instance, students at this stage may observe that all rectangles have four right angles, but they would not realize that this entailed a square was a rectangle.
Level 2: Informal deduction. Students can recognize interrelationships between figures and properties and they can justify these relationships informally. Such students might recognize that a square is a rectangle since it had all the properties of a rectangle, but be unable to produce arguments starting with unfamiliar premises. For example, such students could not construct trivial proofs about objects that were unfamiliar to them even if they knew how that object was defined.
Level 3: Deduction. Students can reason about geometric objects using their defined properties in a deductive pattern. They can use an axiom system to construct proofs. Students at this stage could construct the types of proofs that one would find in a typical high school geometry course (e.g., isosceles triangles have two congruent angles).
Research Sampler 8: Students' difficulties with proof | Mathematical Association of America
What do the levels of proofs stand for?
They stand for the similar steps of finding and solving the proof chart.
If you could describe the level you use what would it be?
I usually go up to level 2 then get stuck but I always find a way to end up on level 3.
In a complete sentence describe how proofs will help you improve your grade?
Proofs can be used for any type of problem if I used proofs my grade can improve because I would be teaching myself the theorems and also learning different ways of studying.