# What are the mistakes in math

## Chapter 20: Calculating Errors

About failure and problem solving: You can explain why mistakes are part of math.

Mistakes belong to mathematics like a fox to a hen. We would like to prevent this combination at all costs. But mistakes all have to occur once so that we know what we want to prevent in the first place. That is the point of the exercise. In training, this is possible without risking life (for fox or hen). We look at the different types of errors.

### 1. What is a bug?

Calculation error. If you make a mistake while calculating, you will get a wrong result. False means: the result is not true. Sometimes calculation errors mean that we cannot continue calculating. Then we get no result at all. There are typical errors in every type of calculation. We want to do them all in exercises so that we can easily recognize them during exams.

Example: You hit a nail into the wall with a hammer. The hammer slips. The nail goes crooked. Solution: training. We drive many different nails into many different walls with many different hammers.

Sign error. This is actually also a calculation error. It has to do with omens. Plus + or minus - are incorrectly combined with each other. Sometimes we get a wrong result. Sometimes a sign error also means that we get no result at all. We can often spot sign errors by considering whether the result makes sense.

Example: You drive the nail into the wall upside down. Solution: Once we've tried, we'll quickly spot the wrong result if we just look.

Methodological errors. Either we are using a wrong method or we are using a method incorrectly. We believe that we get a result through a certain way of calculating. If we do something wrong, we usually get no result at all. We can prevent methodological errors by not throwing away the calculation in the exercises when we make a mistake, but rather by talking about why the chosen method or the way it was applied did not lead to the goal.

Example: You are using a banana to drive a nail into the wall (incorrect method), or you hold the hammer upside down as you drive in (incorrect use of the correct method)

Mistake in reasoning. Sometimes we just get things wrong. We believe it is so, in reality it is different. We can prevent mistakes in thinking by talking to other people about our thoughts. Often when we speak, we notice that we are thinking wrongly. Or someone else notices.

Example: You nail oranges on the wall because you think this would be a good way to store them.

Specification error. We are wrongly transferring a number from the specification of the task onto our paper. If we can't find a bug while troubleshooting, we should also think about a specifying error. We can prevent information errors by writing nicely and transferring all information from the information to our paper in an orderly manner.

Example: You drive 50 nails into the wall when it should actually only be 5 - for 5 pictures.

To forget. That is also possible. We haven't thought of something. We could prevent these mistakes by doing exercises more often. We can calculate an example, and if everything is correct, we copy it off again. Through this repetition, we train the sequence memory and we forget less when doing similar calculations.

Example: You hit the nail right into the wall, but forget what you did it for.

### 2. Prevent mistakes

Make mistakes. Best of all. Each chapter has its own flaws. If you know them, you can know them. And then all that is needed is training through practice. This exercise must take place before the exam.

Example: A pilot trains all possible types of errors in the flight simulator before he controls the aircraft without errors.

Improve learning conditions. Get to class on time. At the beginning there is often important information. Switch your mobile phone to airplane mode. If you are interrupted while practicing, you will not be able to achieve a depth of concentration. Have a say. If you say something wrong, responding to it will help you improve it. Practice regularly. If you do something more often, the environment becomes familiar. Be proud - with mistakes. Mistakes only become weakness when you don't want them to be found.

Mistakes are bridges. We have to look for them. If we know them, we will reach new shores.

Corrections: Maria Fatoba

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