An unusual way to learn mathematics: "Errors in learning mathematics"
The idea is not that we can assume the errors, but that we learn from them, that is to say from a mathematical application if we analyze the errors committed in each exercise that we solve, in each demonstration that we want to make, in the approach of a problem the information is obtained about how knowledge is built in the learning process.
It is an inescapable process that we make mistakes every time we want to learn a mathematical concept, not for that reason to learn we are going to look for mistakes every moment, if we consider it as a natural process of our way of learning, we will notice that every time we make mistakes , that error marks us in our memories, and we will hardly be wrong in that part, that is the advantage of error in mathematics. It is a way of learning taking advantage of the negative, that is to say, no one likes to be wrong, but if that error serves to mark our starting point in which we do not make that mistake, then we will learn many mathematical concepts that will be fundamental in our academic training.
How to build our own style of mathematical learning through mistakes?
The first fact that we must consider is that the errors within the mathematical learning should not be intentionally sought, before this we must exhaust all the traditional resources to acquire mathematical knowledge and be able to learn, then within this same formation, without us wanting it, the errors, those that mark the most explicit senses of our memory, those that remind us at every moment that we should not make the same mistake, so I reflect on the following:
How to know if you are going in the right way?
We will not know if we are on the right path if it is not until someone or something tells us that we must correct and take another path. That someone or something is the error, the error is the exact measure that tells us what to correct, but this correction is what marks my understanding of learning. Now this learning by mistake must be accompanied by an analysis and deep reflection on the fact of correcting the error, it is also the reflection on the fact of the error that will make us learn so that we never forget that knowledge that will mark the seeds of our learning .
When we learn mathematics, there is a succession of continuous moments in which we make mistakes to learn about a specific topic, which is why we should ask ourselves the following question:
What are the types of errors that are committed when solving a Mathematical problem?
If we want to learn from the negative in what mathematical learning has conferred, it is necessary that we know the types of errors that are committed when we enter to solve a mathematical problem. The knowledge that we can have in the type of mistakes that are made will allow us to adapt ourselves in different forms of learning, and that in this way we can even interact in a different way in the fundamental teaching-learning process.
In my own experiences as a teacher at the Universidad Experimental Sur Del Lago (UNESUR), I usually take a test on the first day of classes, so that the student can demonstrate the basic knowledge that he / she must possess in order to enter the learning of the new academic year. From what students respond in that test, I try to focus on the mistakes they made, from there to focus all my teaching strategies and direct them to those errors that result in weaknesses, and then with the application of new didactics of teaching, they can learn, and that ironic but they can learn from their own mistakes.
Errors found in analysis studies done at the university of Calculus students.
One of the most common errors and in which I am responsible for correcting while teaching is the inability to analyze the final results of each exercise, so that these results serve as an interpretation for many applications framed in the area of Engineering.
Reassessing your form of study is essential to work based on the error that students make in their study methodology, we can say that it has only been enough to tell them that rote learning in mathematics without the help of theorems, axioms and corollaries do not work , because by normal nature of human thought, man has always been trained to be analytical and look for the why of things, the study and learning of mathematics does not escape this fact, which is why if I observe that there is a decline in learning by errors in the study methodology, I try to focus all my efforts on changing that way and style of studying mathematics.
Conclusion
These examples of errors found are a peculiar form found in my studies and analyzes found in the classroom, it is necessary that all teachers who want to focus on mathematical learning based on errors found in their students, enter a stage of deep experimentation and diagnose their reality, and through this reality make a teaching methodology that can attack those errors, and where it can be marked and fixed learning for their students.
I've never liked math, and it's never enjoyed my company either. I think I learned math by rote rather than analysis. Contemplation. You sound like a great teacher. Taking that test on the first day is probably disliked by the students, but it benefits them and you together.
Of course you can try a diagnostic test to check if there are errors of a conceptual nature in mathematics, and in this way to focus your pedagogical skills in mathematical learning from those errors. Thanks for comment. regards