I want to start this publication by making known certain aspects of my initial education, when I do my studies at a diversified level (prior to the superiors), the education that was taught in the order of mathematics did not include in their programs, studies related to infinitesimal calculus , that is to say the study and understanding of limits, derived and integral. The new educational order of this generation has tried to include in its diversified secondary education training programs a basic way of teaching the concepts related to differential and integral calculus, in which they may be learned in a tangential way. To somehow know how they arrive prepared regarding concepts related to the differential and integral calculus the students that we receive in our universities, it is necessary to evaluate the following question:

How do teachers of mathematics at medium and diversified levels of education perceive some concepts that will be used at higher education levels?

In order to get an adequate response regarding the way in which middle school teachers conceive this type of concept, I have decided to address the problem by addressing the classrooms of the most important institutions in my area (San Carlos de Zulia, Zulia State, Venezuela), and to carry out a questionnaire of technical questions related to the concepts of differential and integral calculus with the purpose of knowing the level of understanding of these professors, and in this way to evaluate the level of education that our students are receiving prior to their studies at the University .

The questions you ask are described in the following order of ideas: To get an appropriate response regarding the way in which middle school teachers conceive this type of concept, I have decided to approach the problem by addressing the classrooms of the most important institutions of my location (San Carlos de Zulia, Zulia State, Venezuela), and make a questionnaire of technical questions related to the concepts of differential and integral calculus with the purpose of knowing the level of understanding of these professors, and in this way to evaluate the level of teaching that our students are receiving prior to their studies at the University.

The questions you ask are described in the following order of ideas:

1. Do you apply the concept of change ratio in the applications of the derivative?

2. Do they introduce forms of reasoning through demonstrations to the concepts derived from differential and integral calculus?

3. What importance do you give to the theoretical aspects as a basis for learning in the applications that have the aspects of differential and integral calculus?

The questions mentioned above were addressed to two teachers of mathematics for each school, visit a total of 4 schools, which represent a total of 8 teachers consulted, which all confirmed and were correct in the following:

We only provide a basic knowledge for the learning of differential and integral calculus from a series of formulas that lead to solve the exercises that the texts pose, and that for the deep analysis using certain concepts as a reason for change , teaching from demonstrations is a part that they consider limited due to their poor comprehension in the students, and finally they mentioned that the theoretical aspects within the aspects related to the differential and integral calculus are of great relevance and importance for the learning of the students, although they have not adapted the mechanisms so that it is easy to accept and understand in the students.

Based on the study conducted, I can conclude the following:

• In a first level of analysis the questions posed in the questionnaire reveals a null understanding of the concept of derivatives and integrals, and also an encapsulation of the same, this has to do in some way with the difficulties that students have with the understanding that later they have with concepts related to the calculation, such as limit, infinity, the idea of ​​function and demonstration.

• The research also showed that it is possible to involve the teacher in a renewed and meaningful process of comprehension based on the resolution of problems oriented to collaborative work between different educational communities and thus achieve significant learning of the infinitesimal calculus.

• There are several concepts related to various areas of mathematics that are taught at higher levels of education, hence it is interesting to ask teachers at more basic levels conceptions, beliefs, levels of understanding about such concepts.