Maria Gaetana Agnesi: suggestions from the past to new way yo teach calculus

In 2018 we celebrated the three hundredth anniversary of the birth of Maria Gaetana Agnesi, mathematician and benefactress born in Milan (Italy). We have examined the Analytical Institutions,the main work of Maria Gaetana:, that she dedicated to students education. We think that pre-university students can acquire the fundamental mathematical ideas in Differential Calculus using methods and ideas proposed in the books that go back to the origins of the Analysis. From this point of view, we can use many suggestions and examples, contained in Agnesi’s Books. [1] We can propose these arguments or problems by means of laboratory instruments, flipped classroom techniques, or by didactical methods and we think that the media are different but the meaning is the same. According to some scholars, the abstract approach, nowadays we use, can be didactically not very effective for the beginner student. They think that an intuition of infinitesimals can be oriented to lead to mathematical concepts. From this point of view, we present the way in which Maria Gaetana Agnesi presented the cycloid, a traditional curve that nearly every mathematician used as example for demonstrating the power of the differential calculus techniques.