It is well known that learning epsilon-delta definitions is difficult and is the intellectual equivalent of jumping over a tall wall in order to join the enlighted ones on the other side, a feat never accomplished by at least three-quarters of the student population in calculus (a conservative estimate).

It is clear that students need some preparation that would serve as a ladder to help them over the proverbial wall. The use of alternating quantifiers needs to be prepared. This can be done either by giving a series of examples of formulas of increasing quantifier complexity, or by providing a more intuitive approach to the key concepts like the derivative and continuity first.

One recent proposal in the literature is to teach them rigorous infinitesimals as a way of providing a ladder so as to climb the Epsilontik wall. Once the students understand the basic concepts like derivative and continuity via their intuitively appealing definitions exploiting infinitesimals (essentially following Cauchy's approach), they are in a better position to scale the long-winded epsilon-delta paraphrases of those definitions.

It is well known that learning epsilon-delta definitions is difficult and is the intellectual equivalent of jumping over a tall wall in order to join the enlighted ones on the other side, a feat never accomplished by at least three-quarters of the student population in calculus (a conservative estimate).

It is clear that students need some preparation that would serve as a ladder to help them over the proverbial wall. The use of alternating quantifiers needs to be prepared. This can be done either by giving a series of examples of formulas of increasing quantifier complexity, or by providing a more intuitive approach to the key concepts like the derivative and continuity first.

One recent proposal in the literature is to teach them rigorous infinitesimals as a way of providing a ladder so as to climb the Epsilontik wall. Once the students understand the basic concepts like derivative and continuity via their intuitively appealing definitions exploiting infinitesimals (essentially following Cauchy's approach), they are in a better position to scale the long-winded epsilon-delta paraphrases of those definitions.

It is well known that learning epsilon-delta definitions is difficult and is the intellectual equivalent of jumping over a tall wall in order to join the enlighted ones on the other side, a feat never accomplished by at least three-quarters of the student population in calculus (a conservative estimate).

It is clear that everybody would agree that students need some preparation that would serve as a ladder to help them over the proverbial wall.

One recent proposal in the literature is to teach them rigorous infinitesimals as a way of providing a ladder so as to climb the Epsilontik wall. Once the students understand the basic concepts like derivative and continuity via their intuitively appealing definitions exploiting infinitesimals (essentially following Cauchy's approach), they are in a better position to scale the long-winded epsilon-delta paraphrases of those definitions.

It is well known that learning epsilon-delta definitions is difficult and is the intellectual equivalent of jumping over a tall wall in order to join the enlighted ones on the other side, a feat never accomplished by at least three-quarters of the student population in calculus (a conservative estimate).

It is clear that students need some preparation that would serve as a ladder to help them over the proverbial wall. The use of alternating quantifiers needs to be prepared. This can be done either by giving a series of examples of formulas of increasing quantifier complexity, or by providing a more intuitive approach to the key concepts like the derivative and continuity first.

One recent proposal in the literature is to teach them rigorous infinitesimals as a way of providing a ladder so as to climb the Epsilontik wall. Once the students understand the basic concepts like derivative and continuity via their intuitively appealing definitions exploiting infinitesimals (essentially following Cauchy's approach), they are in a better position to scale the long-winded epsilon-delta paraphrases of those definitions.