The Freehold Young Ladies' Seminary emphasised that its "extensive" course of study "requires a longer period than is usually devoted to study by young Ladies; but it is believed not to be more extensive than the present state of society demands."

In 1847, the New York State Legislature created the Free Academy to provide post-grade school education for boys, but no such school for girls yet existed. On 17 November 1869, a newly established Board of Education passed a resolution creating the Female Normal and High School, which would train women to become teachers and provide high school and college level courses. In 1870, the school's name changed to "The Normal College of the City of New York." The goal of this institution was to provide free higher education to women. Thomas Hunter, a former principal, became the school's first president; he insisted on admitting students of all racial and ethnic backgrounds and teaching a combined curriculum of liberal arts, science, and education.

The aim in all courses is to cultivate habits of exact, sustained and independent reasoning, of precision and clearness in the statement of convictions and the reasons upon which they depend; to rely upon insight, originality and judgment rather than on memory. The endeavour is to secure full possession of leading principles and methods rather than of details. From the first, students who show special aptitude are encouraged in the working of subjects, which require more prolonged investigation than the daily exercise of the classroom.

Ely had a strong interest in expanding the offerings of the Mathematics Department, to provide the "elastic character of the curriculum of the college" with "modern mathematical thought." Students were studying solid analytic geometry for which visualisation of algebraic surfaces is an important skill to acquire. She obtained funds to buy the plaster-of-Paris models manufactured by Brill and Schilling in Darmstadt ... .

Although she did not have a doctorate in mathematics, Achsah Ely was thoroughly engaged in the subject, even at the international level. She attended the second International Congress of Mathematicians held in Paris in the summer of 1900, one of seven women among the 250 or so participants listed in the proceedings.

Under the leadership of Ely, the first PhD in mathematics was hired into the department. Ruth Gentry obtained the first PhD awarded to a woman by Bryn Mawr College in 1896, having studied in Berlin and in Paris before taking a position at Vassar in 1894 where she taught until 1902. Around this time the college offered opportunities for graduate study, which included advanced courses on projective geometry, differential equations, and modern methods of analytics. Seniors studied advanced integral calculus, the quaternions, and analytic mechanics.

Miss Ely and I came together to this place, to begin our collegiate course. ... The College was an experiment - it was not wholly a college. Many people did not believe in it at all; some within its own walls doubted if it could pass the experimental stage and result in any essential degree unlike the many seminaries and academies that then represented the finishing stage of a girl's education. ... In this small group of college students of that early day there was no other more earnest and eager and hopeful than Miss Ely. She was imbued with ambition for the successful working of the experiment.

In the words of the president of Vassar College, "She became an inspiration to many students to pursue a life of study. She has gone, but she has left a heritage full of encouragement, a lesson to all of you who are in the college to-day."