Dr. Goodstein received his bachelor's degree from Gallaudet University in 1965, his master's degree from Catholic University and his Ph.D. from American University. His tenure at Gallaudet spanned over 30 years with much of it as a faculty member in the Mathematics Department. His research in developmental mathematics formed the foundation of mathematics education for elementary and secondary teachers of the deaf across the nation.

From 1986 to 1992, he directed the NSF-sponsored Gallaudet Summer Institute in Mathematics for Pre-College Teachers of deaf and hard of hearing students.

In 2002, Dr. Goodstein led the highly successful Deaf Way II conference in Washington, DC., a week-long celebration of Deaf cultures which brought together 10,000 people from around the globe to discuss and celebrate deaf scholars, artists, students, and citizens. In 2004 Gallaudet awarded Dr. Goodstein Professor Emeritus status in recognition of his significant contributions.

Dr. Goodstein served as President of the Maryland Association of the Deaf, on the Board of Trustees of the Maryland School for the Deaf, Vice-President of the National Association of the Deaf, and Chair of the National Association of the Deaf Telecommunications Committee.

Dr. Goodstein currently resides in Arizona with his wife, Astrid Amann Goodstein '65. The Goodsteins have three sons.