About Us

Current Collaborators

Frederick Stern, Ph.D.


Fred Stern

Fred Stern helped to write and create this web site. As a grandson of Catherine Stern and the son of Margaret Stern, he was taught arithmetic with these materials. He has given workshops to teachers on how to use the method. He is a psychologist in private practice in New York. He has also created a web site to help graduate students complete their dissertations: www.dissertationworkshop.com

Teacher Trainers

We have a group of teacher trainers who assist with workshops, conference presentations, and individual tutoring on the Stern Math materials. Read more about them here.

Past Collaborators

Dr. Catherine Stern (1894-1973)


Catherine Stern teaches
her grandson, Fred (1950).

These materials were invented by Dr. Catherine Stern in the late 1920's. She ran a Montessori kindergarten and children's club in Breslau, Germany (now Wrocław, Poland), which was recognized as a training institute for teachers and psychologists. In 1932-1933, she published two books on the psychological aspects of children's learning, books that because of the Nazi repression were barely noticed. Under the same circumstances, she had to discontinue her kindergarten in 1934 and turned to developing better methods for teaching math. In her kindergarten she had used the Montessori math materials which consisted of beads on wires. When putting a string of 5 beads with another string of 5 beads, the wire loops at the ends made the strings of 5 plus 5 longer than the string of 10 beads. This forced the children to count. Catherine Stern decided to represent numbers, not with beads, but with blocks of glued together 1 cm cubes. As a result, two blocks of 5 cubes each, placed end to end measured the same length as the 10-block. She had sets of blocks made in different colors by Mr. Bakelund, the inventor of Bakelite, the forerunner of plastic. He also fashioned a number track in which the blocks could be measured. In the pre-Hitler period, she lectured throughout Germany and in 1934, the Swiss Kindergarten Association invited her to its congress, where for the first time she introduced her new arithmetic materials.

cover of 'Children Discover Aritemetic' bookIn 1938, Dr. Catherine Stern immigrated to the United States. She developed the approach here with larger sized materials at the Windward School in White Plains, N.Y.. From 1940 to 1943, she was research assistant to Max Wertheimer at the New School for Social Research. In working with Wertheimer, the founder of Gestalt Psychology, she came to understand the psychological basis of her empirical, pragmatic experiments: that learning should not be based on rote memory, but on visualization of the structural characteristics of the concept, thus giving pupils insight into the relationships that are to be grasped. Wertheimer named her approach Structural Arithmetic. In 1944, she showed the materials to Albert Einstein, who worked with them for over an hour. He wrote to Harper and Row who published Children Discover Arithmetic in 1949, "I believe, that her (Catherine Stern's) idea is sound and would be of real value in the teaching of the elements of arithmetic."


Max Wertheimer arranged for Catherine to
become his research assistant at the New
School and helped her to conceptualize
her method in terms of his principles of Gestalt
Psychology. These two pages are from his book
Productive Thinking
(1945, 1959).

Dr. Stern was awarded two Carnegie Foundation research grants in 1958 and 1962 to further develop the materials.

Dr. Catherine Stern's publications include:

Margaret B. Stern, M.Ed. (1920-2019)


Margaret Stern reviews the new
English edition of workbook (2005).

Margaret “Peggy” Bassett Stern attended Bank Street College of Education. In 1943, Margaret met Catherine Stern through Catherine’s daughter, Toni S. Gould. Later, in 1947, Margaret married Catherine’s son, Fritz. Catherine, Margaret and Toni ran a nursery school called Castle School from 1944 to 1951 in order to develop and expand the Stern Structural Arithmetic and Structural Reading materials.

Afterwards, Margaret was a math consultant to the Gateway School, where Structural Arithmetic was further developed. She was co-author of several books throughout her career: Children Discover Arithmetic and the Structural Arithmetic Teacher Guides and Workbooks (1965-66) with Catherine Stern, the Structural Reading series with Catherine Stern and Toni S. Gould. She revised and expanded Experimenting with Numbers (1988), and Structural Arithmetic and Teacher's Guides  (1992, Educators Publishing Service) with Gould. She was recipient of the Orton Dyslexia Society Award (1989) and of the Bank Street College of Education Award Outstanding Accomplishment in the Field of Education (1998).

Toni S. Gould, M.A. (1920-2003)

Toni Gould was born in Breslau, Germany, in 1920. In 1938, she won a refugee scholarship to Bryn Mawr where she graduated Magna Cum Laude. She earned her MA at Teacher's College.

Toni then worked as a remedial reading specialist in New York City for over twenty-five years. She taught at Bank Street College of Education, Hunter College and Lehman College, and conducted teacher workshops in schools and colleges all over the country.

She is the author of Home Guide to Early Reading, a book for parents which includes reading readiness games and strategies for preschool children. She is co-author with her mother Catherine Stern and Margaret B. Stern of the widely used Structural Reading Series and Structural Arithmetic Series. She also co-authored the books The Early Years of Childhood and Children Discover Reading with Catherine Stern.

John Roberts, M.S.

John Roberts was the artist of the drawings on how to use the arithmetic materials included in this web site. He earned a BFA at the Rhode Island School of Design and he received an MS in Education from Rochester Institute of Technology, through the National Technological Institute of the Deaf. He was the K-12 art teacher in the Rochester Vermont Public School for 27 years.