# Harold P. Fawcett (1894–1976)

### mathematics students geometry school

Professor of mathematics education at Ohio State University, Harold P. Fawcett was best known for his work on pedagogy in geometry, particularly the teaching of reasoning and proof. Fawcett was born in Upper Sackville, New Brunswick, Canada. In 1914 he received an A.B. from Mount Allison University and obtained a high school teaching position in a New England village. After World War I service with the United States Army in France, Fawcett taught in the home study division of the New York Young Men's Christian Association (YMCA) schools (1919–1924). He was awarded an A.M. in 1924 by Columbia University and continued doctoral work while teaching in Columbia's extension division. In 1937 he received a Ph.D. in mathematics education from Teachers College, Columbia University. Fawcett joined the faculty at Ohio State University in 1932, where he rose to full professor (1943), served as chair of the Department of Education (1948–1956), and retired with emeritus rank (1964). During his early years at Ohio State, Fawcett also taught at the affiliated University School, where he served three years as associate director. In 1958 he was elected to a two-year term as president of the National Council of Teachers of Mathematics (NCTM).

The most enduring contribution by Fawcett to the field of mathematics education was the thirteenth yearbook of the National Council of Teachers of Mathematics, *The Nature of Proof* (1938). The publication was, essentially, his doctoral thesis, which drew upon his experiences and experiments in teaching high school geometry at the University School. Fawcett believed that, with respect to geometry, contemporary classroom practice was incongruous with the new emphasis on the development of critical and reflective thought advocated by national committees and influential mathematicians. If asked, Fawcett asserted, many teachers would express agreement with the new emphases for demonstrative (proof-oriented) geometry to introduce students to the nature of deductive reasoning and to develop in them an understanding of what proving something really means. Fawcett's experience, however, suggested to him that, rather than emphasizing the role of logical processes in developing and establishing a geometrical system, most teachers taught geometry as a given set of definitions and theorems to be memorized.

Fawcett's approach was based upon four assumptions: (1) high school students enter a geometry course with practical experience in reasoning accurately; (2) students should be permitted to use their own approaches to reasoning in geometry; (3) the students' logical processes, not those of the teacher, should guide development of the subject; and (4) students need opportunities to apply the deductive method to situations that have clear relevance to their own lives. These assumptions reflect the influence of broader educational trends of the 1930s, including student-centered pedagogy, an investigation–discovery orientation, the incorporation of experiences external to school, and a concern for transfer of skills to areas outside mathematics.

Classroom implementation of Fawcett's pedagogical approach was unique at the time. Virtually nothing was given to the students. Rather than receiving a published textbook, students developed their own notebooks, with individuality welcomed. Students decided which terms should be undefined and which needed definition. The definitions were developed and refined by the students after discussion, and then entered into their notebooks. If a proposition appeared obvious to the students, it was taken as an assumption. Instead of being given a statement to prove, students were presented with a figure and encouraged to identify properties of the figure that might be assumed. Following this, they were to discover the implications of these properties. With guidance from the teacher, important implications were generalized into theorems, resulting in a limited, but richly understood, structure. In effect the students developed the geometry curriculum themselves, through a process of questions, discussion, and reasoned reflection.

Criteria of success for Fawcett's program was based on its effect on students' behaviors in approaching problem tasks. For example, did students first seek to clarify definitions or conditions of the problem situation? Fawcett's own investigation suggested that his approach, emphasizing reasoning processes rather than skills, improved reflective thinking more than did the traditional course, without significant loss of competence in subject matter knowledge. In light of his ideas on the pedagogy of geometry, Fawcett was invited to join the Committee on the Function of Mathematics in General Education, appointed by the Progressive Education Association's Commission on the Secondary School Curriculum. His work influenced the sections of the committee report that dealt with logic and proof. Renewed interest in Fawcett's pedagogical approach to geometry and his emphasis on helping students to develop critical, reflective thinking processes led the National Council of Teachers of Mathematics to reissue the *Nature of Proof* in 1995.

Although Fawcett championed the role of the student in developing deductive mathematical systems, he viewed the teacher as an indispensable guide to move students toward self-directed, independent learning. He believed that a geometry course could provide opportunities to gain knowledge and develop understanding of deductive reasoning; however, only the teacher could provide the classroom environment in which original and creative thinking could flourish. From his early days as a student in a small Canadian school with an enrollment of just two dozen, Fawcett never forgot the impact of the new mathematics teacher who arrived at the school when he was fourteen years old. He credited her with taming his rebelliousness and inspiring him to pursue a career in education by engaging his intellect in adventurous pursuit of geometric understanding. It became for Fawcett a lifelong quest.

## BIBLIOGRAPHY

CATTEL, JAQUES, and ROSS, E. D. 1948. *Leaders in Education: A Biographical Dictionary,* 3rd edition. Lancaster, PA: Science Press.

FAWCETT, HAROLD P. 1964. "Reflections of a Retiring Teacher of Mathematics." *Mathematics Teacher* 57 (7):450–456.

FAWCETT, HAROLD P. 1970. "The Geometric Continuum." *Mathematics Teacher* 63 (5):411–420.

FAWCETT, HAROLD P. 1995. *The Nature of Proof.* Thirteenth Yearbook of the National Council of Teachers of Mathematics (1938). Reston, VA: National Council of Teachers of Mathematics.

EILEEN F. DONOGHUE

## User Comments

about 2 years ago

While I did not live during his time - I had the opportunity to work with a Thai national level supervisor and her 2 associates (professors in math education at Chulalongkorn University) who took courses at Ohio State under him. And they had high praise for him and were trying to implement some of his approaches.