BACK TO THE MATH HOMEPAGE

     There have been a variety of different ways that the study of mathematics education has been approached.  Some have suggested that mathematics should be examined in two streams, the first being the requirement to educate all members of society in the necessary skills needed to "survive", and the second being the need to educate the future generation of mathematicians, scientists, engineers and other specialists (Moon, 1980).  Fennell (1981) suggests that mathematics can be logically divided into three criterion.  The logical criterion relates to the organization and structure of the subject matter, the social criterion relates to the way in which mathematics applies to everyday life, and the psychological criterion concerns itself with how children learn.  Each of these criterion have shared the spotlight in math education over the last half century.
     The pre-war mathematics program was purely arithmetic and didactic.  Number facts and math drills were common practice, with an understanding of the underlying principles of the discipline not considered.  "Arithmetic programs from 1910 through the 1940s placed major emphasis on the acquisition of skill in computation, with little attempt to show children how these computation skills could be used in daily life.  While the trend continued in the late 1940s, growing awareness in the fields of developmental and educational psychology by the likes of Bruner, Piaget and Gagne, would offer a new perspective that quickly spread through the curriculum, resources and programmes in Ontario's schools.
In their discussion of post-war mathematics development, the National Council of Teachers of Mathematics (1970) explain how psychology helped to inform practice in Ontario.

General mathematics has resulted in less formal arrangements and more concrete beginnings.  The treatment is less rigorous but more explanatory and illustrative material is included.  The exercises are made as practical as possible and the development is influenced by psychology.  General mathematics serves as an instrument for motivation, articulation and exploration.  Motivation is provided through applications of one subject to the development of another (p. 398).

     This phenomenon not only promoted the idea authenticating experiences for students, but proposed that the curriculum be integrated as well.  Teachers were quite receptive to the shift in mathematical purpose.  They had long realized that "learning arithmetical ideas is primarily the product of relevant experience," and that "we must abandon the idea that arithmetic can be taught incidentally" (Bidwell & Clason, 1970, p. 626).  Textbooks became infused with providing mathematics problems as practical applications for students; the 1950s saw the birth of a math that students could relate to, and the trend would continue for the much of the decade.  Quite clearly, educational progressivism left its mark upon mathematics education.
     While providing an experiential framework for mathematics was a great leap forward for math education, many questions still confounded educators (Howson, Keitel & Kilpatrick, 1981).  How could math be best evaluated?  How should the program be developed to ensure student success?  What about the underlying principles behind mathematics?
     The real thrust to improve mathematics education, however, came from pressures outside of educational circles.  Post-war urbanization was filled with problems for Ontario.  "Among these were the recurring seasonal unemployment natural to a northernly situated country like Canada and so-called technological unemployment - the result of automation" (N.C.T.M., 1970, p. 400).  The close of the century was filled with a sense of unease.  "The Russians launched the Sputnik satellite in 1957.  This technological achievement in the Cold War climate of the time created a sense of alarm.  Critics of the schools claimed that the youth of the Soviet Union were much further advanced in mathematics and science, and called for drastic reform of mathematics and science programmes in our schools" (Fennel, 1981, p. 11).
     What was clear to math educators was that a paradigmatic shift would be needed in the math programme.  The 1960s saw the birth of "new math," an organism that would shift the scope of math education completely.  While the former arithmetic approach to math dealt with computational skills involving numbers, fractions, decimals and percents, new math encompassed far more in its prodigious domain.  It included "such mathematical topics as sets, place value, logic, number bases, geometry, probability, statistics and algebra" (Fennel, 1981, p. 11).  It is often conceded that new math was indebted to the Bourbakists, a group of French mathematicians who in the early part of the century systematized common threads of a diverse mathematics so a coherent and logical math program could be developed for schools (Pittman, 1989).  While the topics were not particularly new, they shift from arithmetic to mathematics at the elementary level was.  It is not surprising, then, that new math had more than its share of teething programs.
     Bob Moon (1986), in his book The 'New Maths' Curriculum Controversy: An International Story discusses at length the strain new math put on elementary school teachers.  Teachers who lacked a substantial base of mathematics understanding themselves, found new programs incredibly difficult to implement.  Moon explains as well, that teachers' colleges became vehicles for new math's pedagogical development with little more success; teacher candidates were put into the unlikely position of having to reconceive of their entire understanding of mathematics.  The results were a hodgepodge of successes and failures, and new math endured a slow evolution.  While the 1960s offered hosts of resources for teachers to apply the more global understandings of mathematics, teachers tended to gravitate towards workbooks which would offer them quick and easy ways to meet the needs of the new curricular expectations.  The Report of the Royal Commission on Education (1968), known as the Hall-Dennis Report, also left its mark on practice, with it's sense of a "pedagogy of joy".  By the 1970s, math centres, activities, and flashcards spread in their use to offer multimodal pedagogical techniques in teaching. While the merits of new math had withstood the test of time, the enchantment in some of the approaches to it did not.
    Nowhere is it truer than in mathematics, that the gap between research and practice is a wide one.  The National Council of Teachers of Mathematics (1990) discuss research in mathematics education as the search for a magic cure, which would "supply unequivocal answers to our questions or cures for our educational problems" (p. 1).  They recognize that this partially contributed to the failure for new math to quickly achieve its aims in the 1960s and 1970s.  They suggest that research in math education should involve a bi-directional relationship between mathematics educators and classroom teachers.  The 1980s saw the slow progression of this reciprocal trend, and the slow development of curricula and resources which would be palatable to every classroom teacher.  Some researchers (Pitman, 1989) consider the 1980s as involving a mathematics with an emphasis on problem solving, though such a trend might have begun much earlier in attempting to authenticate experiences for students.  Nonetheless, broader notions of mathematics were finally beginning to see effective and diverse instruction in Ontario's schools.  The use of manipulatives in mathematics was becoming far more common to allow children tactile products with which to learn about the underlying mathematical concepts.  As well, more recently, the use of math journals in which students write about their understanding of the process of solving mathematics work, has become more popular.  Some current textbooks even ask students to write about how they solved problems, as well as simply solving them.
     While the late 1980s and the 1990s saw the continuation of the slow but meaningful advancement of mathematics education, other factors developed which contributed to a 'back-to-the-basics' movement in mathematics.  Concerns grew surrounding mathematics and new technologies, as well a the developing economic strain between Canada and technologized counterparts in Asia.  Declining scores on standardized achievement tests, rising costs of education promoting demands for accountability, and a renewal of the interest in instructional methods had once again charted a new course for mathematics.  We would suggest, however, that the current idea of 'back to the basics' in mathematics is actually quite felonious; it never really existed, so it cannot possibly be returned to.  Rather, the movement is towards an intensive, demanding, concomitant multi-stream approach to mathematics which revisits all of the apprehensions of the pre-new math teacher, except in the 1990s.  With the newest provincial documents only a year old, it will be interesting to see whether they will improve achievement testing scores or offer the accountability that the Provincial government seeks.  While the hope is that mathematics education in the 1990s will prove to be a golden age for students, it is more likely that the trepidation caused by  hurried changes and a failure to sufficiently consider the teacher in the educational equation will result in student mediocrity rather than excellence in the field.