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Foreshadowing Ideas in Abstract Algebra: Reflections from the Secondary School Mathematics Curriculum Improvement Study

  • J. Philip SmithEmail author
Chapter
Part of the Research in Mathematics Education book series (RME)

Abstract

Blossoming in the wake of Sputnik and the perceived “crisis” in American mathematics and science teaching, the Secondary School Mathematics Curriculum Study was perhaps the most mathematically challenging of the curricular initiatives of its day. Funded by the National Science Foundation and Teachers College, Columbia University, SSMCIS developed and field tested materials intended for “mathematically capable” students in grades 7 through 12. The SSMCIS material was never intended for wide adoption, but was rather written to see what might be achievable by those interested in bringing the curriculum of the upper grades into the modern era and incorporating the mathematical structures, rigor and applications that were perceived as missing in the more widely available textbooks. In this chapter, I explore the nature of SSMCIS algebra-related materials intended for grades 9–12, which include: algebra of vectors, linear programming, vector spaces and subspaces, linear mappings, determinants, matrices and eigenvalues, algebraic structures, extensions, and homomorphisms. Enlivened with a number of illustrative, interesting, and creative examples of both content development and homework problems, the chapter is intended to explore the audacity and creativity that went into exploring the “realm of the possible” in an age that was, perhaps, too ambitious and shortsighted, but which still offers lessons for those creative souls among us today.

Keywords

Abstract algebra Curriculum development Secondary school 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Science and Technology, Teachers CollegeColumbia UniversityNew YorkUSA

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