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Algebra as Part of an Integrated High School Curriculum

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And the Rest is Just Algebra

Abstract

Traditional high school mathematics curricula in the United States devote 2 years almost exclusively to development of student proficiency in the symbolic manipulations required for solving algebraic equations and generating equivalent algebraic expressions. However, recent design experiments have shown that a focus on functions, mathematical modeling, and computer algebra tools enables effective integration of algebra with the other core strands of high school mathematics.

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Notes

  1. 1.

    In the 1950s, the importance of DNA was not well known in biology, black holes were not known to exist, and tectonic plates were still considered heresy by earth scientists.

  2. 2.

    The term standards-based generally refers to curricula that embody recommendations of the 1989 National Council of Teachers of Mathematics Curriculum and Evaluation Standards for Teaching Mathematics and the 2000 Principles and Standards for School Mathematics.

  3. 3.

    The notion that proficiency in mathematics includes certain habits of mind, as well as knowledge of specific facts, concepts, and procedural skills , has been reflected in all professional curriculum guidelines over the past quarter-century, most recently in the Common Core State Standards for Mathematics .

  4. 4.

    The trigonometric functions are developed in an earlier geometry /trigonometry unit titled Circles and Circular Functions. This is one example of the integration of strands in Core-Plus Mathematics that are roughly categorized as algebra/functions, geometry /trigonometry, statistics/probability, and discrete mathematics.

  5. 5.

    For example, in his famous 1902 retiring presidential address to the American Mathematical Society, E. H. Moore urged schools to “abolish the ‘watertight compartments’ in which algebra, geometry , and physics were taught.” Similar recommendations appeared in the 1912 Report of the American Commissioners of the International Commission on the Teaching of Mathematics, the 1923 Mathematical Association of American National Committee on Mathematical Requirements’ The Reorganization of Mathematics in Secondary Education (Jones & Coxford Jr, 1970; Kilpatrick & Izsak, 2008).

  6. 6.

    Emphasis on functions and interrelationships within mathematics had been made as early as the middle of the nineteenth century by the distinguished German mathematician, Felix Klein . That same thematic recommendation was picked up by curriculum advisory reports in the United States throughout the twentieth century.

References

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Fey, J.T., Smith, D.A. (2017). Algebra as Part of an Integrated High School Curriculum. In: Stewart, S. (eds) And the Rest is Just Algebra. Springer, Cham. https://doi.org/10.1007/978-3-319-45053-7_7

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  • DOI: https://doi.org/10.1007/978-3-319-45053-7_7

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  • Publisher Name: Springer, Cham

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