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Mathematicians and Curriculum

Mathematicians and Curriculum. The New Math. Inspired by the foundations work of first half of 20 th century Emphasized set theory Mathematicians and teachers worked together to write textbooks Abandoned – teachers could not adapt. AfterNewMath.

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Mathematicians and Curriculum

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  1. Mathematicians and Curriculum

  2. The New Math • Inspired by the foundations work of first half of 20th century • Emphasized set theory • Mathematicians and teachers worked together to write textbooks • Abandoned – teachers could not adapt

  3. AfterNewMath • The structure of US curriculum changed from having an arithmetic core to having a strands structure. • (L. Ma, Notices of AMS, NOV 2013) 1963: 8 strands 1972: 9 strands 1975: 9 strands (not the same 9) 1980: 7 strands under umbrella of problem solving

  4. 1989 (NCTM Standards): 13 standards, • with 56 substandards • 2006 – NCTM Focal Points - 3 topics per year • 2011 – CCSSM Standards

  5. Problems with Strands • (after L. Ma) • Instability • Discontinuity • Incoherence

  6. Curriculum Review • The 1998 California insurgents told publishers, “Consult with mathematicians”. • Harcourt , Pearson, EDC • What happens to your comments?

  7. Writing • Place Value • The transition to algebra • First grade

  8. Place Value • Taking Place Value Seriously • http://www.maa.org/sites/default/files/pdf/pmet/resources/PVHoweEpp-Nov2008.pdf • What is place value, and why should we care? • https:mathematicsteachingcommunity.math.uga.edu/ • The Five Stages of Place Value • http://www.teachersofindia.org/en/article/five-stages-place-value

  9. Five Stages of Place Value 342 = 300 + 40 + 2 = 3 x 100 + 4 x 10 + 2 x 1 = 3 x (10x10) + 4 x 10 + 2 x 1 = 3 x 102 + 4 x 101 + 2 x 100

  10. Transition to Algebra • From Arithmetic to Algebra - in Mathematics Journal, (Chinese math ed journal)

  11. First Grade 3 Pillars of Elementary Mathematics • Beginnings of computation, incorporating place value ideas (addition and subtraction within 20) • Word problems (many types) • Connecting measurement number with counting number

  12. Pillars on the web • www.math.ubc.ca/~cwsei/math230/reading/3Pillars.pdf‎ • http://commoncoretools.me/2012/02/08/article-by-roger-howe-three-pillars-of-first-grade-mathematics/ • http://de-morgan.org/2011/10/29/roger-howe-three-pillars-of-first-grade-mathematics/

  13. www.achievethecore.org/file/233

  14. 3 Pillars of First Grade Mathematics, and Beyond in: Mathematics Curriculum in School Education G. Lappan and Y. Li, eds. Springer Verlag, 2013 link.springer.com/chapter/10.1007%2F978-94-007-7560-2_10

  15. Effective Use of the Number Line?

  16. Desiderata • The mathematics curriculum is a good candidate for Most Complex Cultural Artifact. • It has to be taught by millions of teachers.

  17. The curriculum is best served by continuous improvement. • The US has no mechanism to enact such change.

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