Mathematicians and Curriculum The New Math Inspired by
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
After. New. Math • 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
• • 1989 (NCTM Standards): 13 standards, with 56 substandards 2006 – NCTM Focal Points - 3 topics per year 2011 – CCSSM Standards
Problems with Strands • (after L. Ma) • Instability • Discontinuity • Incoherence
Curriculum Review • The 1998 California insurgents told publishers, “Consult with mathematicians”. • Harcourt , Pearson, EDC • What happens to your comments?
Writing • Place Value • The transition to algebra • First grade
Place Value • Taking Place Value Seriously • http: //www. maa. org/sites/default/files/pdf/pmet/res ources/PVHowe. Epp-Nov 2008. 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-stagesplace-value
Five Stages of Place Value 342 = 300 + 40 = 3 x 100 + 4 x 10 + 2 x 1 + 2 = 3 x (10 x 10) + 4 x 10 + 2 x 1 = 3 x 102 + 4 x 101 + 2 x 100
Transition to Algebra • From Arithmetic to Algebra - in Mathematics Journal, (Chinese math ed journal)
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
Pillars on the web • www. math. ubc. ca/~cwsei/math 230/reading/3 Pil lars. pdf • http: //commoncoretools. me/2012/02/08/articleby-roger-howe-three-pillars-of-first-grademathematics/ • http: //de-morgan. org/2011/10/29/roger-howethree-pillars-of-first-grade-mathematics/
• www. achievethecore. org/file/233
• 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%2 F 978 -94 -0077560 -2_10
Effective Use of the Number Line?
Desiderata • The mathematics curriculum is a good candidate for Most Complex Cultural Artifact. • It has to be taught by millions of teachers.
• The curriculum is best served by continuous improvement. • The US has no mechanism to enact such change.
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