Category Archives: Common Core Standards Math

Place Value Notation already depends on multiplication

23 = 2 * A + 3 where A = 10. Place value notation is a way of writing compactly multiplications and additions. Children are taught place value notation in grade K.  They are taught multiplication in grade 2.  This … Continue reading

Posted in Common Core Logical Inconsistencies, Common Core Standards Grade 2, Common Core Standards Grade K, Common Core Standards Math | Leave a comment

Natural Numbers are about order Common Core is clueless on this

The natural numbers are about order.  The Common Core Standards don’t get it.  So they don’t get natural numbers. Keith Devlin’s repeated writings on multiplication ain’t repeated addition display a learned approach to not getting it either.  Devlin doesn’t get … Continue reading

Posted in CCPAP, Common Core Peano Axioms Project | Leave a comment

Common Core is teaching behavior which is why students hit a wall at algebra one

  The Common Core Standards (CCS) are teaching behaviors not concepts.  This is true because they have the wrong order.  They have multiplication in grade 2 when teach place value in grade K.  So they teach behavior not concepts. Algebra is … Continue reading

Posted in CCPAP, Common Core Peano Axioms Project, Common Core Standards Math | 2 Comments

Common Core Standards Peano Axioms Project

As a project I will be publishing ebooks on the Common Core Standards from the point of view of the Peano Axioms. Some resources. http://www.corestandards.org/ http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf http://www.corestandards.org/assets/CCSSI_Mathematics_Appendix_A.pdf http://www.p12.nysed.gov/ciai/common_core_standards/ http://dc.gov/DCPS/In+the+Classroom/What+Students+Are+Learning/DCPS+Common+Core+State+Standards http://www.ixl.com/promo?partner=google&phrase=standards-VA&redirect=%2Fmath%2Fstandards%2Fvirginia&gclid=CNy5nPm_9rICFcqj4AodkXQAaw http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml Place value notation and counting with tens and hundreds … Continue reading

Posted in Common Core Peano Axioms Project, Common Core Standards Math | Leave a comment

Common Core Standards Grade 4 Number and Operations Fractions

Given a denominator n, such as 8, we can consider fractions as having a successor type relation.  So (m,n)’ = (m’,n) where ‘ is successor, so m+1 = m’. So (3,8) = (2′,8) = (2,8)’ = (1′,8)’ = (1,8)” = … Continue reading

Posted in Common Core Number and Operations Grade 4, Common Core Standards Grade 4, Common Core Standards Math, Common Core Standards Number and Operations, Object Oriented Rational Number, Uncategorized | Leave a comment

Is Place Value Notation already Algebraic Thinking?

Place value notation and related algorithms are a complicated set of machinery based on the associative, and commutative laws of addition and multiplication. 21 = 2 * 10 + 1 The manipulation of such expressions is by the laws of … Continue reading

Posted in Algebraic Laws, Arithmetic Laws, Arithmetic's Relation to Algebra, CC Standards Grade 2 Operations and Algebraic Thinking, Common Core Standards Grade 2, Common Core Standards Math, Place Value Notation | Leave a comment

Re: A Brief History of American K-12 Mathematics Education in the 20th Century by David Klein

David Klein has written a 39 page history of math education reformations and counter reformations in the 20th century. A Brief History of American K-12 Mathematics Education in the 20th Century This is a struggle of drills, skills, concepts, algebra … Continue reading

Posted in Common Core Standards Math, David Klein math ed history US 20th century, Math Education, Math Education 20th Century US, New Math, New Math 1960s | 3 Comments