# Monthly Archives: October 2012

## Grade K 5=4+1 in VA SOL already so go to 5 = 4′

The VA SOL, see a previous blog post, already require for grade K that understand and can write equations like 5 = 4 + 1 So it is just a step backwards in fact to require 5 = 4′. The … Continue reading

## Teacher rating unfairness hits LA math teacher

http://articles.latimes.com/2012/oct/28/local/la-me-teacher-evals-20121029 How to measure the worth of Los Angeles math teacher Kyle Hunsberger? The teacher at Johnnie Cochran Jr. Middle School works 60-hour weeks, constantly searches for new teaching ideas and makes every minute count in class. During a fast-paced … Continue reading

## Virginia Standards of Learning Kindergarten v Peano Axioms

http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/sol_ccss_comparison_mathematics.pdf Page 7 to 9 == and Cardinality K.CC Know number names and the count sequence. 1. Count to 100 by ones and by tens. K.4 The student will a) count forward to 100 and backward from 10; b) identify … Continue reading

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## Search “counting on” “definition of addition”

“definition of addition” “counting on” About 6,430 results (0.32 seconds) “definition of addition” “counting on” http://en.wikipedia.org/wiki/Addition   Understanding Numbers in Elementary School Mathematics By Hung-Hsi Wu, Hongxi Wu http://www.meridianschools.org/Staff/DistrictCurriculum/MoreResources/Math/All%20Grades/Misconceptions_Error%202%5B1%5D.pdf ftp://math.stanford.edu/pub/papers/milgram/class-notes-foundations.pdf https://scholar.vt.edu/access/content/user/wilkins/Public/JECP_2001.pdf When we search on addition “counting on” we get … Continue reading

## Teachers don’t get that addition is defined from counting by one

Teachers do not get that addition is defined from counting by one.  They may grasp that intuitively at times.  But they don’t understand this is the complete definition with no more needed and that all properties of addition follow from … Continue reading

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## Addition is defined from counting by one

Right additive identities that define addition completely: x+0 = x x+y’ = (x+y)’ where 1 = 0′, 2= 1′, etc. This defines addition from counting by one. So addition is derived from counting by one.  The term successor just means … Continue reading

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## Self-discovery Wolf Child as Paradigm

Is the Wolf Child the paradigm for self-discovery?   A wolf child learns neither language nor math. Euler in his 1765 Algebra is searching for answers but presents his half baked answers as if complete.  But they aren’t. We know that … Continue reading