# Category Archives: 21st Century Peano Addition Authors

## Review of Introduction to Mathematical Thinking by Keith Devlin

This is a review of the book Introduction to Mathematical Thinking by Keith Devlin.  This is a paperback book of length x + 92, i.e. 102 pages.  This is a paperback that can fit into a large boxy like extra … Continue reading

## Euclid’s confusions about number types are the pedagogy of 2012.

Euclid’s Elements present a somewhat confused presentation of the concept of number, proportion and magnitude from the modern perspective.  Euclid lacks the sharp clarity of Grassmann, Dedekind, Peano and others who crafted the modern concepts of natural number, rational number … Continue reading

This is a continuation of the discussion of procedural v conceptual in the context of Khan Academy videos. It also brings in the Keith Devlin initiated debate on multiplication as repeated addition for natural numbers as opposed to an operation … Continue reading

## #MTT2k Prize Khan Academy Video Contest Critique Chronology

June 18, 2012 John Golden and David Coffey do the first critique video and a blog post on it. MTT2K – Episode 1 http://www.youtube.com/watch?feature=player_embedded&v=hC0MV843_Ng 16,329 views as of July 7 2012 89 likes, 122 dislikes John Golden blog post http://mathhombre.blogspot.com/2012/06/mystery-teacher-theatre-2000.htmlContinue reading

## Multiplication of Negative Numbers Recursive Continuation

Recently, the subject of how to teach or justify rules for multiplication of negative numbers has come out.  The following is an approach based on the Peano Axioms. Natural numbers are 0, S(0), S(S(0))), … 1= 0′. S(0) = 1 … Continue reading

## Re dy/dan An Incomplete History Of The Math Edublogosphere

The blog dy/dan by Dan Meyer has a post titled An incomplete history of the math edublogsphere.  This has a comment thread of math teachers who blog and apparently regularly follow dy/dan. Number 7 Jeanette links to http://algebra1teachers.com/ This in … Continue reading

## Keith Devlin Transition to College Math MOOC

Keith Devlin of Stanford University will have a MOOC course on transition to college math.  This will not be a full course, but a partial course.  He is hoping to get schools to use it as part of their courses.  … Continue reading

## Virginia Standards of Learning Math v Peano Axioms

The difficulty of the Peano Axioms is not greater either in abstraction or in formulas from algebra I.  Natural numbers are defined by the Peano Axioms below. To give away the answer, they are 0,1,2,.. Note the natural numbers are … Continue reading

## David Groisser Initial Segments before addition from Peano Axioms

Richard Dedekind in 1888 did order before addition.  Dedekind first did properties of closed sets under a function that is 1 to 1.   Then he applied this to tail sets under successor in effect.  Tail sets are natural numbers from … Continue reading

## re: Alexandre Borovik Why is arithmetic difficult?

Math professor Alexandre Borovik has a post on understanding why arithmetic is difficult to learn.  It is because it has a greater conceptual structure than is realized.  He points out this complexity goes from hidden to explicit by use of … Continue reading