Category Archives: Recusive Inductive Definition of Addition

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

Posted in Analtyic Continuation, Analtyic Recursive Continuation, Angela Chen Chronicles Higher Education, dy/dan Dan Meyer, Inductive Definitions, It Ain't No Repeated Addition, James Tanton Math Videos, Justin Reich, Keith Devlin Stanford, Khan Academy, Math Video Series, MTT2k, MTT2k Prize, Mystery Teacher Theatre 2000, Recursion, Recursive Continuation, Recursive Definitions, Recursive Inductive Definition of Multiplication, Recusive Inductive Definition of Addition, Uncategorized | 50 Comments

Pair of Number Lines and Successor Identities

This post concerns using a pair of number lines to illustrate the successor identities.  At lower grade levels, we can simply use a pair of number lines to “prove” the successor identities.   We actually make them plausible, but at an … Continue reading

Posted in Addition Right Identities, Addition Right Successor Identity, Addition Right Zero Identity, Lesson Plans, Lessons Lower Elementary Grade Levels, Number Line Induction, Number Line Recursion, Pair of Number Line Method of Addition, Recusive Inductive Definition of Addition, Teaching prime notation with number lines, Teaching x and y with Number Lines | 1 Comment

Milgram Russia uses implicit Peano Axioms from Grade 1

Professor R. James Milgram of the Stanford Math Department is extensively involved in math education at the elementary school level. Milgram stresses that in Russia, the elementary school math program is better devised than in the US.  The math program … Continue reading

Posted in 21st Century Peano Addition Authors, Addition Proofs, Difficult Math Problems for Grades 1 to 3, Multiplication Associative, Multiplication Commutative, Multiplication Distributive, Multiplication Proofs, Peano Axioms, Peano Axioms Implicit First Grade, Proof Addition is Associative, Proof Addition is Commutative, Recursive Inductive Definition of Multiplication, Recusive Inductive Definition of Addition, Russian Math Education, Use of x early | 1 Comment