The concept of fractions in no way depends on operations with whole numbers ... other than on counting. It depends only on (what amounts to) FACTORING "whole things" into *quantities* ... such as 19(8ths). It is accessible to children as soon as they can perceive *partitioning* numerous wholes into "equivalent" parts. Once they can perceive that kind of *fractioning*, they easily perceive the *scalar* operations in each denomination (which Wu ignores: scalar additions, subtractions, and whole-number multiples).
Children can easily learn all of that, LONG before they have mastered the complexities of "long multiplication" and "long division" ... even long before they have fully mastered the additions/subtractions of Arabic numerals. Without that kind of commonsensible comprehension of fractions, all else is scholastic gibberish.
- -------------------------------------------------- From: "Jonathan Crabtree" <firstname.lastname@example.org> Sent: Sunday, October 28, 2012 3:00 PM To: <email@example.com> Subject: Re: The Teaching of Fractions
> "I would not start teaching fractions until multiplication and division > (with whole numbers) are firmly established." > > Thank you for this post Bob. > > If we are to truly benefit from exploring and discussing this topic, we > should start off with accepted definitions relevant to children. > > So what is your definition of multiplication? > > What is your subsequent definition of division? > > What is your subsequent definition of fractions? > > Jonathan Crabtree