I have found the following resource online:
"Fractions: pikelets and lamingtons", State of New South Wales Department of Education and Training, 2003 PDF online, accessed 29/3/2014 (Note that according to the acknowledgements, most of it was written by Peter Gould, though he is not listed as the author.)
This document contains activities designed to support children's learning of fractions, as well as discussion of how children learn fractions and some review of literature. The activities described begin with children's natural language of "half" and "quarter", and then move directly to sharing numbers of pikelets and lamingtons between children in such a way that they must be cut into halves and quarters. So basically, the concept of "and a half" is introduced before other types of fractions.
I can't find further references to this idea in other literature yet, but I will add them to the answer if I do.
The following teaching sequence is described on page 61:
Students’ informal notions of partitioning, sharing and measuring provide a starting point for developing the fraction concept. Drawing on the research on developing the fraction concept and the identified problem of representing fractions as a/b, the following sequence is used to develop the fraction concept.
- Subdividing continuous quantities into halves and quarters using the names halves and quarters and identifying the sub-units.
- Sharing of numbers of continuous models. First using the halving strategy (e.g. Share 6 pikelets between 2 people, share 3 pikelets between 2 people, share 3 pikelets between 4 people) then coordinating the partitioning with the number of sharers.
- Recordings using sharing diagrams for the continuous model (typically circles or rectangles) showing the partitioning.
- Traditional recording of fractions used as “environmental print” linked to sharing diagrams. If a student choses to write one-quarter as 1/4 it is accepted as a common shorthand form.
- Comparison of units by re-dividing a continuous quantity, such as a paper streamer, leading to representing equivalent fractions (e.g. fraction wall).
- Identifying fractions as numbers and locations on a number line (comparison of location, Which is larger, 1/3 or 1/2?)
- Addition and subtraction of fractions using representations of equivalent fractions as subdivisions of the same unit of length ( 2/3 + 1/4). For example, addition or subtraction using the “fraction wall”.
- Symbolic operations with fractions based on students’ coherent and stable meanings for fractions that may be expressed symbolically.
It is important to build meaning for fractions arising from the process of division. In this
way halves, quarters, thirds and fifths arise from problems of sharing rather than being defined as abstract numerical quantities.
The teaching sequence described in the document builds fraction ideas on the foundation of equal sharing, and starts by using children's natural language of "half" and "quarter"begins with the idea of sharing things equally among people (pikelets and lamingtons actually), introducing the idea of sharing three pikelets among two people in only the second activity