explain how children's concepts of partitioning need to be refined to produce a concept of fractional parts
Since this is not my area of expertise, I searched Google under the key words "children's concepts fractions" to get this:
http://www.google.com/search?client=safari&rls=en&q=children's+concepts+fractions&ie=UTF-8&oe=UTF-8
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.