Fractional Thinking in Kindergarten

The cover story of this month's NCTM publication, Teaching Children Mathematics, certainly catches the eye of anyone involved in teaching young children mathematics. The article, Can Kindergartners Do Fractions,is a very information piece on the author's rigorously designed research project in which she explored young children's fractional thinking through the concept of fair sharing. The researcher, Julie Cwikla, reports quite strongly that "the results indicate that pre-K3 children can fairly and properly distribute whole items but are confused with the "leftover" one or two items". Using drawings, writing and the spoken word Cwikla interviewed the students as they were given fair share tasks to solve. This meant that children were given plenty of opportunity to communicate their thinking in a variety of ways. The  interviews were video and reviewed by the researcher.

Perhaps the most interesting thing for me about this research is the selection of fractional thinking as a form of fair sharing or even the definition of fractions as a way of thinking. I find this particularly interesting because in sort of flies in the face of the provocative title of the piece "Can Kindergartners Do Fractions?".  If you were to present this title as a simple question to any person not involved in education you would probably be laughed at or at best receive a resounding "of course not".

I always wonder why it is that anything related to math is preceded by the verb "do" as in "do the math", "how do you do multiplication?"; "doing division"; "do some problem solving"; "do fractions". Also, if you say "doing fractions" to most people they will conjure up images of  1/3 or 4/7 or 3/4 x 4/5 or regale you with horror stories of how awful their experiences with fractions were in elementary school. And, of course, the conversation usually ends up with "change the sign and invert the second fraction"; a mystifying process to most people.

What this wonderful article does most  importantly is to remind us that fractions are a way of thinking about the world, a way of looking at parts of whole numbers, an important part of the quantitative literacy part of our growth and development. This idea of fractional sense has to develop naturally, as the author suggests from as early as age 3 so that later in school (grade 3 according to the Common Core Math Standards) students will be ready for the formal procedural aspects of learning about,understanding,  and communicating with, fractional terminology.