This spring, the Coordinating Units team will begin looking into how students develop an understanding of fractions. We have been reading the research in this area done by Dr. Leslie Steffe. In his research with students he theorizes that if students have a fully developed whole number sequence and are able to use it flexibly, they are able to apply this understanding of whole numbers to fractions because they are able to see their number sequence on top of an item that is to be partitioned. He called this the reorganization hypothesis. We as teachers do our students a disservice when we teach fractions as separate and different from whole numbers.
While reading Steffe’s research, I thought about our current common core standards. It makes sense that the formal introduction of fractions is pushed to third grade. We want to make sure that students develop a strong foundation of number in kindergarten through second grade. When we introduce the concept of a unit fraction in third grade we want our students to see fractions as a unit that is countable.
As elementary teachers, we sometimes forget the power we have in providing our students with experiences that will lay the foundation for concepts they will build on in later grades. In the case of fractions, first grade teachers may think they do not need to worry about developing an understanding of fractions with their students. The only experiences with fractions, called out in the language, such as “halves,” “fourths,” and “quarters,” is found in the geometry standards in relation to partitioning shapes. But if we look at the first cluster of the Measurement and Data domain – measure lengths indirectly by iterating length units- the second standard in this cluster has students:
1.MD.A.2. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.
This particular standard provides students with a very concrete experience of seeing a countable sequence over the top of another unit, which is what we would like them to be able to do with fractions. When I was a classroom teacher I did not spend a lot of time on measurement, especially the way this standard describes, having students measure items with a non-standard unit of measurement. If we were really rushed we might just look at the picture in the textbook of a pencil with 3 paper clips beneath it and have my students fill in the blank, “The pencil is ____ paper clips long.” The more I read, however, the more I realize It is important for them to have the experience of measuring with real objects, not just look at a picture in the textbook. When exploring this standard with our students, we K-2nd grade teachers are not only teaching students about measurement, but we are providing experiences that will help lay the foundation for their work with fractions. I invite you to continue to follow our journey into fractions by reading and responding to our blog as we begin our work with fractions this spring.