As the Fall semester comes to a close, we are preparing for Spring at our school sites. Next on the list for our team is fractions. I am so excited to begin working with students to understand how they think about fractions and what we as teachers can do to give them opportunities to increase their conceptual understanding in this area.
As a highschool teacher, I experienced firsthand the phobia fractions would cause students. They would be able to work problems without a second thought, but throw in a fraction and it became a whole new level of complication. I am sure if you are a teacher reading this, you have experienced the disconnect that is presumed between fractions and whole numbers. It would sometimes feel as though the students didn’t really think fractions were numbers at all. Dr. Les Steffe has proposed that this is due to the way we present fractions to students (Steffe, 2010).
Dr. Steffe calls this his Reorganization Hypothesis. He claims that students can “reorganize” their whole number concepts in order to use them in continuous scenarios. A continuous scenario would be something like a string. It is countable if you choose a unit by which to measure, such as an inch. Then you can begin to overlay your number sequence onto the string and count. This can then turn into fractional understanding when the children also begin to partition items. For instance, sharing a candy bar among five people is a task that allows students to use their number concepts to fit within a whole. They have to use the whole candy bar to make five equal pieces. Steffe’s understanding is that students use their whole number concepts to do this, and that by separating fractional understanding from whole number understanding, we have created problems for students.
So this is what the Coordinating Units team will be exploring this Spring, and I have been reading for over a year now to prepare. If fractions are of interest to you in your classroom, then keep reading this blog, and feel free to write questions and comments. I will be sharing what we learn as we go.