4-VA

Summary

The researchers from VT have done extensive research on upper elementary and middle school students' fraction schemes and have validated a hierarchical framework that identifies how upper elementary and middle school students make sense of situations involving fractions.  The researchers from JMU have engaged in research pertaining to prospective PreK-8 teachers' mathematical knowledge for teaching. 

Our current collaborative research has validated a similar developmental trajectory of the fraction schemes/operations for PreK-8 prospective teachers as were identified for younger students.  We have also documented that although most of our participants demonstrated evidence for the lower fraction schemes/operations in the hierarchy, only 53% demonstrated evidence of the Reversible Partitive Fraction Scheme (RPFS) and only 27% demonstrated evidence of the Iterative Fraction Scheme (IFS), the two most sophisticated schemes in the hierarchy.

We have also used the findings from our 2013-2014 study to inform course redesign for the mathematics course for the PreK-8 prospective teachers that involves fraction instruction,  In particular, we have identified instructional tasks that should promote the advanced schemes and operations (i.e., RPFS, IFS).  We plan to administer the written assessment used in our 2013-2014 study before and after course instruction to identify changes in prospective teachers' fraction schemes and operations (n = 125).  We will also conduct clinical interviews with a sample of 30 prospective teachers, chosen based on their performance on the written assessment, to further validate the written assessment items.  The implementation of the instructional tasks and the pre/post-instruction written assessments as well as the clinical interviews form the basis of the pilot study.