Petit and Laird's Presention on Formative Assessment and Fractions Instruction at NCSM

Vermont Mathematics Partnership’s (VMP) Ongoing Assessment Project

Marjorie and Robert presented a session titled: Facilitating the Use of Formative Assessment When Teaching Fractions: A Case from Research to Practice - Vermont Mathematics Partnership’s (VMP) Ongoing Assessment Project (OGAP) which was by far the most informative session that I attended at NCSM.  Therefore, I thought it might be valuable to share some of the key points.

The presenters have spent the past few years researching effective methods of instruction in fractions and delivery of professional development.  The workshop presented information on student learning and methods for improving teacher's understanding and ability to use formative assessments.  Three points I found very interesting, yet disturbing, had to do with teachers' lack of deep understanding in the effective use of formative assessments.  Marjorie and Robert found that teachers really do not understand formative assessment, don’t understand how to look at student errors and identify the misconceptions about fractions, and do not know how to use information gained in analyzing errors to plan the next instructional step.  Therefore it is important that staff development approach all these needs by providing teachers with the research basis for instructional approaches, a format for understanding misconceptions in student errors, and the instructional strategies to address the misconceptions.  This workshop provided an overview of what the research states, what teachers need to know to make good instructional decisions, and their approach to professional development.

Marjorie and Robert focused the workshop on the research about how students develop an understanding of fraction concepts and how a lack of understanding of fractions links to many different topics covered in middle school.  They have compiled all of their research into a new book, A Focus on Fractions: Bringing Research to the Classroom, which I have already ordered.  Three key findings I found interesting:

1. Magnitude and equivalence are critical skills that many middle schools students have not mastered.  Activities such a comparing and ordering are critical.
2. Many students approach fractions using whole number reasoning.  While this did not surprise me, what did is that the presenters state that this is so common that middle school teachers should plan their instruction presuming that this is true for all of their students.
3. Students often treat a fraction such as ¾ as a caption when working with part/whole models, but the number line forces them to see a fraction as one number and they struggle with that.

Another outcome of the Ongoing Assessment Project was the development of a Fraction Framework in which they have identified 5 types of reasoning students may use when solving fraction problems.  This framework can be found at the Vermont Assessment Project website and is an excellent resource.  My fellow participants and I used the framework to analyze real student responses.  By identifying the level of reasoning a student is using to solve a problem, the teacher can then determine the next lesson(s) to help the student develop an understanding of fractions and fraction strategies.

This was a comprehensive session, and I have barely scratched the surface in summarizing all of the valuable information presented.  If you have an opportunity to attend a session conducted by Marjorie Petit and Robert Laird, I suggest you take advantage of it.  Your time will be well spent.