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Fraction Reasoning in the Classroom: Ongoing Assessment and Instruction for Teachers Grades 3-8

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Appropriate for Teachers Grades 3-8

Course Description:

The ability to reason fractionally, compare and order fractions, understand the part/whole relationship and operate with fractions is essential for students in elementary and early middle grades to access the mathematics expected of them in middle school. Fractional reasoning is the cornerstone concept for intermediate mathematics knowledge and the foundation of middle school mathematics. The Fractional Reasoning Course is a professional development opportunity for teachers based on the cognitive research currently available on misconceptions and developing understandings for students in fractional reasoning. Teachers will become familiar with the cognitive research by interacting with materials developed, through an NSF grant, which makes the research transparent and explicit by developing materials for them to use in their classrooms. Teachers will provide intensive math instruction for students in their own classrooms by modeling and putting into practice strategies and content learned in the class. Teachers will assess their students’ understanding in the area of fractional reasoning and develop instructional strategies to address student misconceptions and developing understandings. They will work closely with their colleagues to analyze the ongoing information they collect and to develop intervention strategies to increase their students’ understanding. There will be a direct link between the research, instructional methods, and the CCSS-M. Teachers will learn and practice using strategies and methods that reflect current research in mathematics instruction. An important aspect of the course will be the opportunity for teachers to use formative assessment materials in order to gain a deeper understanding of their students’ knowledge to regularly inform their instruction and make instructional decisions for the purpose of increased student understanding.

This course will incorporate a variety of teaching strategies with the purpose of modeling research-based best practices. There will be lecture, discussion, small group collaborative learning, participant presentations, and constructed understanding through teacher facilitation and modeling.

Course Goals and Objectives:
• To provide familiarity with CCSS related to fractional reasoning
• To understand current research on student misconceptions and developing understandings of fractional reasoning
• To understand and use ongoing assessment strategies and tools for the purpose of making instructional decisions
• To examine materials and methods for teaching mathematics related to fractional reasoning
• To collaborate with colleagues to plan, deliver, and evaluate instruction
• To increase understanding of methods that allow teachers to meet the needs of a diverse population of students in the regular classroom
• To increase ability to examine student work to understand student knowledge and inform instruction
• To become familiar with gaps in program materials related to fractional reasoning research and plan for addressing them
Course Requirements:
• Assigned readings and responses
• Review and design of instructional program
• Implementation of formative assessment practices
• Implement the OGAP Fractional Reasoning Materials
• Documentation of classroom implementation
• Reflection on and sharing of classroom implementation
• Attendance and active participation

Required Text:
Petit, M., Laird, R., Marsden, T. (2010). A Focus on Fractions: Bringing Research to the Classroom. New York, NY: Routledge Group

Mary Abele-Austin has spent the last 11 years focused on improving math instruction through imbedded professional development for classroom teachers. She currently works at with teachers Pre-K to 8th grade in the Waterbury / Duxbury School District as their math coach / coordinator. This is her 10th year in this capacity. Mary is actively implementing the lesson study model of professional development with her math teachers. Mary is trained facilitator for the On-Going Assessment Project (OGAP) in Fractions, Multiplicative Reasoning, and Proportionality. Before becoming a math coach, Mary worked as a 3rd/4th grade classroom teacher. Mary graduated from the University of Vermont in 1989 with a BS in Elementary Education. She received her Master’s Degree from UVM and the Vermont Mathematics Initiative in May of 2010.

Luke Fisher has been an elementary educator for 18 years. Currently he is a 5th and 6th grade math teacher at Woodstock Elementary School and the Windsor Central Supervisory Union (WCSU) district K-6 math coach. Prior to that he taught kindergarten for 12 years. His longtime interest in mathematics, and mathematics education, led to his enrolment in VMI, graduating with a CAS in 2010. Since then he has also been an instructor with VMI. Luke’s focuses as a math coach have been to help teachers develop more effective teaching practices, differentiate lessons, and align Investigations more effectively with the CSSM.