Making Sense of Rational Numbers (fractions and decimals)

and the Four Operations

Sponsored by

The Salem State Collaborative Project for Math,

Science and Interdisciplinary Education (CPMSIE)

Location: Lynnfield High School Essex Street, Lynnfield, MA 01940

Presenter: Donna M. Buonopane, Ph.D.

Dates: Wednesdays, Oct. 14, 21, 28, November 4, 2009 Time: 3:45-6:00 pm

Audience: Gr. 4-7 teachers, instructional aides

Cost: $50 for Member Districts $195 for non-member Districts

For Member List see website www.salemcollaborative.org

PDP’s: 10 Hours with Completed Project

We know from extensive research that many people – adults, students, and teachers – find the rational-number system to be very difficult. This number system requires that students reformulate their concept of number in a major way. They must go beyond whole-number ideas, in which a number expresses a fixed quantity, to understand numbers that are expressed in relationship to other numbers. These new proportional relationships are grounded in multiplicative reasoning that is quite different from the additive reasoning that characterizes whole numbers. (p. 310, How Students Learn: Mathematics in the Classroom, National Research Council, 2005).

This seminar is designed to help teachers understand typical student misunderstandings and the problems that students have with rational numbers. The NCTM Standards and the MA Curriculum Frameworks urge a significant shift towards students’ mathematical understanding with meaning and away from merely memorizing procedures. For many teachers, one of the most difficult concepts to teach is computation using rational numbers. A major misunderstanding that students have is the continued use of whole-number reasoning in situations where it does not apply. An understanding of rational number concepts underpin many topics in advanced mathematics and carry significant academic consequences. For example, students cannot succeed in algebra if they do not understand rational numbers (p. 310, How Students Learn: Mathematics in the Classroom, National Research Council, 2005).

Teachers will consider students’ development of rational number concepts and carrying out the operations of addition, subtraction, multiplication, and division– knowledge about whole numbers and place value, the characteristics of each operation, and the transition of whole number concepts to rational numbers. Teachers will analyze students’ thinking in cases, view videotapes of students, do mathematics together and read related readings. Instructional approaches of a learning- centered classroom environment and activities will be presented and discussed.

Please register at our website www.salemcollaborative.org, or email the following information to Jim Kearns at registration@salemcollaborative.org. If you have registration questions, please either email (preferred) or call Jim at 781-771-4860.

Make checks or Purchase Orders payable to CPMSIE and Bring to the First Session

DEADLINE to sign up for Making Sense of Rational Numbers is October 8, 2009