Deborah Schifter, Virginia Bastable, and Susan Jo Russell
The
Reasoning Algebraically about Operations Casebook was developed as
the key resource for participants’ Developing Mathematical Ideas seminar
experience. The thirty-four cases, written by teachers describing real
situations and actual student thinking in their classrooms, provide the basis
of each session’s investigation into the generalizations underlying the
study of the operations in the elementary and middle grades and teaching
strategies that support students’ efforts to make sense of the concepts.
Reading and discussing the cases under the guidance of the
facilitator actively engages participants in their own learning enterprise as
they—
learn to recognize the key mathematical ideas
with which students are grappling;
consider the types of classroom settings and
teaching strategies that support the development of student understanding;
become aware of how core mathematical ideas
develop across the grades;
work on mathematical concepts and gain better
understanding of mathematical content; and
discover how to continue learning about children
and mathematics.
The casebook is composed of eight chapters: the
first seven consist of classroom cases from kindergarten through grade 7;
chapter 8 is an essay providing an overview of the research related to the
situations described in the first seven chapters. The chapters are as follows:
Chapter 1: Discovering rules for odds and evens
Chapter 2: Finding relationships in addition
and subtraction
Chapter 3: Reordering terms and factors
Chapter 4: Expanding the number system
Chapter 5: Doing and undoing, staying the same
Chapter 6: Multiplying in clumps
Chapter 7: Exploring rules for factors
Chapter 8: The World of Arithmetic from
Different Points of View