Number and operations, Part 2. Making meaning for operations.
Series: Developing Mathematical Ideas (DMI).
Grades: K 1 2 3 4 5 6
Publisher: Dale Seymour Publications
Arithmetic. Concept formation. Instructional issues. Learning theory. Operations. Process skills. Professional development.
This professional development kit, part of the DEVELOPING MATHEMATICAL IDEAS (DMI) program, contains seminar materials designed to help current and future grades K to 6 teachers explore the meaning of arithmetic operations and understand how students develop these concepts. The DMI program offers field tested seminars examining the big ideas in elementary school mathematics. Each seminar is designed as a stand alone course typically presented over a full year to teachers who meet at regularly scheduled intervals. Seminar materials include a facilitator's guide with detailed agendas and background reading on the issues of facilitating teacher change; a casebook for each participant; and a videotape featuring actual students in classrooms organized around student thinking.
The participant's book for this seminar contains 28 cases exploring the types of actions and situations modeled by addition, subtraction, multiplication, and division, and the ways students come to understand these operations for whole numbers and fractions. The casebook is divided into chapters that correspond to the eight sessions of the seminar. The introduction to each chapter describes the set of cases, highlights the general mathematical themes they address, and gives the reader questions to consider while reading the cases. At each session, participants discuss the cases and are involved in a related mathematics activity designed to be challenging to adult learners. In the course of the sessions, participants look at and discuss innovative curricular materials, consider research findings related to mathematics education, and create and discuss a portfolio of their assignments. References are included. (Author/JRS)
Table of Contents:
Counting up, counting back, and counting by
Insects and spiders and counting on
Mr. McIntosh's apples
Going up and down with numbers
Complexities of counting backwards
Counting days and counting by
Bunnies and eggs
Thinking about division
Addition and subtraction as models
Red, blue. and yellow paint
Enough for a class
Rocks, trips, and writing groups
What is multiplication? What is division?
What is multiplication?
How do kids think about division?
More insects and spiders
Candy canes for the school
Student drawings for 12 divided by 4
Are these kids or seeds?
When dividing gives an answer less than one
Can you divide 39 into 5?
Can you divide 39 into 5? revisited
Combining shares, or adding fractions
Sharing brownies or adding fractions
How many ways can you add one-third to one-fourth, or interesting stuff happens!
Doling out and fractions
Taking portions of portions, or multiplying fractions
A fourth into three parts: one thirty-twoth?
Clock faces and equivalence
Multiplication of mixed numbers
What I want my students to understand about multiplication
Expanding ideas about division in the context of fractions
Who says that's not the right equation? My own experience vs. students' thinking
Highlights of related research, by Lisa Yaffee
Modeling addition and subtraction
Numerical reasoning begins
Modeling multiplication and division
Making meaning for multiplication and division
Encountering fractions in sharing situations
Understanding fractional amounts
Revising ideas for operators with fractions
Orientation to the materials
Tips for facilitators
How to use the agendas
Preparation for the seminar
Session 1. Counting up, counting back, and counting by
Session 2. Addition and subtraction as models
Session 3. What is multiplication? What is division?
Session 4. When dividing gives an answer less than one
Session 5. Combining shares, or adding fractions
Session 6. Taking portions of portions, or multiplying fractions
Session 7. Expanding ideas about division in the context of fractions
Session 8. Highlights of related research
January 26, goals for the seminar
January 29, session 1
February 12, session 2
February 26, session 3
March 12, session 4
March 26, session 5
April 9, session 6
April 23, session 7
May 10, session 8
Two portraits of change
Dale Seymour Publications
Pearson Learning Group
PO Box 2500
Lebanon IN 46052
Fax: (800) 393-3156
Description: 1 casebook (paperback)
Note: Facilitator Package; Facilitator Guide; and Videotape all sold seperately.
Description: 1 facilitator guide (paperback)
Description: 1 videotape
Description: 1 facilitator package
Note: Facilitator package includes 1 casebook, 1 facilitator guide, 1 video.
Dale Seymour Publications
|Authors: TERC; Education Development Center.|
National Science Foundation (NSF).
1 casebook (149 pages : illustrations ; 26 cm.)
1 facilitator guide (159 pages ; 28 cm.)
1 videotape (VHS, 13 min. : sound, color ; 1/2 in.)
Record Created: 10/05/2000 Last Modified: 08/03/2005