Number and operations, Part 2. Making meaning for operations.
Series: Developing Mathematical Ideas (DMI).
Grades: K 1 2 3 4 5 6
ENC#: ENC018073
Publisher: Dale Seymour Publications
Date: 1999
Ordering Information


Subjects:
 Mathematics Arithmetic. Concept formation. Instructional issues. Learning theory. Operations. Process skills. Professional development. 
Resource Type: Professional development.
Abstract: 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: [Casebook:] Introduction 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 Valentine stickers 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 onethird to onefourth, or interesting stuff happens! Doling out and fractions Taking portions of portions, or multiplying fractions A fourth into three parts: one thirtytwoth? 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 Stretching elastic 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
[Facilitator guide:] Orientation to the materials Tips for facilitators Detailed agendas 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 Maxine's journal Introductory note 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
Vendor: Dale Seymour Publications Pearson Learning Group PO Box 2500 Lebanon IN 46052 (800) 2373142 (800) 3213106 Fax: (800) 3933156 http://www.pearsonlearning.com
  
Pricing Information:
 Description: 1 casebook (paperback)  Cost: $34.95  Note: Facilitator Package; Facilitator Guide; and Videotape all sold seperately.  ISBN: 9780769001722  Order#: 21964   Description: 1 facilitator guide (paperback)  Cost: $35.95  ISBN: 9780769001739  Order#: 21965   Description: 1 videotape  Cost: $19.95  ISBN: 9780769000923  Order#: 21895   Description: 1 facilitator package  Cost: $79.95  Note: Facilitator package includes 1 casebook, 1 facilitator guide, 1 video.  ISBN: 9780769001746  Order#: 21966  
Publisher: Dale Seymour Publications Contributor(s):
 Authors: TERC; Education Development Center. 
Funding Agency: National Science Foundation (NSF). Specifications: Kit includes: 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
