



Children's Mathematical Development
Sponsored by Project MIPS  Summer, 1998
8:30 a.m.3:30 p.m. (MTh), 8:30 a.m.noon (F)
Day 1  Early Number Development, Number Fluency, Developing Operations 
8:30 a. m.  11:45 a.m. 
Who are we?
 Completing project data collection forms as needed (including CGI Beliefs survey and MSEN Beliefs/Registration forms)
 Exploring metaphors about our own teaching
What's this workshop about? What's in the notebook?
Warming up! How fluent are you?
What is number fluency? (Reference Richardson, Notebook articles, pp. 16)
 What sized numbers should kindergarten students be fluent with? 1st graders? 2nd graders? 3rd graders? 4th graders? 5th graders? Fluent in what ways?
Working with "smaller numbers":
 Counting
 Number combinations
Video interviews conducted by Kathy Richardson
What are the implications across K5?
What's involved in learning to count? What is the nature of counting across K5?
CGI  what's it all about? Exploring CGI problem types
 Problem sorting activity
 CGI problem types for addition and subtraction.

11:45 a.m.  12:45 p.m.  Lunch 
12:45 p. m.  3:30 p.m. 
Investigating addition and subtraction problems focused on our own number fluency and number sense. A look at children solving the same problems.
More with CGI:
 Children's solution strategies for addition and subtraction
 Looking at tapes of students solving problems
 Writing CGI problems
 Role playing solving problems (in triads).
Journal: What insights have we gained? What do these mean for how we think about teaching and learning mathematics K5?
Homework: Read Cognitively guided instruction, pp. 1135 (Section Notebook, p. 111) 
Day 2  Developing Operations, Place Value 
8:30 a. m.  11:30 a.m. 
Review CGI work with addition and subtraction and discuss reading.
A look at CGI in classroom settings.
More with CGI:  CGI problem types for multiplication and addition
 Children's solution strategies
 Looking at tapes of students solving problems
 Writing CGI problems

11:30 a.m.  12:30 p.m.  Lunch 
12:30 p. m.  3:30 p.m. 
Investigating multiplication and division problems focused on our own number fluency and number sense. A look at children solving the same problems.
Planning for CGI interviews with children on Wednesday morning
Working with place value:  Using DMI Cases 1.1
 Reading, discussions in pairs, quads, whole group
 Playing game: "Close to 100"
Journal/discussion: What insights have we gained? What do these mean for how we think about teaching and learning mathematics K5?
Homework: Read Cognitively guided instruction, pp. 3758 (Section Notebook, p. 111) 
Day 3  Developing Operations, Place Value 
8:30 a. m.  11:30 a.m. 
Interviewing children using CGI problem types
 Are we ready to interview?
 Conducting interviews in pairs: Observer/recorder and interviewer roles
 Making sense of what we heard and saw
Review CGI work with multiplication and division and discuss reading.
Linking CGI problem types with literature
Teams (grade level): Writing CGI problems for our students
How might we use CGI problems to encourage the development of grouping by 10's, 100's? 
11:30 p. m.  12:30 p.m.  Lunch 
12:30 p. m.  3:30 p.m. Building systems of 10s, 100s 
Working with systems of ten: Using DMI Cases 1.2  Viewing Video
From Investigations in Number, data, and space
Making 10s: Setting up choice time/ Exploring games
Making 100s: Using the Hundreds Chart/Exploring games
Quiet time: Reading "Landmarks in the Number System"
Journal/discussion: What insights have we gained? What do these mean for how we think about teaching and learning mathematics? What we want to look for in a mathematics curriculum?
Homework:
DMI Cases 1.2  More with systems of ten
Jigsaw reading: (Notebook articles)
 A. Hankes (pp. 2531;
 B. Kamii, Lewis, & Bookes (pp. 3336);
 C. Chambers (pp. 79) & Carey (p. 3739)

Day 4  Place Value Tied to Operations 
8:30 a. m.  11:30 a.m. 
Discussion of DMI Cases 1.2
Building students' understanding of 1000
 Extending the model for using the Hundreds Chart to working with 1000 taken from Investigations in Number, data, and space
Establishing grade level groups and identifying facilitators
 Getting familiar with new curricula: Looking for sequence and strategies for working with concepts related to place value in Everyday Math, Trailblazers, and Investigations in Number, Data, and Space.
Looking as classroom teachers exploration of CGI 
11:30 p. m.  12:30  Lunch 
12:30 p. m.  3:30 p.m. Invented Strategies and the Role of Algorithms; Fractions 
Jigsaw discussion groups:  "Like article" groups summarize key points
 "Sharing articles" groups listen/discuss
What do we want to see maintained in children's "mathematical talk" as they develop invented strategies, record their work, and move to algorithms?
Exploring fractions (Reference, Notebook articles, Empson, pp 7579)
What do we want to emphasize?
 Using the context of A Doorbell Rang
 Using the context of Geoboards.
Journal/discussion: What insights have we gained? What do these mean for how we think about teaching and learning mathematics? What we want to look for in a mathematics curriculum?
Homework:  Rowan & Robles, Notebook articles, pp 1116
 Read Cognitively guided instruction, pp. 91 108 (Section Notebook, p. 111)

Day 5  Invented Strategies and the Role of Algorithms 
8:30 a. m.  noon 
What does it mean to articulate a framework for children's mathematical development across K5? Use what we've done/read/discussed to help us think about this.
 View TERC Tape: The Development of Addition and Subtraction K5
Grade level groups: What are three "most important concepts" in mathematics related to number at your grade level? What is the nature of the development of these concepts as it should occur at your grade level?
 Report back results to begin to articulate a developmental framework.
MIPS Project: What's expected during this coming year? Planned follow up at school level facilitated by grade level leaders/instructional specialists/principals (emphasis on DMI cases). Planned followup meetings with either Susan or George (emphasis on Ginsberg book and sharing current student work portfolios).
 Completing project data collection forms as needed (including CGI Beliefs survey and MSEN Evaluation form)
Journal/discussion: What insights have we gained? What do these mean for how we think about teaching and learning mathematics K5? 
Video References
(CGI) Cognitively guided instruction, Wisconsin Center for Educational Research, School of Education, University of Wisconsin, Madison, WI. Set of video tapes (Contact E. Fennema)
Richardson, K. (1990). A look at children's thinking (Videotape and study guide). Norman, OK: Education Enrichment, Inc.
TERC (1996). Developing mathematical ideas: building a system of tens/making meaning of operations (videotape). Cambridge, MA: Author.
WBGH Boston (1995). Teaching math: A video library, K4 (videotapes and study guides) South Burlington, VT: The Annenberg/CPB Math and Science Collection, P.O. Box 2345 (8007657373)

