Summer Workshop Plans

InMath Summer Workshop Agenda

InMath is working with 6 elementary school districts in West Michigan who are implementing the Investigations in Number, Data and Space program (Investigations). This curriculum is centered around four major strands: number, geometry and measurement, data, and change. Our project will focus on 1 or 2 of these strands in each of the next 3 summers. The workshop for this summer focuses on the number strand of the curriculum.

How long do your workshops last?

This summer we offered a one-week workshop.

How many teachers do you involve in your workshops?

Approximately 250 teachers (and principals) will attend the workshop this summers. This workshop is being offered twice to accommodate the large numbers. 165 attended the June workshop and approximately 85 will attend in August.

What are your major goals for your workshops in terms of content and pedagogy?

The summer workshops were developed to engage teachers in thinking carefully about the content and teaching of the Investigations program. More specifically, the goals for this summer are:

• To assist teachers in gaining an understanding of the K-5 development of number sense and computation skill in Investigations. This includes strategies for putting together and taking apart whole numbers, fractions, and decimals, and learning how an understanding of the number system can be developed by using landmark numbers.

• To model instructional practices for effective implementation of Investigations. Teachers will investigate and explore the mathematics in the same way that they will have their students do mathematics with this new program and discuss their reactions to doing mathematics in this way.

• To engage teachers in the process of analyzing student work, reflecting on their own assessment practices, and understanding the variety of assessments built into the Investigations program.

Yes, all teachers in our project are using the Investigations curriculum.

	Monday	Tuesday	Wednesday	Thursday	Friday
8:30 am - 10:10 am	Introduction: Whole group (45 minutes) 9:25 - 10:10: Grade level Break-out (M1)	Sessions 1, 2, 3 & 4: held concurrently with 4 rotating groups	Sessions 1, 2, 3 & 4: held concurrently with 4 rotating groups	Sessions 5, 6, 7, & 8: held concurrently with 4 rotating groups	Sessions 5, 6, 7, & 8: held concurrently with 4 rotating groups
10:10 - 10:25 am	BREAK
10:25 am - 12:05 pm	Sessions 1, 2, 3 & 4: held concurrently with 4 rotating groups	Sessions 1, 2, 3 & 4: held concurrently with 4 rotating groups	Case Discussion 1 (3 groups) Counting by Ones and Counting by Groups	Sessions 5, 6, 7, & 8: held concurrently with 4 rotating groups	Sessions 5, 6, 7, & 8: held concurrently with 4 rotating groups
12:05 - 1:00 pm	LUNCH
1:00 - 3:00 pm	Grade Level Breakouts (M2) Book cover-to-cover and Choice Time	Grade Level Breakouts (T) Book cover-to-cover and Choice Time	Grade Level Breakouts (W) Discuss Choice Times from Mon./Tuesday Classroom Routines/Ten-Min. Math	Grade Level Breakouts (Th) Assessment: Assigning grades, Rubrics, & Managing Observations	Case Discussion 2 (3 groups) Issues around Invented Procedures Evaluations

Session Titles:

• Session 1: Basic Fact Strategies
• Session 2: Understanding Addition and Subtraction
• Session 3: Understanding Multiplication and Division
• Session 4: Understanding of the Number System
• Session 5: Computation: Addition & Subtraction
• Session 6: Computation: Multiplication & Division
• Session 7: Fractions
• Session 8: Decimals

STRUCTURE OF THE WEEK

To accommodate the large number of participants -- 165 attended the first week -- each participant was assigned to two different groups:

• A "color" group for K-5 development sessions, mainly held in the morning. Each of the 4 color groups had representatives from every participating district, every grade level, and administration.
• A "grade level breakout" group for afternoon discussion of issues pertinent to particular grade levels. The grouping used in June was were: K-1, 2-3, 3-4, 4-5. [This grouping was determined by the numbers of teachers at each grade level.]

Sessions 1-4 were run concurrently four times, with each color group rotating through these sessions in varying orders, so that participants completed these sessions before Wednesday's case discussion. The same was done for Sessions 5 - 8. [Each leader was responsible for two sessions, one from each block, and facilitated the session 4 times. Each leader had the same grade level breakout group for the entire week.

For example, here is Tuesday's detailed schedule:

8:30 - 10:10	K-5 DEVELOPMENT SESSIONS
	Yellow	Session 2	Prairie V
	Pink	Session 3	Prairie VI
	Blue	Session 4	Oaks
	Green	Session 1	Prairie IV
10:10 - 10:25	BREAK
10:25 - 12:05	K-5 DEVELOPMENT SESSIONS
	Yellow	Session 3	Prairie VI
	Pink	Session 4	Oaks
	Blue	Session 1	Prairie IV
	Green	Session 2	Prairie V
12:05 - 1:00	LUNCH
1:00 - 3:00	GRADE LEVEL BREAKOUTS
	K-1	Prairie IV
	2-3	Prairie V
	3-4	Oaks
	4-5	Prairie VI

BRIEF SUMMARY OF EACH OF THE K-5 DEVELOPMENT SESSION

Session 1: Basic Fact Strategies

This session focused on the activities that Investigations uses to help students develop fluency with basic facts. This includes: quick images, clue cards, counting around the classroom, and activities with the 100 chart. The role of timed facts tests, flash cards and memorization vs. strategy development and fluency were discussed.

Session 2: Understanding Addition and Subtraction

Participants investigated addition and subtraction story problems, analyzed their similarities and differences, and discussed the strategies students typically use to solve such problems. Discussion centered around the role of stories in the curriculum as the way students come to understand what it means to add and subtract.

Session 3: Understanding Multiplication and Division

This session focused on investigating contexts for multiplication and division, analyzing their similarities and differences, and the strategies students use to solve such problems. Participants were introduced to the use of rectangular arrays, and their role in helping students understand multiplication and division.

Session 4: Understanding of the Number System

The purpose of this session was to help participants extend their notion of place value. Participants looked at activities involving the 100's chart and created 1000's charts using different factors of 1000. Discussion revolved around the ways this model (100 chart) is used in Investigations to develop an understanding of the patterns within our number system.

Session 5: Computation: Addition & Subtraction

In this session, participants explored strategies for doing mental addition and subtraction computation in ways that built on their ability to break apart and put together numbers. Strategies were analyzed for sophistication, efficiency ant understanding about number displayed by the students using these strategies. [Portions of a DMI Video tape highlighting different student strategies were shown.]

Session 6: Computation: Multiplication & Division

In this session, participants explored strategies for doing multiplication and division computation in ways that built on their ability to break apart and put together numbers. Strategies were analyzed for sophistication and efficiency and discussion included the necessity of understanding the meaning of multiplication and division and the understanding about number displayed by students using these strategies. [Portions of a DMI Video tape highlighting different student strategies were shown.]

Session 7: Fractions

In this session, participants explored different approaches to creating equal shares. Models for fractions, and informal comparisons using benchmarks and computation with fractions were also explored.

Session 8: Decimals

This session extended the work on breaking apart and putting together whole numbers to decimals. The relationship between fractions, decimals and percents was explored and the use of the 100-grid as a model for decimals was investigated.

BRIEF SUMMARY OF THE GRADE LEVEL BREAKOUT SESSIONS

Breakout M1: (only 45 minutes, 9:25 to 10:10)

• Intros of participants & intros to what will be done in breakouts for the week

• Jigsaw on parts of the book: About the Mathematics, Teacher Notes, Dialogue Boxes, About the Assessment, Routines, ...

• 1:00-2:00pm
  Go through book* cover-to-cover with Grade level A while Grade Level B does choice time

• 2:00-3:00pm
  Go through book* cover-to-cover with Grade level B while Grade Level A does choice time

• 1:00-2:00pm
  Go through book* cover-to-cover with Grade level A while Grade Level B does choice time

• 2:00-3:00pm
  Go through book* cover-to-cover with Grade level B while Grade Level A does choice time

• Discuss Choice Times from Monday & Tuesday

• Classroom Routines or Ten-Minute Math

• Assessment: Looking at Student Work

• Bridges Project Videotape for grade 2-5

• Kathy Richardson Videotape for grade K-1

• Assigning Grades, Rubrics, and Managing Classroom Observations

Video References

• Bridges Project: 4th Grade Assessment (27 x 4), TERC/COMAP, 1998. [Used in the grade-level breakout sessions for grades 2 - 5 in discussing assessment issues.]

• Kathy Richardson. Math Time: A Look at Children's Thinking. Educational Enrichment Inc., 1998, 1990. [Used in the grade-level breakout sessions for grades K-1 in discussing assessment issues.]

• Developing Mathematical Ideas: Number and Operations: Building a System of Tens. TERC, 1988

• Developing Mathematical Ideas Project. Module 1: Building a System of Tens., Dale Seymour Publications, 1999.

• Developing Mathematical Ideas Project. Module 2: Making Meaning for the Operations, Draft Version (soon to be available from Dale Seymour).