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Implementing Investigations in Mathematics (InMath) 2001 Summer Workshop Summary

submitter: Implementing Investigations in Mathematics (InMath)
published: 07/24/2001
posted to site: 07/24/2001

Implementing Investigations in Mathematics (InMath)
2001 Summer Workshop Summary

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 analysis, 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 focused on the data analysis and change strands of the curriculum.

How long do your workshops last?

This summer we offered a three-day workshop.

How many teachers do you involve in your workshops?

Approximately 236 teachers (and principals) attended the workshop this summers. This workshop was offered twice to accommodate the large numbers. 129 attended the first June workshop and 107 attended the second June workshop.

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 data analysis and change in Investigations. This includes: exploring issues in collecting, representing, analyzing and interpreting both numerical and categorical data; understanding the limitations of any one statistic in representing a data set; comparing data sets using a variety of measures; analyzing probabilistic situations; and exploring issues surrounding the collection, representation, analysis and interpretation of change situations.
  • 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 reflecting on teaching, with a particular focus on the mathematical emphasis of lesson(s), providing a supportive environment for student learning through better questioning techniques; and understanding the variety of assessments built into the Investigations program.

Are you offering professional development on specific curricula that you are hoping will be used in the classroom? If so, which curricula are you using?

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

Are you using specific professional development materials?

A few of the sessions include ideas from the Bridges Manual created by TERC for doing professional development on Investigations.

Agenda for InMath Summer 2001 Workshop

Data Analysis and Change

Time Monday Time Tuesday Wednesday
8:30 a.m.-
9:10 a.m.

9:10 a.m.-
10:50 a.m.


Numerical Data: Yellow
Categorical Data: Pink
Change I: Blue

8:30 a.m.-
10:10 a.m.
Numerical Data: Pink
Categorical Data: Blue
Change I: Yellow
Comparing Sets of Data: Blue
Change II: Yellow
Probability: Pink
10:50 a.m.-
11:00 a.m.
Break 10:10 a.m.-
10:25 a.m.
11:00 a.m.-
12:40 p.m.
Numerical Data: Blue
Categorical Data: Yellow
Change I: Pink
10:25 a.m.-
12:05 p.m.
Comparing Sets of Data: Yellow
Change II: Pink
Probability: Blue
Comparing Sets of Data: Pink
Change II: Blue
Probability: Yellow
12:40 p.m.-
1:30 p.m.
Lunch 12:10 p.m.-
1:15 p.m.
1:30 p.m.-
3:30 p.m.
  • Reflecting

3-5 Choices:
  • Exploring a Book
  • Math Extension
1:15 p.m.-
3:30 p.m.
K-2 Choices:
  • Exploring a Book
  • Math Extension


  • Reflecting
(Using student work from data units):



Morning Sessions
The morning sessions were devoted to K-5 development of mathematical content. To accommodate the large number of participants - 129 attended the first week - each participant was assigned to a different color groups. Each of the 3 color groups had representatives from every participating district, every grade level, and administration. Sessions 1-3 were run concurrently three times, with each color group rotating through these sessions in varying orders. After all groups had rotated through the first three sessions, the same was done for Sessions 4 - 6. [Leaders of the AM sessions were each responsible for two sessions, one from each block, and facilitated their sessions 3 times.]

Afternoon Sessions
In the afternoon we offered a variety of sessions for participants to choose from, many of which were geared towards a particular grade level or grade level band (e.g., K-2, 3-5). Afternoon sessions were approximately 2 hours long and were lead mainly by InMath Teacher Leaders.

For example, here is Tuesday's detailed schedule:


Tuesday, June 19th

Change I
Numerical Data
Categorical Data
10:10 - 10:25 BREAK
Comparing Sets
Change II
12:05 - 1:15 LUNCH
Math Extension K-2
Reflecting 3-5, A-K
Reflecting 3-5, L-Z
Exploring a Book (K)
Exploring a Book (1)
Exploring a Book (2)



Session 1: Numerical Data
The purpose of this session is to familiarize participants with the issues surrounding the collection, representation, analysis and interpretation of numerical data. Particular attention was paid to describing data sets in ways that provide substantive information about the set, determining what is "typical", and understanding the effect of altering the intervals used in a histogram on the perceived shape of the data.

Session 2: Categorical Data
The purpose of this session is to familiarize participants with the issues surrounding the collection, representation, analysis and interpretation of categorical data. Particular attention was paid to understanding the effect that different categorization schemes have on the data analysis process, from determining how to construct a survey, to the analysis and interpretation of the data.

Session 3: Change I
In this session, participants think about how to represent change over time, and the assumptions that they make about what happens between data points. Participants explored continuous and discontinuous data, the concept of net change, and connections to the number strand.

Session 4: Comparing Data
Participants explored the complexities of comparing data sets through collecting, analyzing and interpreting two related sets of data. The participants were then confronted with making a decision about an issue based on descriptions of two different data sets, without being able to see the actual data. This second activity drove home the importance of good descriptors, and the limitations of comparing data sets based solely on the basis of a single descriptor.

Session 5: Change II
This session extended the first Change session by having participants explore graphical and tabular representations of change situations, and the relationships between these two representations. Particular emphasis was placed on describing the shape of the data, and learning to interpret what aspects a graphical representation of change (for example, the steepness of the graph) mean in the context of a particular situation.

Session 6: Probability
The purpose of this session is to encourage participants to think about the development of probabilistic concepts. The session began with an exploration of likelihood, and why a half-green spinner doesn't necessarily come up green half the time. The main activity involved the participants investigating a real-life situation in which they had to make predictions about the outcome, create a simulation experiment to allow them to create an experimental data set for the situation, conduct the experiment, and analyze the results.

Description of Afternoon Choices

Exploring a Book (offered once for each grade level):
These sessions will involve an exploration of the following data units by grade level. Topics for discussion will include: understanding the mathematical emphasis of specific investigations, sharing what students struggle with and suggestions for guidance, discussing the possibility of using extensions and excursions within the units, etc. These sessions are intended for experienced as well as new teachers.

Kindergarten: Counting Ourselves and Others
Grade 1: Survey Questions and Secret Rules
Grade 2: Does it Walk, Crawl, or Swim?
Grade 3: From Paces to Feet
Grade 4: The Shape of the Data
Grade 5: Patterns of Change

Reflecting on Teaching Sessions (offered once for each grade range (K-2 and 3-5):
These sessions will be similar to the grade-level meetings we have held for the past two school years in Grand Rapids. We will use a videotape of a lesson from Investigations to discuss the launch and closure of the lesson as well as how students are supported as they work through a particular investigation. We will not be able to offer grade-level specific Reflecting sessions, but rather will use a lesson from one grade level to discuss issues pertinent to a range of grade levels. These sessions are intended for both new and experienced teachers.

Math Extension Session (offered once for each grade level range (K-2 and 3-5):
This session will focus on mathematics beyond what is expected in Investigations in order to increase your understanding of mathematics. Participants will explore/investigate a mathematics problem involving change, make predictions about what might happen, pose possible solutions, and discuss the reasonableness of solutions. In other words, you will experience learning mathematics in the same way as your students are expected to learn in the Investigations program and you will deepen your understanding of mathematics. This session is intended for all teachers.

Assessment Sessions (offered once for each grade level range (K-1, 2-3 and 3-5):
These sessions will focus on issues pertaining to assessment. As our approach to "teaching" mathematics changes to focus on sense making and understanding, our approach to assessment must also change in order to capture what it is students are understanding. The challenges of assessing "understanding" will be addressed and some of the new end-of-unit assessments will be shared.


We are recommending specific sequences for the afternoon choices (depending on your level of experience with Investigations) and strongly encourage you to follow the recommended sequence. We also hope that everyone is able to attend a Reflecting on Teaching session.

K-2 Teachers new to Investigations or to the data units at their grade level:
Monday: Reflecting on Teaching Session
Tuesday: Exploring a Book
Wednesday: Assessment

K-2 Teachers with experience teaching data units in Investigations:
Monday: Reflecting on Teaching Session
Tuesday: Math Extension
Wednesday Assessment

3-5 Teachers new to Investigations or to data units at their grade level:
Monday: Exploring a Book
Tuesday: Reflecting on Teaching Session
Wednesday Assessment

3-5 Teachers with experience teaching data units in Investigations:
Monday: Math Extension
Tuesday: Reflecting on Teaching Session
Wednesday Assessment