Summer Workshop PlansImplementing Investigations in Mathematics (InMath) 2001 Summer Workshop Summary
Implementing Investigations in Mathematics (InMath) |
Time | Monday | Time | Tuesday | Wednesday |
8:30 a.m.- 9:10 a.m. 9:10 a.m.- |
Welcome Numerical Data: Yellow |
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. |
Break | |
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. |
Lunch | |
1:30 p.m.- 3:30 p.m. |
K-2:
|
1:15 p.m.- 3:30 p.m. |
K-2 Choices:
3-5:
|
Assessment (Using student work from data units):
K-1 |
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:
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8:30 - 10:10 | K-5 DEVELOPMENT SESSIONS | ||
Yellow Pink Blue |
Change I Numerical Data Categorical Data |
2020 1035 1040/1050 |
|
10:10 - 10:25 | BREAK | ||
10:25 - 12:05 | K-5 DEVELOPMENT SESSIONS | ||
Yellow Pink Blue |
Comparing Sets Change II Probability |
1035 1040/1050 2020 |
|
12:05 - 1:15 | LUNCH | ||
1:15 - 3:30 | AFTERNOON CHOICES | ||
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) |
2020 1035 2016 1030 1060 2030 |
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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.
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 |