# Data Analysis, Statistics and Probability Summary

## Wednesday, July 3, 2002

We started the session by going over the Introduction and Chapter One of Gail Burrill's rough draft of the Data Analysis version of the Navigations series. This book will be able to be used as a framework for jumping off into different FATHOM activities. Conversation took place as to whether the definition of "bias" was needed within the text. We decided after talking with Gail that the explanation given in Chapter One was appropriate (Gail already explains the process of determining bias in an experiment, referencing the Randon Rectangles activity). Gail also reinforced the concept that it is necessary to have a large set of data to determine bias. Carol mentioned that we need to decide how to put the data from the Random Rectangle activity into the Case Table with two columns: one from 1-100 and a second area column. It was suggested that we could each enter 15 quantities into Excel and then copy and paste the data into FATHOM.

We need a set of sample answers to the Long Jump problem, so each member is to write up a solution (as an Algebra II student would) and send them to Suzanne. Suzanne will help us with the "mentoring" process on Friday. However, it was decided that we should work in pairs monitoring the solutions that come in. Right now, because time might be an issue, this "PCMI Problem" (changed from PoW) will only be used with the FATHOM members' students, with hopes of expansion later on. The possibility of including some of our students as "monitors", as long as direction and explanations are given, as well as using rubrics and the scoring process was also discussed for a while. A note was made that the lack of computer accessability might hamper our plans. We also decided that the problems need to be written so either FATHOM or a graphing calculator can be used to solve them.

The FATHOM members have not yet determined how many of these "PCMI Problems" we are willing to tackle this year.

A copy of the FATHOM project from last year was distributed to all members. Carol received an extra one for Herb. Beverly and Carol explained the project and how they used it in their classes this past year. This project is a good tool to use FATHOM to discover relationships and a good exercise in analyzing actual data.

Suzanne then went through the process, reminding us that the Math Forum was equally interested in mathematics communication. There are two parts--what the student will see and what we (as mentors) will see. Reminder to us as we create these problems--think FATHOM and/or graphing calculator.

• Go to http://mathforum.org/pcmipow/
• Use "Print this Problem" link to get hard copy of the problem
• Be sure to fill in all red star info (required fields)
• Select size of group
• Select state
• "On to next step"
• "On to next step"
• Enter personal info (use Suzanne's email while here)
• "On to next step"
• Fill in the explanation/answer (the short answer box has been eliminated, but can be put in if needed for future problems)
• Be sure that complete sentences are used and explanations are given as to how they arrived at the answer
• You can preview the long answer if wanted
• Use the "Text" option
• CC:to us (but Suzanne while we are here)
• Suzanne will investigate the "graphics" help because it is necessary to be able to insert graphics in the solutions (FATHOM and graph link documents)
• Submit solution
• Suzanne suggested that we start this new project with only a small number of students as a pilot program so we do not become overwhelmed
• Use the PCMI website "Discussion" option to discuss problems/solutions/ questions among ourselves

We then went to the lab and worked on the Sampling I and Sampling II activities in the Data in Depth book.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.