# Data Analysis Summary

## Monday, July 23

We met with the Math Ed Researchers for the first hour and a half of our session. We told them how to access our PCMI web site (along with the passwords needed to log in). A long discussion ensued. Don explained why we were studying data: it is an integral part of the High School curriculum, and students are expected to understand how to use and analyze data on standardized tests. We have been studying FATHOM to become familiar with it and to prepare a presentation for our HSTP group. Carol explained that we need to find a way to massage and incorporate FATHOM into our classroom. All 4 of our members are trying to get enough copies of FATHOM for their school, so they can let students actually play with it, rather than just watch the teacher.

We then described our project for our presentation (including how we gathered the data, found some questions ambiguous, selected the attributes we are going to use, etc.) The Math Ed Research group was invited to our presentation tomorrow at 5pm. Bill Finzer will be present. We told them that we felt that FATHOM is user friendly.

They asked whether FATHOM would affect the content taught. Carol has used it in her classroom, and she remarked that the automatic graphs have forced her to change her grading rubric, and to ask different questions to have students analyze and interpret what they know in much more depth. She feels that this definitely has increased the level of understanding in her classroom.

The researchers then asked us what problems we see in the High School classroom today. Topics such as graphing lines, solving equations, finding slope, and statistics topics (univariant vs. bivariant data, etc.) The typical statistics topics include collecting and comparing data, mean, median, mode, standard deviation, the normal curve. Time and curriculum was mentioned as problems when considering how in depth we go as teachers. It was suggested that science and math teachers corroborate to create a shared curriculum using the science classes to collect data and the math classes to manipulate the data. It was impressed upon the group that a general understanding of the topics should be acquired before using any software.

The researchers would like to know the usefulness of their work. How could they make their info useful to math teachers? One particular researcher analyzed basic statistical ideas that students had learned from a typical stats course, and held a workshop with AP Stats instructors (and others) where they shared issues of difficulties that students have and why they exist. Another said they were trying to engage elementary students in the basic concepts of statistics, so that by the time students reach high school, we can then ask for understanding at a deeper level (students now seem to know how to perform certain calculations, but not know why).

It was suggested that we ask researchers at the universities to establish a collaboration with high school teachers, to help us with data, projects, etc. We then went to the room and practiced our presentation.

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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.