Data Analysis Summary
Thursday, July 26
July 26, 2001 Data Analysis Summary Carol opened the session by telling us that our first lesson (pilot product) needs to be up for all to see by September 15. By the end of February, we should have tried the pilot, and reworked any problems we might have encountered, so that our lesson can be sent out for independent review by some mathematician (possibly Bill Finzer?). We can then revisit the lesson next year and revise it a final time (with input from everyone).
We decide that our lesson was to be a "Survey about Us" to be used in all of our classrooms at the beginning of the school year. We will try to adjust the survey that we gave to the HSTP group using meaningful mathematics where we can look at and analyze data (to give kids an intro to FATHOM).
Bill pleaded that we join the LISTSERV for FATHOM on the math forum web site. He also gave us insight as to the type of questions we should include on our survey (quirky questions like which way the toilet paper should be put on the roller, ethnicity, add categorical as well as continuous data, i.e. birth order, ask teachers for results of previous surveys, GPA, number of absences, etc.). We need to test preconceptions by looking at data. We should also think about the mathematical concepts we want to deal with: distributions, reading graphs, discovering patterns (linear vs. non-linear). We should always include an attribute for place (state, country), age, and personal interest questions so we can combine data from other members and then analyze that data. Bill also advised us to make the questions fun, yet very clear. Within the lesson we should involve the kids by asking/showing them how to identify "dirty" data and "clean" it, as well as massage the data we already have. This would be an important experience for both the students and the teachers. It might be better to clear up possible problems at the beginning by asking someone else to edit our survey. If we pre-number the surveys and have the students rotate a group of them, we might be able to head off problems as well as get input from the students as to how to fix them. It was decided that we should post a list of tips for designing surveys so that anyone can reflect on the whole process.
Carol told us she would share the results of the PCMI/HSTP evaluation with us.
Bill asked to be included in our discussions during the year. He challenged us to find ways to use data in our curriculum. His suggestions included analyzing grades, collecting attitudes towards math, individual classwork, etc. We decided to make a list of the data we encounter in our teaching or ask the students to note when they are asked to deal with data (or find data somewhere), and post these to our discussion and comment about them. He warned us to watch for the difference between summary data and raw data. He also warned us about merging documents‹to make sure that the same attributes are named the same. Also use "group" as an attribute in your survey to make it easier to combine, analyze and compare data. We also need to watch for "data structure" problems (use these as an added instructional opportunity).
For the rest of the hour we worked on the area vs. perimeter activity from Data in Depth. Bill posed a problem that we then investigated and discussed . He wanted to know what would happen if we just dragged perimeter to the x-axis of a new graph. What would the graph look like? What other comments could we make? Many questions were asked/investigated by the group members, showing that this activity could be used from a middle school math class through a calculus class.
Bill finished by challenging us to be inventive and come up with mathematically rich, approachable, deep activities that would be enhanced by the use of FATHOM.
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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.