# Depicting and Analyzing Data: Enriching Science and Math Curricula through Graphical Displays and Mapping

## Graphics Creation and Statistical Interpretation: Relating Local Economics and the Global Environment

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## Rationale

This unit places an emphasis on interpreting and applying statistical methods to real data sets acquired by the students. Within certain limitations, the data explored should reflect student’s interest in phenomena that may be viewed at both a local level and a national or global level “scale”. Doing statistics with real data sets acquired by the students helps by making the data relevant to the students, especially when they are the ones who acquired the data. By analyzing household economic factors, students can become aware of the different facets of the cost of living, as well as the rates of increase of prices. In the context of studying statistics and data representation, household factors can be related to larger scale environmental factors, like the production of raw materials, rate of consumption of raw and manufactured materials and goods, and the end result of consumerism, waste management. Classroom discussion of both economics and environmentalism should help students to become more economical as consumers, and more aware as citizens of the 21
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century, where environmental and economic policies and behaviors may effect generations to come.

**
Teaching Strategies
**

This section discusses some of the overall strategies that will be used in instruction of this unit. If strategies for a particular lesson vary from those given here, it will be noted in the particular lesson in which the deviation occurs.

Prior to this series of lessons, students will be separated into groups by interest. The basic interest groups could include food, water, housing, health care, and transportation. These choices may provide an opportunity for students to explore potential career paths. Students in a particular group will follow a theme involving their selected variables, and will frequently report back to the class with their findings. This reporting may be done via email, as in the case of sharing graphics, data sets, or data set resources. This may also be accomplished through classroom discussion, as in the case of observations made or questions raised while interpreting an environmental, economic, statistical, or graphical concept or data set.

Convenient data sources will be used to acquire relatively small data sets about local phenomena. Then, students will search for large scale or global trends in the same data, usually using the Internet, as there is a vast amount of information available in graphical or tabular form. These data may include the costs of housing, food, transportation, health care and education.

Students will be encouraged to identify similarities and differences in measures of center and variability in different data sets that measure the same variables, particularly in comparison of large populations and small populations. Students will also be encouraged to take notes to summarize the main ideas of statistical and graphical concepts, through used of the primary text, as well as online resources about these concepts.

### Local and Global Comparisons

While most of the example data sets and graphical representations deal with national or world data, the teacher needs to ensure that students acquire data on a smaller, more local scale, perhaps the city of New Haven, or the state of Connecticut. For the purposes of this unit, it is not necessary that the local population be a subset of the larger population. This could be made so in the case of a more advanced class, so that inferential statistical methods could be used to compare sample and population parameters.

### Technology

As much as possible, technology will be incorporated into the processes of acquiring, organizing, displaying, and interpreting data. Technologies that may be used include graphing calculators, spreadsheet programs, graphing software, and slideshow presentation software. Data representations (graphics) will be created using both manual methods and technological methods. When possible, the introduction to an environmental or economic concept will be aided by teacher presentation of data maps or cartograms, reinforcing student geographic knowledge, and practicing map reading skills. Practicing map reading skills will foster spatial reasoning. Looking at maps will help students grasp the idea of being part of a much larger picture, and provoke discussion about the reasons for the differences in environmental and economic data for different geographic areas, and populations.

Since students will be acquiring much of their data through the use of the Internet, electronic communication should be the norm for individual discourse between the teacher and the student. Students will need email accounts, and parents will be notified of the requirement. Accommodations will have to be made for students without computer or Internet access outside of school, perhaps notification of public or school library hours. School computer labs can be made available during class time, as well as outside of school hours. Students will be required to keep an electronic portfolio of all sources used, data acquired, graphics created, and interpretations made. They will use materials in this portfolio to create the final cumulative assessment, which consists of a slideshow presentation.

In the creation of graphical displays of data sets, particularly with technology, students should be prompted to adhere to the following recommendations by Tufte: “Principles of Graphical Excellence”, including giving the viewer the greatest number of insights in the shortest time with the “least ink in the smallest space”, “Graphical Integrity”, particularly “the representation of numbers should be directly proportional to the numerical quantities represented”, and “clear, detailed, and thorough labeling should be used to defeat graphical distortion and ambiguity”. The “Principles in the theory of data graphics” can be used as a process model for creating efficient graphical displays
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