the shape of this graph compare with a graph showing the relationship between the radius and diameter of each bowl? Given the emphasis on graph literacy found in many stan- dardized tests, this can prove to be a valuable exercise.
Travel Then and Now
The local train station offers a spark for several data inves- tigations. While students are at the station they can gather information on locations they can travel to, travel time, and fares. Back in the classroom, students can work in teams to compare options. Is the train more efficient than a bus, a plane, or a private car? In which ways? Throughout this process, students will have to wrestle with an operational definition of efficiency: Time, cost, and energy usage will each provide a dif- ferent lens through which efficiency can be considered. The time and cost issues are relatively straightforward, but perceptive students will also note that options other than a private car have the inefficiency of traveling on a fixed schedule. Also, air travel has the added time required to clear security. Car travel might be the most efficient option time-wise, but there are other trade-offs, including the carbon foot- print. Web searching should allow students to determine the footprint associated with different means of travel. Note again as this unfolds how many rich, complex discussions unfold from a simple visit to a train station. An extension to the travel investigations presents itself in my home
town, courtesy of the old feed store building across the street from the train station. Local lore says this was the community “gas station” of the horse-drawn era. Can your students do research to determine how long it would take to get to a given destination by horse? Data tools might help to plot the relationships involved. From there students can reflect on how much the modern world has opened up through quicker means of transportation. For example, could major league baseball function the way it does today without easy access to airplanes? Would it be as easy to visit distant relatives?
Tying it Together
For each of these sample investigations along a math trail, a simple observation raises a number of interesting questions that help to make math come alive for stu- dents. No longer just a textbook exercise, math provides the tools and the language to make sense of the world. Depending on the time you have available, you can take the students along a predetermined math trail, or you can make a “starter” trail with a few examples like I have done here and ask students to generate their own stops along the way. They can then challenge classmates to try out the new stops on a sub- sequent walk along the trail. If time in the field is tight, make new stops a homework assignment. Either way, math will come alive as you take your students out of the classroom and into the community.
Bob Coulter is the director of Mapping the Environment, a program at the Missouri Botanical Garden’s Litzsinger Road Ecology Center that supports teachers’ efforts to enhance their science curriculum through use of the Internet and Geographic Information Systems (GIS) software. Pre- viously, Bob taught elementary grades for twelve years. firstname.lastname@example.org
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