Creating a Unit on Air Quality
Many mathematics teachers insist that what they teach is free from social context. Both traditional and reform math curricula is filled with that orientation, as in this example from Discovering Algebra: An Investigative Approach:
The first three members of the stilt-walking relay team finished their laps of the race with a mean time of 53 seconds per lap. What mean time for the next two members will give a mean time of 50 seconds per lap? (Murdock et. al. 2002, p. 48)
Students attempting to solve this problem often remark, "Who cares?" Since they don't, they lose interest not only in the exercise, but ultimately in the overall connection of math to life.
An increasing number of math teachers say the best way to counter that long-term disconnect is to reach students' imaginations by putting math into a social context, one that also is directly relevant to life. The National Council of Teachers of Mathematics said much the same in 2000 in a document identifying national mathematics content standards (NCTM, 2000).
While many mathematics teachers have responded by becoming thoughtful about context, they often do not expand that context to include social justice. And even though most mathematics texts written in the last 10 years claim to address the diversity of students place mathematics in " real-world" context, this effort falls short in requiring students to think about the real-world implications of what they can understand through numbers.
The good news is that teachers can take the initiative by providing social justice-oriented tasks that are both interesting and accessible to students. Indeed, once the infinite links between math and society are perceived, it's almost impossible not to use mathematics as a platform for community activism and struggle against injustice.
One such area is as obvious as the air we breathe, the quality of which often reveals much about inequalities based on factors such as class and race that determine where we live, work and go to school.
Evidence from research studies in the United States shows that in economically stressed cities, for example, air pollution-related morbidity and mortality are worse than in more prosperous cities. One effective way to investigate that in the class is to use math for an Air Quality Unit.
Lesson Plan: The Air Quality Unit
For this six-period activity, assign students in the class to small working groups. This enhances cooperative learning and improves mathematics achievement. Discuss with them the relation of math to social context, and identify the objective of the unit: the measurement and evaluation of the air in a city or location.
Give them a brief introductory overview of what they will be doing each day of the unit. It is recommended that data is collected 20 days prior to starting the unit. Data can also be collected daily over a longer period of time, but should be available to students at the beginning of the unit. Then, every day, make them aware of the way that the use of their evolving math skills is helping them with real-world issues. Be sure to acquaint them with the various online resources (below) that will be used to research and solve the activities.
Day 1: Measures of Central Tendency
- What is Air Quality Index (AQI)?
- For a city: find the AQI and temperature for 20 days. It is recommended that each member of a group select a different city. Find the AQI and the temperature.
- Find the mean median and mode for each city and for all of the cities combined.
- What might account for variations in air quality? Is this a cause and effect relationship or a correlation?
- If you had to select the city with the worst air quality, which measure of central tendency would you use? Explain your answer.
- Find a city with better air quality.
How did you determine your selection? Explain.
What might account for the better overall air quality?
Day 2: Bar Graphs
- Make a bar graph of the data for your city.
- Look at the data and list five questions that might be answered using the bar graph.
- How does your bar graph compare to others in your group?
Day 3: Box Plots and Stem and Leaf Plots
- Display the data for your city in a box plot and a stem and leaf plot. Explain how to construct these plots.
- Describe a situation in which these displays might be useful to assist in the understanding of the data.
Day 4: Two Variable Data
- Graph the temperature and the air quality for 20 days.
- Describe the relationship between the temperature and air quality. Is there a positive or negative correlation? How do you know?
- What might account for this relationship?
Day 5: Presentation
- Each working group concludes its study by making a poster that includes a display of data on air pollution. Include at least one type of data that has been discussed in class.