‘No way! I can’t write that!”
Prices at the local pump had just topped $3.40 per gallon, and I asked my students to write down a word or phrase they’d heard recently about gas prices.
I knew I was on the right track.
This was the beginning of a two-week unit on the social implications of our driving economy. I wanted students to use math to come to a reasoned judgment of the causes and effects of rising prices.
My 8th grade students would apply their understanding of equations for linear and nonlinear relationships to analyze increasing consumption of fossil fuels. They would learn to use statistics to analyze driving habits in their community; they would make histograms and box-and-whisker plots to understand how much their families were spending on fuel. At the same time they would study the economic impact of rising prices on people from different socioeconomic classes and occupations. Their understanding of graphs would allow them to look back at the gas crisis of the 1970s and look ahead to the effects of peak oil.
Peak oil is a phrase that’s shorthand for the point in time at which the rate of fossil fuel extraction is at its peak. After this theoretical peak, supplies will gradually decline as remaining reserves become more difficult, expensive, and energy-intensive to access. Without social, economic, and technological changes, shortages in fossil fuel supplies are likely to cause widespread social and economic upheavals. My students would learn some lessons about peak oil from Cuba’s experience when the supply of Soviet fuel abruptly came to an end in the early 1990s.
Throughout the two-week unit, they considered the question, “What is the future of driving?” on a personal and societal level. Ideally, I wanted my students to get past personal outrage to consider the social, environmental, and economic impact of our dependence on fossil fuels.
Pain at the Pump
Though they have dropped in recent months, fuel costs had doubled nationwide in the 12 months previous to my teaching this unit. In our community, families were feeling it. My students
live at the edge of Olympia, Wash., a medium-sized capital city. Growth in our county has been among the fastest in the nation, and in spite of efforts to grow sustainably, affordable housing has leapfrogged into the county while bus service has declined. While homes in the urban core have increased tremendously in value, farm and forest land in outlying areas provide for comparatively inexpensive new housing. To make matters worse, about five years back an initiative to cut vehicle taxes resulted in the loss of about half of our rural bus service. In addition, many of our families work in occupations that depend on heavy equipment and trucks. To top it off, our traditional but waning industry is forest agriculture. Most of the large trees are gone, and efforts to preserve what’s left have dramatically changed our local economy in the past 15 years. It’s gotten harder to make a living wage without commuting to nearby cities. Personal economic circumstances have changed faster than the infrastructure that will support sustainability.
I wanted to broaden students’ awareness of the economic tension caused by rising prices while building their mathematical knowledge of statistical analysis. First, I assigned my students the task of finding out what it cost their families the last time they filled up the tank with gas. I assured them that “nothing” was a viable answer, because some families either choose to or have to manage without a car. It turned out that every one of the 90 or so families represented by my classes had a car. The next day I had each student write his or her answer to the homework question on a sticky note, to be posted on the white board.
Casey and Nicole couldn’t stop grinning as they came forward. Chris’s sticky note said $7. Nicole’s said $350. They were sure, in fine 8th grade form, that their answers would sidetrack the lesson and skew the data. I chose to plumb the unexpected.
“Casey, what rig is your family driving?” I asked.
“Doesn’t cost much to fill it, does it?”
“Nicole, what about yours?” I asked
“My dad drives a truck,” she said with a quiet smile.
“$350! What kind of truck?”
It turns out he drives a Kenworth. He clears land and hauls and grinds stumps for a living. That line of work takes one of those huge dump trucks with side-barrel fuel tanks and fuel economy of about six miles per gallon. Luckily the runs are short from local land-clearing jobs to the landfill. Her sticky note remained the highest value. Rather than short-circuiting the lesson, Nicole and Casey’s answers expanded it beyond where I anticipated we’d be able to go.
Using our data, we built a box-and-whisker plot, which is a statistical tool that shows the range, median, and four quartiles of data at a glance, all against a number line. It makes it easy to interpret the data without the often-skewed picture generated by calculating an average.
With Casey and Nicole’s class, we went beyond the basic curriculum by learning about outliers — those numbers that are more than one and a half times the inter-quartile range from the nearest quartile.
All Pain Is Not Equal
Gas costs about the same per gallon for everyone in our community, but economic impact varies. While many of us can reduce expenses by voluntarily driving less, the capacity to do so is limited by personal resources, including time and money. My recent commitment to bike the 15 miles to and from school once a week will take an hour each way and a considerable investment in waterproof panniers and lights. In addition, if you drive a taxi for a living or haul stumps, driving isn’t voluntary. Every cost increase at the pump that can’t be passed along means a loss in income.
It turned out that Casey and Nicole’s dollar amounts represented the two sides of the coin. Casey’s example represented voluntary reduction in fuel consumption; Casey’s brother had recently sold a car and bought a motorcycle. The bike got his brother to and from work at the warehouse for under $20 a month. On the other hand, Nicole’s value was about making a living. Her father couldn’t stop driving that big truck without changing his line of work.
I gave students a two-day assignment to interview their families about their driving habits. Their responses would get us deeper into the question of how and why rising prices were so painful, and they would also give us lots of numbers to work with. We’d be able to practice making more box plots and compare values with histograms. I had them ask the following questions:
- How many total miles a week does your family commute for work?
- Does your family drive more or less than it did a generation ago?
- How far do you live from the store where you buy most of your food?
- How many working vehicles does your family own?
- How many drivers are in your family?
Along with data, my students reported involved discussions with their families.
Students worked in groups of four to create box-and-whisker plots (see above) for distances to work and the store, or histograms (see page 43) for number of vehicles and drivers per household. They also made bar graphs for the question about whether or not their family drives more than previous generations. This was a lot of information to analyze at once, and as a result, some of the opportunity to bring forward math concepts was lost. Next time, I would have students focus on one question at a time and compare box plot and histograms for the same data.
All the same, as students did a walkabout to make observations, it emerged that our community’s entanglement with automobiles was deep, but that it varied tremendously. For example, while about 30 percent of families reported driving more than previous generations, the same proportion drove less. The number of working vehicles per family ranged from just one to eight. (It turned out that five of the eight were for sale, and the sixth was a retired Crown Victoria that cost too much to drive.) The number of drivers per household was similar. Likewise, commute and distance from the store varied tremendously. We found that the median weekly commute was more than 250 miles in two classes and that it topped 600 in the third. In other words, half of the families in two classes commuted more than 250 miles per week. No wonder my students felt re-luctant to write the words they’d heard at the pump.
When I get my students excited about something that seems unjust to them, I like to get them to think about how others may be experiencing similar, or worse, frustration. Knowing we have lots of company is one key to envisioning change that goes beyond consumer choices. Our dependence on fossil fuels runs deep and is nearly intractable without sweeping infrastructural change. Choosing to retire the Crown Vic will save one family money, but it won’t bring back the city bus. That kind of change takes awareness of the bigger picture.
A few weeks before we started looking at gas prices, the New York Times published an article about the impact of rising fuel prices across the United States. [“As Gas Prices Go Up, Impact Trickles Down,” April 30, 2006. ] It featured profiles of eight different Americans all affected in various ways by rising gas prices. Among them were New York City taxi drivers, a college student, a retail worker who could not afford to visit his fiancée, a fossil fuels industry analyst, and a commuter looking for a carpool. Students read, summarized, and presented the vignettes in pairs. One theme was that while a gallon of gas costs about the same for everyone, some feel it more.
“Who will feel it the most?” I asked.
Vickie answered: “The poor, and people who drive for a living.”
Grant perked up. “Does Bill Gates have his own gas station?” he asked. “He was a quiet student who’d spent most of the year hoping to pass his math class without doing much. The last time he spoke out loud had been to exclaim that his hair was finally long enough to get to his mouth.
“What do you think?” I asked.
“Well, he’ll get one if he needs one.” Someone else chimed in, “Yeah. With his friends. The rest of us will be walking.” I wish I had had the time to graphically model fuel costs against personal income. A $100 a month increase inside a $1,500 paycheck looks a lot different than it does inside a $10,000 a month paycheck.
I then probed students to think about what part of the driving they had read about was a choice. Could the people they read about elect to drive less? The culture in our school is deeply individual. Students really hang their hope on one person’s capacity to shape his or her own reality. And my students are young and some haven’t yet experienced the expense and heartbreak of moving and unemployment. The voices that dominated our discussion insisted that all the individuals in the article could just move or get another job. Next time, I will provide space to bring forward the family stories of just how hard it is to generate that kind of change. Insistence on individual responsibility dominated my students’ perceptions throughout our study, to the detriment of understanding the importance of systemic change.
Muscle Cars and SUVs
This wasn’t the first time fuel prices had skyrocketed. In fact, during the 1970s, the inflation-adjusted price of gas was even a bit higher and rose just as rapidly. Drivers felt that crisis even more acutely because it also came with a real shortage. In many parts of the country, gas stations ran out of fuel. The response was systemic change at the level of fuel economy. Strict fuel economy standards for passenger cars went into effect in the late 1970s. The weight of cars decreased dramatically in the course of a few years, but most of the fuel-efficient cars were made overseas. U.S. companies fought back with an invention calculated to circumvent regulated fuel economy and expand their market share: the sport utility vehicle (SUV). The birth of the SUV coincided with the exploitation of new oil fields on Alaska’s North Slope and falling world fuel prices. So, while the capacity for better overall fuel economy increased through technological innovation, average fuel economy is little more than it was 35 years ago.
I wanted my students to know that the potential for positive change lies just under the surface. I showed parts of the documentary Driving Passion, which chronicles the rise of the muscle car, culminating in the oil crisis of the 1970s. While the narrative of the film romanticizes the American lust for speed, the footage provides a graphic look at both the manufactured desire for high-powered cars and the ensuing oil crisis of the ’70s. According to the film, starting in the early 1940s, automakers joined forces with Hollywood to promote large engines and fast driving. Speedways sprang up all over the United States and advertising shifted from practicality to power. After watching a bit of a chase scene from the 1940s, I stopped the video and asked students to name every chase scene they’d watched in the last month. They could have gone on for an hour. When I started the video again, Lee Iacocca was describing “Car Lot Mondays,” a 1970s-era industry term for high sales of muscle cars after a weekend at the movies and at the race track, both of which were effectively lifestyle advertising.
That kind of advertising is a huge part of my students’ world. Far more than half of my students had been to NASCAR races. My afternoon math boys relished what felt to them like a free hour devoted to researching their dream car and analyzing its fuel economy compared to others in the same price range. Three-quarters of them dreamed of something from the 1970s with a lot of horses under the hood. All the same, footage from Driving Passion of lines at the pump in 1973 and signs saying “No gas today” made an impression. It began to dawn on them that change had happened in the past. High gas prices had hastened the end of the muscle car era. I planted a seed: “If things changed in the 1970s, they could change again. You are the future. I’ll be asking you to write an essay using mathematical evidence to predict the future of driving.”
Peak Oil and National Trends
Nationally, the number of drivers is increasing at a rate of about two million per year. Every year, people in the United States consume one-half million more barrels of oil each day — just for driving. From our data, we wrote and graphed linear equations. We determined that the number of drivers, unless things change, would double in 65 years. Likewise, fuel consumption would also double in about 65 years, according to numbers we found at www.greencarcongress.com. At the same time, petrogeologists predict that world oil production is set to decline dramatically.
Peak oil is a mathematical model for predicting world fossil fuel supplies. After the easy oil is extracted and depleted, what remains becomes harder and harder to extract. It’s like squeezing a sponge full of water: At first it gushes and then, even though it’s still damp, it takes more and more energy to extract a drop. On a graph, unlike the steadily rising line for increasing demand, the line for peak oil curves downward. Most models show the supply in steep decline starting in about 2000.
After students wrote their equations, I drew a graph of increasing demand on the white board and led a discussion about its causes. Students mentioned everything from leaf-blowers to barbeques. Then I explained the theory of peak oil and sketched the mountain-shaped model over our line for increasing demand. Students were quiet — sometimes a good sign. “Talk to your partner about what this means,” I said. As I circulated among my students, it was clear they understood that supply was in jeopardy. I heard students speak about how prices were going to go up higher and higher — until they’d never be able to drive. They were grasping the problem from the personal perspective of the consumer: If supply goes down, I’ll have to pay more. I wanted them to go further and think about the inevitability of change when supply will not meet demand. We had already studied points of intersection, those places on the coordinate plan where lines cross. My students knew that usually these indicated that something interesting was happening. I handed Grant a yardstick and asked him to come point to the intersection of the lines.
I reminded them, “When lines cross, something is happening.” Evan looked up, squinted and cupped his chin in his hand.
“Ohhh,” he began slowly. “I get it. That’s a problem. It’s like eating two hamburgers when you only have one.”
“Say more,” I replied.
“Well you can’t do that. If you only have one, you can only eat one.”
“So what does it mean that these supply and demand lines cross?” I asked the class. Some students held to their belief that it would mean simply that prices would continue to rise, which is probably true.
“On the other hand,” I said, “If Evan is right, is this a possible situation? Can we consume more than we have?”
“No,” someone replied.
“So what has to happen?”
Learning from Cuba
The island nation of Cuba has no endemic source for fossil fuels. Under an aggressive program to develop a self-sufficient national food supply system, agricultural practices were highly industrial by the end of the 1980s. This industrial agriculture had all but eliminated hunger; however, it left Cuba dependent on the Soviet Union to provide fuel for tractors and the raw materials for fertilizers. When the Soviet bloc fell in 1990, the Cuban people, still under a U.S. embargo, had to change or starve.
The film The Power of Community: How Cuba Survived Peak Oil (available from www.teachingforchange.org) chronicles Cuba’s transition from fossil fuel dependence to fossil fuel freedom. For my purposes, the film was perfect: It framed Cuba’s situation as a preview of a global scenario. Demand so outstrips supply that people have no choice but to find other ways of getting around. It points to real, practical solutions based on collaboration and local community-based agriculture. While it does gloss over cultural and political differences between the United States and Cuba, the solutions it depicts are concrete enough that it’s not difficult to imagine ways that, with organizing, they could happen here. It’s also an algebra teacher’s dream in that it features about a dozen clear graphical models of fuel cost, supply, and consumption.
After five minutes of footage featuring bicycles, buses, horse-drawn plows, and walking, I overheard Bill say to his partner, “I’m not worried. I’ll be dead by then.” I knew I had a little explaining to do regarding the timing of the peak oil predictions.
I stopped the film during the explanation of the future of our global fossil-fuel supply and brought the class’s attention to the graph of peak oil and consumption to clarify the values on the x-axis.
“When is this happening?” I asked.
“Now,” one student said.
I repeatedly stopped the film to query and develop students’ understanding of our deep dependence on oil for food as well as transportation. The film does a very good job of demonstrating the real change that occurred in everyday Cuban lives as a result of being cut off from the world oil supply. Most striking is the transition from industrial, rural agriculture to urban local food supplies grown within walking distance of where people live. At one point, I stopped the film and asked my students to brainstorm the crops grown near our school. Together they were able to name corn, pumpkins, cabbage, broccoli, potatoes, flowers, carrots, and a dairy farm. I pointed out that the majority of those farms produce for local markets. I asked them if they could imagine getting more of their food from local growers, and what impact that would have on fuel costs.
Erin said, “We could, but we don’t. Maybe gas doesn’t cost enough yet.”
As we finished watching, Cody, one of my muscle car afternoon math boys, quietly said to me. “You know, Ms. Dean, we’re part of the problem.”
Before I could respond to him, his buddy Nathan said, “Yeah, but we’re also part of the solution.”
Change Is Coming and We’re Part of It
As a culminating assignment, I asked students to write an essay using mathematical evidence to support a reasoned prediction for the future of driving. I asked them to consider the price of gasoline, peak oil, rising consumption, distances from work and food stores, and past changes that took place in the United States in the 1970s and in Cuba during the 1990s. Most of my students demonstrated that they understand how we can use mathematics to analyze the present and to predict the future. They could generalize from the graph we had studied that without change, supply will outstrip demand. But their ability to use the numbers to support a statement was weaker than I had hoped. All the same, every student reflected that change is coming, and most of them named themselves and their community as part of the solution.
Josiah’s response was typical: “People in our community are like maniacs. They drive everywhere. If it’s under three miles, they should walk.” Equally present were somewhat magical technological fixes. Andy said, “Our economy is going down so fast that soon we are going to have to make cars that run on water.” Such dreaming can result in sitting back and allowing others to solve our problems for us.
Using gas prices to teach about statistics was more time consuming than it would have been if I had just used our text, but I think the results were worth it. I devoted about three days of 12 to building nonmathematical background knowledge. But that background knowledge gave students an opportunity to use math to read the world. In terms of keeping the algebraic door open to students who typically struggle with math, I think it was effective as well. It gave them a reason to dig into the math and come to terms with understanding it.
Angel, a student who had struggled all year, wrote the following:
We are already at the peak of peak oil. Soon the line will be going down fast. If we continue using our cars the way we do, it will decline even more rapidly. We can control it. If we use our bikes more, carpool, and ride the bus, we can slow it down. There is no way to stop this problem completely, but we’re the problem and if we keep learning we have the potential to be the solution.
Ultimately, I hoped my students would use mathematics to synthesize their understanding. For example, I wanted them to speculate that if our commute distances could be cut in half, so would our demand for fuel. It is that sort of big-picture mathematical thinking that is necessary for people to unite for change. It is that sort of calculating that can convince people that now is the time to invest in mass transit, alternative energy, and sustainable community infrastructures. While I gave my students information that they could use in that way, I didn’t explicitly model that kind of thinking.
In walking the fine line between allowing my students to reach their own conclusions and telling them what to think, I didn’t push hard enough this time. One or two days devoted to “what if” questions such as, “What if we all rode our bikes once a week?” or “What if we could drive half as far to get to work?” would have brought my students further mathematically and it would have done much more to bring out the huge difference we could make together. And that’s where the math is: It is in multiplying the difference that each of us makes when we support each other.n
Connected Mathematics 2: Samples and Populations
Prentice Hall, 2005
While not related to the topic of gas prices, peak oil and driving, the Connected Mathematics series provides a template for structuring mathematical concept development while connecting learning to relevant current events.
“Corporate Average Fuel Economy: Lax Fuel Economy Standards Costs American Families Money and Lives”
Public Citizen, www.citizen.org/autosafety/fuelecon
Critical background on the development of the SUV as a way to sell powerful cars that meet the lower fuel economy standards for light trucks.
Driving Passion: America’s Love Affair with the Car, Part One
Documentary produced by Turner Home Entertainment, 1995.
Green Car Congress
An active current website devoted to reporting and analysis of technological and political developments relating to sustainable tranportation.
The Power of Community: How Cuba Survived Peak Oil
Video produced by the Community Solution, www.communitysolution.org
This video provides extensive, well-researched and referenced background on peak oil.