Mathematical literacy aims to develop more effective self-managing individuals, contributing workers, lifelong learners and critical citizens. With mathematical literacy we are not only concerned with teaching students the mathematical skills needed for each of these life roles, but also with developing appropriate attitudes and values to contribute responsibly to the world in which we live.
Consider electricity; as a country we are facing enormous challenges in meeting the electricity demands of households and industry. The inability to meet demand led to ‘load-shedding” (power cuts) across the Western Cape and other provinces in 2006 with more expected during the winter of 2007.
In an effort to reduce the demand for electricity, people are being urged to replace their regular (incandescent) light bulbs with energy-saving light bulbs or compact fluorescent lamps (CFLs). The media carries advertisements and public service announcements promising that these energy-saving light bulbs last up to six times as long and use 80% less electricity. Yet the consumers who need to make the choice are faced with the reality that the energy-saving light bulb costs nearly five times as much as a regular light bulb and the perception is that the energy-saving light bulb does not emit the same amount of light.
Would being mathematically literate empower an individual to make the choice more easily? The answer is hopefully yes. In addition, being mathematically literate may do more than merely enable the self-managing individual to make a short-term economic decision. Being mathematically literate would also enable critical citizens to see that the decision they make will impact on more than just their personal expenses; their decisions will have an impact on both the use of fossil fuels and the emission of greenhouse gasses which in turn leads to global warming — a major international concern.
In addressing the perception that the energy-saving light bulbs do not emit the same amount of light as the regular light bulbs, we would need to teach people to read and interpret information presented in a table. The table alongside compares the ‘light output”, measured in lumens, for the different light bulbs (a lumen is roughly the same as the amount of light produced by a candle). The mathematically literate person can read this table and see that a 20W to 28W CFL will emit the same amount of light as a regular 100W bulb.
Having selected the CFL that emits the same amount of light as the regular light bulb they want to replace, the next challenge for the individuals is to compare the long-term cost of buying the CFL rather than the regular bulb.
The watt (W) rating of an electrical appliance tells us how much electricity the appliance uses. A 100W bulb uses 100 watts of power in one hour. Electricity is sold in units called kilowatt-hours (kWh) — where 1kWh corresponds to the work performed by one kilowatt of electric power in one hour. Put differently, a 100W bulb uses 100 ÷ 1000 = 1 ÷ 10kWh in one hour. In Cape Town, the consumption charge for electricity is 30,05c/kWh. Knowing this enables us to calculate that it costs 1 ÷ 10kWh x 30,05c/kWh = 3,005c per hour to use the 100W bulb. A similar calculation shows that the 20W CFL would cost 20 ÷ 1000 kWh x 30,05c/kWh = 0,601c per hour. The CFL is quite clearly more economical to use, but it costs more to buy — will the consumer benefit in the long run?
Manufacturers of the two types of bulbs claim that while the CFL lasts for 6 000 hours, a regular bulb typically lasts for 1 000 hours. Using this information and the cost of purchasing each light bulb (R5,20 for the 100W bulb and R25,18 for the 20W CFL), we can calculate the cost of using each light bulb for its lifetime. For the 20W CFL the cost would be R25,18 + 6 000 hrs x 0,601c/hour = R61,24. Similarly the cost for the 100W bulb is R5,20 + 1 000 hrs x 3,005c/hour = R35,25. It follows that to get the equivalent number of hours of light from the 100W bulb, it would cost 6 x R35,25 = R211,50. If we assume that the amounts quoted are correct then the consumer would spend 70% less over the lifetime of the CFL by using a CFL — despite its higher initial cost.
Of course, there are other factors: if the consumer does not have R25 plus to spend on a CFL on the day that he or she must buy a light bulb, then the less expensive 100W bulb will be the better option. Mathematically literate persons will be able to distinguish between the short-term and long-term implications of his or her decision.
In addition to the long-term cost saving that the self-managing individual is concerned with, the critical citizen can also think beyond the personal cost to the wider implications of their decision.
Assuming that approximately one ton of coal is consumed to produce 2 000kWh of electricity, we can now calculate that using a CFL for 6 000 hours will use approximately 240kg less coal than using 6 x 100W bulbs for 1 000 hours each. And since burning coal produces carbon dioxide — a greenhouse gas that in turn contributes to global warming, we see that the impact of the decision to switch to CFLs may be greater than the money that we would personally save in the long-term.
Looking back over the calculations we have used, it should be apparent that the mathematics itself was elementary, the application was, however, sophisticated. This is a hallmark of mathematical literacy — it is the application of elementary mathematics in sophisticated ways to empower individuals to be more effective self-managing individuals, contributing workers, lifelong learners and critical citizens.