Even though it is the middle of January, I still find myself asking people about their Christmas and wishing people a happy new year. I feel somewhat justified as the Catholic church just ended the Ecclesiastical Christmas season this past week with Three Kings day and the baptism of Jesus. Glossed over in the joy of the Christmas season is a morbid story associated with the three kings or three magi. In Matthew’s gospel, he describes how the magi stopped in Jerusalem to ask the current king Herod, where they might find the newborn king of the Jews. After identifying Bethlehem as the prophesied city of birth for the savior, Herod sent the magi on their way, but asked that they return and tell him where he might go to worship the new king (in reality he wanted to kill the newborn king). After the magi visited Jesus, they went back to their country a different way and did not go back to see Herod. When Herod figured out he was double-crossed, he sent his army to Bethlehem to kill all of the baby boys under 2 years of age, hoping to eliminate the threat. Fortunately for civilization, Joseph was warned in a dream and took Jesus and Mary to Egypt to wait out the reign of Herod.
I was reminded of this event, when I heard another morbid news item over the holidays: Chicago experienced a significant decrease in the murder rate for 2013, to its lowest level since 1965. This is hopeful news. However, the Chicago murder rate is still significantly higher than New York and Los Angeles, which are bigger cities. The vast majority of the murders in Chicago are gang-related and the vast majority of gang members are high school dropouts. I can’t help but feel that Herod’s attempt to maintain the status quo by murdering his own citizens is similar to modern society’s attempt to maintain the status quo which leads to excessive killing of our own citizens.
At first blush, you may feel I am using hyperbole and being sensationalistic. However, researchers at the University of Chicago Crime Lab have found a link between freshman algebra and Chicago’s gang violence problem. Other researchers have found that in large urban districts like Los Angeles and Chicago, students who pass algebra class by the end of 9th grade have nearly a 100% chance of graduating from high school. If they fail to pass algebra by the end of the 9th grade, they are more likely to drop out than to graduate.
Given that algebra can mean life or death for our urban youth and the central role that the abilities involved in setting up, manipulating, analyzing, and applying quadratic functions play in passing and performing well in Algebra I, one would think that quadratic equations must be an essential life skill and the lynchpin of democratic society. I searched the Internet for real world examples of quadratic equations. The top hit is a Math is Fun web site. Here are the examples that they provide.
In managerial economics, quadratic equations (and more sophisticatedly, differential equations) are a powerful tool for combining supply and demand curves to set a product price that maximizes net income. In manufacturing, quadratic equations are useful in instances where you want to maximize volume and minimize materials, such as the least amount of steel needed to make a steel frame. In optometry, quadratic equations are useful for designing corrective lenses. I am sure there are many other examples, especially for students going into STEM fields.
However, when you examine these three example domains more closely, you realize that the use of quadratic equations are not the best approach for solving problems of practice. In the managerial economics example, only MBA marketing gurus in the largest companies have sufficient market data to have realistic supply and demand data that can feed into quadratic equations. If you talk to any small business advisor (most people work in small businesses), they will tell you that pricing for small businesses is a crapshoot. Market data is unreliable and pricing is more often dictated by market forces. Therefore, for small business owners the precision of quadratic equations is misleading and small business owners may not have the market capacity to dictate price anyways. In small business, cash flow is king. Accounting may be more useful than quadratic equations.
In the manufacturing context, optimizing volume and minimizing waste is a common problem. However, it is an issue that is solved once and then implemented in the manufacturing process. Therefore the frequency with which manufacturers would be faced with this dilemma will depend on the breadth and turnover of the product lines. For large manufacturers, such as auto companies, they have engineers that use mathematical equations to solve these maximization problems for a wide variety of parts. However, for small manufacturers, they do not run into the problem often enough to have full time engineers. In addition, experienced fabricators develop powerful spatial intelligence for working with a wide variety of products. In addition, fabricators are also able to balance the need to minimize waste with also minimizing the complexity of the manufacturing process.
The web site also provides examples that do not have practical value, but provide an opportunity to appreciate the aesthetic qualities of quadratic equations. They can be used to characterize the flight of a ball that is thrown into the air - specifying the height of the path and the location of landing. Also, quadratic equations can characterize the speed and length of a river boat that cruises upstream and then downstream.
I challenge my readers to provide any example of the use of quadratic equations that would warrant the importance they play in dictating the survival our urban youth. Most of the debate around the Common Core standards ignores the tragic lost opportunity to deeply reflect on what is of importance for the next generation. What was important one hundred years ago, when less than 10% of the country graduated from high school, may not be important for everyone to know today. While algebra is important for a variety of fields, it seems to be overweighed in importance for all students. Taken from this standpoint, it is not far fetched to think that algebra continues to play an important role in maintaining the status quo and thwarting economic mobility. Rather than force feed math that drives high drop out rates, let’s focus on math that will drive economic mobility. Given the technological revolution of the last 40 years, maybe computer science for all is better at driving economic growth than algebra for all.
