You may wonder why word problems are important when it comes to studying math, but they really can help us answer questions in our everyday lives. Word problems can be as simple as “If I haven’t started my science project that is due tomorrow and it’s going to take four hours to complete, how much time should I set aside to work on it tonight, keeping in mind all of my other homework?” We practice solving simple word problems in school so that we can later solve more complex problems. Some of these problems affect the larger community, for example, “If the farm next to my school uses pesticides, at what rate will they leak into the water or spread through the air?” But some of the problems that we work on are just fun, for example, “If you are having a party but you are inviting people at random, and you want to be sure that you have either five people that know one another or five people that do not know one another, then what is the smallest number of people that you could have to invite to your party?” This problem is interesting to me, because as of 2004 mathematicians do not know the answer (the catch here is the “at random” part).
Some word problems start with a mathematical conjecture (similar to a scientific hypothesis), which is a math statement that is speculated to be true but has not been proven to be true. For example, “The farm next to my school uses pesticides in which the rate of leakage into our water system is one pint a day.” This may or may not be true, and we can conduct mathematical investigations on science experiments to find the answer.
In my work as a mathematical researcher, I take data from complex word problems and put the information onto a graph. Seeing the information on a graph usually makes the problem easier to solve. This type of work is called “graph theory,” but the graphs I use are not the bar graphs that we often think of when looking at charts, instead they’re made up of dots (called vertices ), and lines (called edges) between some of the dots. These types of graphs are sometimes called networks. For the party problem, we might assume that the people are the dots, and that we have a line between two dots if the people know one another. One can see this example at the Mudd Math Fun Facts website.
In a way, my professional life looks like a word problem. What are the odds that a Hispanic woman from an inner city single parent household would go on to college, study mathematics and earn a Ph.D.? I am now an associate professor in the Department of Computer and Mathematic Sciences at the University of Houston-Downtown. My most important responsibilities in this job are teaching college math to university level students and continuing to try to solve mathematical conjectures.
When I was a child, I never imagined that I would have a career in mathematics. Growing up in Houston, Texas with a single mom, we experienced difficult times financially. In order to help my mom, I had the job of caring for my three younger siblings everyday after school while she worked. Looking back at that time in my life, I realize that taking care of my siblings taught me that I could handle responsibility. Even though I did very well in school, I never thought about attending college until I received encouragement from my 9th grade algebra teacher, Mr. John Patronella. It was very helpful that he continued to encourage me throughout my college years. I attended the University of Texas, Pan American, where I earned my B.S. and teaching certificate. I then earned my Master’s and Ph.D. at the University of Houston. Someone recently asked me how it is that I accomplish all of this, my best answer is that it was the responsibility I learned as a child, the support of my mother and the encouragement of my teacher that led me to where I am today. In essence, they are all factors in the word problem that describes my life.
The field of math is wide open - there are many unsolved mathematical problems needing to be proved or disproved and many conjectures to be developed. I enjoy the challenge of solving word problems and formulating conjectures because they help in providing solutions to problems that affect us in our daily lives and some that are simply fun.
If you like math and think it’s a subject you’d like, take plenty of math and science courses. Otherwise, I encourage students to take as many courses in different subjects so that when the future becomes the present, you’ll be prepared and can make good decisions for yourself!