Mathematics

Making Change

What do cashiers have to do with The March on Washington? It’s probably not what you think.

As a child, I was regularly asked to walk to the neighborhood market a few blocks away to get some groceries for my mother. The grocers knew my family, along with many others in the neighborhood. Still, my mother taught me to always check the receipt (and give it to her), and she taught me how to make change. If the items totaled $17.45 and I gave the grocer (or cashier) $20.00, I had to know how much change I should get back.

As a young child, mental math (as we used to call it) was not my forte. In early elementary school we were taught math facts. We were drilled with flash cards. It was basic memorization of addition and subtraction, and then, multiplication tables, soon to be followed by short division flash cards. As one who never had a flair for remembering numbers or dates, or memorization at all, this mental math approach was arduous and mostly problematic for me. Yes, I did force myself to learn elemental math facts, but I was utterly turned off and avoided whatever I could. At least I did learn the basics. I learned that I had to subtract: $20.00-$17.45= $2.55.

But subtracting in my head (especially when I was quite young) was likely to lead to careless errors. So, my mother taught me how to make change. Essentially, she was teaching me that I could add instead of subtract. I remember struggling with the concept because I didn’t get that I was merely doing addition instead of subtraction. It just seemed like a magic trick that it all added up. Then, when I got the concept of counting back change from the total to the amount I gave, it was no longer like a magic trick–just magic in the way that something perfect seems magical.

Flash forward several years, and cash registers become calculators. Cashiers no longer  need to do anything but make sure that if the cash register says $2.55 change,  they can count the correct bills and coins. They do not have to figure out the change. For a generation now, cashiers have not had to do any math beyond counting what they are told to provide. On the occasions when I do make cash purchases, I am always dumbfounded that cashiers don’t (and often can’t) make change. They can’t figure the difference. There’s no human agency in making change; no critical thinking. I suppose it doesn’t matter all that much if cash registers are more efficient calculators than the people who use them, but I wonder about this ability (or lack thereof) to make change.

For me, the process of making change resonated more than merely knowing the numbers. That has always been true for me. It struck me this week as we have been commemorating the 50th anniversary of The March on Washington for Jobs and Freedom,  that while August 28, 1963 marks the historic date, the processes of change inform how we make change. Noting the differences from where we started to where we are now is not sufficient if we are to be the ones who make change. We must understand the processes of change–of additions, subtractions, multiplications and divisions, and miscalculations.

The March on Washington 50 years ago was historic for many reasons. Of course, Dr. Martin Luther King Jr.’s “I Have a Dream ” speech was pivotal, and remarkable, and truly one of the greatest pieces of oration in our history; but the peaceful participation by so many was equally historic and inspiring. Everyone who rallied at the mall in Washington was participating in making change, and inspired so many others to become agents of change. It is easy to just take the change that others make. It is easy to allow changes to be dictated by technology. It is more important, though, to be able to make change.

The After Life of Pi

Happy Pi Day!

Pi Day is celebrated on March 14th (3/14) around the world. Pi (Greek letter “π”) is the symbol used in mathematics to represent a constant — the ratio of the circumference of a circle to its diameter — which is approximately 3.14159.

Pi has been calculated to over one trillion digits beyond its decimal point. As an irrational and transcendental number, it will continue infinitely without repetition or pattern. While only a handful of digits are needed for typical calculations, Pi’s infinite nature makes it a fun challenge to memorize, and to computationally calculate more and more digits.http://www.piday.org/learn-about-pi/

The idea of and for Pi Day is to celebrate Pi (which also happens to be Albert Einstein’s birthday). In elementary schools and university Mathematics departments, students and teachers celebrate with anything associated with the number 3.14….. and eating pies, and probably watching the movie The Life of Pi (which has nothing to do with figuring out how many digits follow 3.14159 or the ratio of the circumference of a circle to its diameter). For the young students, Pi Day can be an introduction to geometry, ratios, and noticing numbers and the significance of patterns. For the university level (and beyond), Pi Day is celebrated with contests and the joy of playing with numbers and seeking to go beyond our current level of calculations. For the rest, those beyond the early education years and not serious math enthusiasts, Pi Day is cute, and reminds us of the very basic math concepts and rules that our younger students are celebrating today. For too many, our abilities and interests  in Math do not extend beyond the elementary Pi Day.

If Pi Day (or Black History Month, or Women’s History Month), or any other demarcated subject celebration, is to truly have an impact, we must go beyond the superficial celebrities of the celebrations. Pi Day (and Black History Month and Women’s History month etc…) may have initially raised awareness and interest in subjects and important personalities associated with the subjects, but when we keep these celebrations as peripheral to our everyday learning, we limit our abilities to expand .

Too often, after the early years, Math is taught as a series of rules, and those who are not particularly interested in using these rules, often miss opportunities to connect the rules to other applications, or developing mathematical awareness. So many people who are not driven toward studying or working in STEM fields, somehow get through their math courses without acquiring much mathematical knowledge. Few develop the appreciation to see mathematically.

As one who has more of an artistic temperament and appreciation than a mathematical habit of mind, I encourage others to learn more about seeing mathematically. One of my favorite writers on the subject of math is Steven Strogatz. He wrote a series in the New York Times entitled “The Elements of Math”, where he made mathematical concepts available to anyone by real life examples that were expressed in delightful prose. It was like being a tourist with a personable, interesting, caring, and joyful tour guide through some mathematical terrain.  I also recommend Strogatz’s book The Joy of x: A Guided Tour of Math, From One to Infinity.

http://www.stevenstrogatz.com/the_joy_of_x.html

Whether it’s Pi Day or any other subject celebration, we need to use these reminders that rather than superficial celebrity celebrations or simple associations, these are starting points. We can integrate these important lessons into other subjects and contexts and develop greater understanding and appreciation, as well as cultivate new habits of mind that we may have missed along the way.

So, Happy Pi Day!  And may you explore infinite possibilities!