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On the Importance of Travail in Mathematics
  • Education
  • Formation
  • Maths and Sciences
  • Suffering
Melissa Neacsu

Christ is Risen! Indeed, He is Risen!

I am writing this post on Bright Monday morning. My back is sore and I am still fatigued from the week of services culminating in the beautiful service of the Resurrection followed by midnight Liturgy on Holy Saturday evening. If you have not yet experienced an Orthodox Holy Week, I encourage you to attend this self-emptying wave of prayerful worship, Scripture reading, enchanting music, wonder, and repentance next year. Be sure to arrive an hour early to reserve a seat on Holy Saturday, lest you be forced to stand in heels the entire time and end up with back pain because you are somehow 44 years old.

Fully participating in Holy Week is not easy. On Holy Thursday evening we observe the service of the “12 Gospels,” a 3 to 3.5-hour service in which Scriptures recounting Christ’s crucifixion and the events leading up to it are read. These readings include John 16:20-21, wherein Christ tells his disciples that they should expect great suffering to precede its transformation into everlasting joy in His Resurrection:

"Most assuredly, I say to you, that you will weep and lament, but the world will rejoice; and you will be sorrowful, but your sorrow will be turned into joy. A woman when she is in labor, has sorrow because her hour has come; but as soon as she has given birth to the child, she no longer remembers the anguish for joy that a human being has been born into the world."

As a math teacher, it is a great temptation to spoon-feed my students strategies and information. My intentions are good, I think. I want my students to see that they can easily digest high school mathematics all the way through beginning Calculus with the right amount of scaffolding, work ethic, and support. I want them to sense that they are surrounded by faculty who thoughtfully curate their education, care about their success, believe in their potential, and are there for them in times of trial, but sometimes I rush too quickly to their aid and forget that travail is necessary for real and meaningful growth.

The Church teaches that Christ’s Crucifixion and Resurrection are necessary aspects of our salvation. Similarly, the discomfort of grappling with a problem you just don’t know how to solve, of feeling the despair of your own ignorance and then holding on to hope in this darkness, of trying something new, something creative, and failing, of gaining pride-crushing insight into what doesn’t work and why, but then after much struggle – possibly three days – experiencing a flash of insight, making a connection, recognizing a pattern, and then seeing a logically-ordered world that suddenly makes sense in a new way resurrect before your eyes. This God-given, God-mimicking ability to reason overcomes the inner darkness of the mind. The joy of finding things out, of discovery, of conquering the unknown cannot be overemphasized in the human experience. Travail is essential for the nurturing of a mathematical mind.

I can hear my students’ response: “But Mrs. Neacsu, we experience plenty of travail in your class already! The homework! The worksheets! The tests! It is nothing but travail.” They may have a point to some degree. There are already plenty of great questions built into the Saint Constantine curriculum waiting for students to uncover and do battle with, but like an artist who isn’t sure the painting is quite right yet, I wonder if the questions they encounter in their algebra textbooks are truly provoking of inquisitiveness, connection-making, exploration, and wonder. Every now and then I want to shake my students from their cram-pass-forget complacency and expose them to the vast world of deep, even unanswered, questions in mathematics. The material I teach is worthy. It has been gathered, distilled, and repackaged from the works of brilliant mathematicians throughout millennia, but it cannot be appreciated by a mind that hasn’t encountered its necessity while stumbling in the dark of a really hard and worthy problem. Mortimer Adler writes:

“A mind not agitated by good questions cannot possibly appreciate the significance of even the best answers. It is easy enough to teach the answers parrotwise. But to develop actively inquisitive minds alive with real questions, profound questions—that is another story.”

As I approach the end of the semester and set priorities for the future of the Saint Constantine mathematics program, one goal is to “agitate” my students’ minds more frequently by giving them space to play with mathematical ideas, form and investigate their own questions, and see why math is in large part a creative artform with as much power to elevate and enliven the human spirit as music or poetry. Paul Lockhart characterizes the essence of mathematics in just this way in his essay, “A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form:”

“Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion— not because it makes no sense to you, but because you gave it sense and you still don’t understand what your creation is up to; to have a breakthrough idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive…”

I want more days of being alive, of actually doing mathematics, more days of travail that lead to the revelation of meaningful mathematical truths. Engineering such academic days is a precarious task, especially as I attempt not to lose any of the good we already have in our upper school math classes. Please pray for discernment for our mathematics department as we grow and develop our program for the sake of our students’ authentic engagement with this beautiful and powerful subject.