Some children struggle with math. Proposed solutions abound, such as limiting struggling students’ math adventures to cooking, measuring, calculating money, and other “real-life” pursuits. But if we assume such a pragmatic approach, what do our children miss? Is there more to math than “useful” application?
In a classical education we view arithmetic and mathematics as far more than useful arts, though they are useful. Rather, we believe that these arts elevate the mind, enhance perceptions of harmony and order, sharpen the memory, and aid in apprehension of the divinely created universe.
When my son contracted COVID-19 well over a year ago, he did not suffer from the typical respiratory effects; instead, he developed a debilitating encephalopathy. To this day he does not remember anything from Christmas through New Year’s Eve of that year. The condition left him unable to respond intelligibly, walk, make decisions, or add, subtract, or manipulate the smallest numbers. Once a joyful student of algebra, Michael could no longer fathom or perform the math sentences 1 + 2 = ___ or 1 – 0 = ___.
His short-term memory evidenced dysfunction as well. At the hospital I repeatedly prompted his language in an effort to restore his cognition. I would ask things like, “Michael, they have Greek yogurt; would you like black cherry or vanilla?” Whereas just weeks earlier he would have said, “Black cherry, hands down!” he stared blankly. Then he managed, “Grape vanilla.” Prior to encephalopathy, not only would he have made a clear choice, but he could have detailed the purported benefits of Greek yogurt over other forms of yogurt. We had much work to do.
When Michael was finally home and medically stable, we began in earnest. We worked on language, both receptive (understanding) and expressive (speech). He needed rest periods, but we encouraged him to participate in small decisions.
We began again with arithmetic. With perpetual concern, his twin sister volunteered to serve in the role of tutor and dutifully taught him with addition flashcards. Michelle knew, whether instinctively or from experience, to take things slowly. She did not seek to overwhelm the student, but to teach him. She began with 1 + 1 = 2. She stayed with the lower addition cards for weeks. I could hear progress from across the room, as her constant refrains of “Very good!” and “That’s it!” encouraged him to try another.
We wanted our son to regain basic arithmetic, but we wanted more: We wanted him to regain his awe of mathematics, his love of order and harmony on the piano he once played, and his fascination with the wondrous design of the created world. In short, we sought to reintroduce our son to the quadrivium—arithmetic, music, geometry, astronomy—that had pervaded his education from his earliest years into adulthood. In the initial recovery of classical education that began decades ago, much discussion surrounded the trivium, the three language arts of grammar, logic, and rhetoric. As the movement matured, the quadrivium—the mathematical arts—began to receive due focus. Simply summarized, the four mathematical arts that comprise the quadrivium turn our minds to a harmony and beauty higher than ourselves:
arithmetic – number
music (harmonia) – number in time
geometry – number in space
astronomy (cosmology) – number in space and time
While formal studies of the advanced mathematical arts may occur later for many students, for our purposes with our children we need to know only that all of these are desirable, all of these are important, all of these are related, and all of these can be woven throughout our children’s education at all levels. The quadrivium is not merely for those who pursue esoteric university studies in mathematics. Whether for a child with learning disabilities, autism, or acute encephalopathy, little by little, we teach. We do so to the greatest extent possible for each child. If we need to move more slowly, more carefully, or with more demonstrations before requiring practice and mastery, so be it. This is and has always been the art of teaching any child. As Quintilian instructs, “It is for us to ascertain how much the minds of boys can receive at any one time.”
Notice how well-balanced the combined liberal arts are for us as human beings. A true liberal arts education encompasses all that is right to contemplate and learn. In a classical education we seek to resist the temptation to reduce education to a means of economic gain. We lead the child not only to the liberal arts but also to the liberal sciences—moral, natural, and theological—that draw us to yet higher pursuits no matter our callings in life. We seek to assert the child’s very humanness at every level he can accomplish. A classical education is worthy of our full exploration, because of the implications for all of our children and for ourselves as human beings. Together the trivium and quadrivium form the seven liberal arts which, when placed together with the great music, art, literature, languages, and ideas of Western civilization, comprise a classical education. All of
this is permeated by Truth, Goodness, and Beauty. And for the Christian classical educator, all of this points us to our Creator.
With this approach and by the mercy of God, my family is thankful to report that we have witnessed a slow, steady, remarkable recovery in Michael. He was deemed by his twin “graduated” from flashcards in all operations (addition, subtraction, multiplication, and division). As his mental calculations improved, we began playing nightly and increasingly complex board games, which stymied him initially, but which now he is pleased to win on occasion. Michael has resumed his studies on the piano. He plays scales, enjoys the outdoors, and is learning renditions of classical pieces and hymns. He is once again reading the Holy Scriptures and contemplating higher things.
Reassuringly to me, Michael has also embarked on his own study of geometry. He says he finds the pursuit challenging but also “quite fascinating.” Thanks be to God.