Math, Truth, and Wonder

Dr. Gaelan Gilbert, Headmaster

It is one of the axioms of classical education that mathematics provides a solid basis for recognizing the reality of objective truth. In a world of competing social and moral perspectives, mathematics offers stability in its reliance on consistent laws and logical principles. Math suggests that there is an inherent order to the created universe which human reason can access and, to an extent, comprehend. Mathematics is the language human beings use to understand that rational order embedded within the created world. 

The ancient Greek mathematicians, like Euclid, Pythagoras, and Archimedes, thought so, too. Like all sciences, mathematics has a history. It is a discipline of knowledge whose advancements can be studied and understood as developments that cumulatively build on the achievements of thinkers in the past. While it is true to say that mathematicians discover truth, rather than inventing it, at the same time there is an undeniable process in the improvement of the linguistic and symbolic tools and methods used in the mathematical discovery of truth. This improvement is part of the adventure of history – and knowledge.

The Math curriculum at Christ the Savior Academy – Singapore Math – is among the most advanced and successful in the modern world. Yet Singapore Math also fits nicely into a framework for teaching math within a classical educational approach. This is no accident: among the seven liberal arts disciplines, two are directly mathematical – arithmetic and geometry – and two others rely on math for the accuracy of observation (astronomy) and composition (music). From a classical perspective, the teaching of math should emphasize four related principles: 

  1. Concrete to Abstract
  2. Part to Whole
  3. Historical development 
  4. The place of wonder and beauty 

A classical/Singapore math approach also recognizes that a robust sense of numeracy is gained through analytic and narrative techniques, which supplement memorized math facts. If students grasp the concrete/spatial aspect and partial aspect of an integer, they are all the more enabled to think in multiple, agile ways about how to calculate and problem-solve. Sheer memorization is vital – but it’s not enough. 

Mathematics provides a solid basis for not only a wide variety of careers, but for an understanding of the created world and its inherent, if mysterious, order. For the ancients, the discipline of mathematics was a preparation for being initiated into deeper levels of wonder and understanding about the beauty of creation. For Christians, who put their faith in Jesus Christ the Logos, mathematics can be a way of not only learning with our God-given reason to use the created world responsibly for improving human lives, but also of searching for and finding the Creator in His works. Nature itself is, as St Maximos the Confessor taught, one of the two “books of God” – the other being Scripture. The better we learn mathematics, the better we shall be able to read “nature” as a book of God, and see in both its complex intricacy and also its colossal immensity, the hand of Him through Whom all things were made (John 1:3; Colossians 1:15-17).

What is a “Successful Education”?

THE TOPIC of Education is a complex one, and any discussion of it inspires a great many questions. But for parents and teachers there are a few chief questions that we must ask ourselves as we confront the problem of deciding what kind of education to give our children. First among them are: What do we envision as success for our children? and, What kind of persons do we want our children to be? Only once we have begun to answer these can we ask another, namely, What should Education be?

When parents first enroll their children in school, they often see this as the first step in a long process culminating in a college degree. And rightly so. However, it is also so much more than that. The notion that motivates most parents (and unfortunately most teachers as well) is that of school as a preparation for college. You go to elementary school so that you can get to middle school; you go to middle school so that you can get to high school; you go to high school so that you can get to college; and you go to college so that you can get a good job. The chief consideration in all of this is ultimately an economic one – education is all about getting a good job, and a good job equals a good life. This, very often, is how we define success. But is not real success in fact something more?

In this assembly line approach to education, school – especially primary school – turns into a kind of daycare system in which students learn important problem-solving skills. The teacher’s job becomes concerned chiefly with presenting information, teaching skills, and preparing for tests. We measure the success of our students’ education by the scores they get on tests and the grades they are assigned in class. In such an understanding, many parents who care a great deal about their children’s education end up confusing a high intensity education with a high quality one. This is often the case with teachers too. After all, they spend so much time and effort in educating children, yet there seems to be so little obvious return. As a result, they tend to fall back on quantifiable results such as grades and standardized test scores to justify, if only to themselves, all the work they have done.

But education must be a great deal more than learning skills and solving problems, because students are a great deal more than simply cogs in a big industrial machine. To be truly successful, children must grow in a great many ways, and a school should be there not just to help with what falls within certain narrow academic limits, but to guide all of that growth, whether intellectual, emotional, moral, or spiritual. Still, many parents seem to think that if they can just get their children to college, they will be all right. But of course this is far from true, for the things that really make them all right transcend a college experience.

Childhood and adolescence are a time of intense becoming. Students are sorting out their identity; they are gradually figuring out who they will be. Their identity must be informed by a moral and spiritual vision if they are to discover a source of meaning and are to mature. Such a vision will fuel their wonder, and this will give them inspiration and, in turn, motivate them to do and to achieve. This is the key to a successful and fruitful academic life. As Antoine de Saint-Euxupéry, the author of The Little Prince, observed:

The way to get people to build a ship is not to teach them carpentry, assign them tasks, and give them schedules to meet; but to inspire them to long for the infinite immensity of the sea.

In a healthy society much of this happens naturally, for there is a strong upward pull on a child by culture, religion, and education (all of which are closely intertwined). But in an unhealthy society, where culture has atrophied and religion has been marginalized, it may not happen at all. For there entertainment and recreation become the chief source of our values, and the ‘vision’ given by pop media, namely in the films, advertising, music, TV shows, and professional sports that fill most of our waking life, comes down in the end to Hedonism, in one form or another. It tells us that feeling good is the purpose of life. And this neither inspires nor motivates. Rather, as we have seen all too often, it only exasperates, enervates, and depresses.

In such a case, the school is often all that is left to exert the necessary upward pull that raises our children from a lower life to one higher; from a life like that of an animal, characterized by the pursuit of pleasure and the escape from pain, to one filled with meaning, purpose, and inspiration. The first kind leads to a prolonged adolescence, in which the student may never mature emotionally, morally, intellectually, or spiritually. The second, however, can lead a student to his or her full human potential.

Yet a school cannot provide meaning or inspiration unless it has at the center of its culture and curriculum a concern for Truth and Virtue. These values must be at the core of our children’s identity also, for they alone can help them to answer the questions about what they should believe and how they should live. A school that is centered on a spiritual vision, that explicitly undertakes the task of introducing students to Truth and Goodness and Beauty, that seeks to inspire its students and lead them to wonder at the nature of things, is one that raises its students’ lives to a higher and nobler level. We cannot love what we do not know. If we truly wish to give our children the best of everything, then should not this include making known to them the rich patrimony of Western Civilization, with all of its beauties, strivings, and achievements? Should it not also include the sublime treasures of the life-giving culture of the Church?

Some may fear that such an emphasis in education will come at a cost and will take its toll in the students’ regular academic work, and that as a result they will fall behind in their studies. But in fact it is possible to give our students what they need while at the same time instructing them well in their fundamental academics. It is indisputably the case that we need to fill them full of numbers and words, but all this can happen in a larger and more meaningful context. We can teach them a lot. They can work hard. We can test them often. We can be very serious academically. Indeed, we may well prove more rigorous than most of our peer schools. The difference is that this is not our chief goal. We are not primarily about getting them ready for college. Indeed, preparation for college should be a subsidiary goal, though doubtless that will sound radical to many.

Our chief goal instead must be helping them become what they should be. And the emphasis should be on primary and secondary school, for these are the years in which they begin to form their identity and to establish what kind of persons they will be. If we do this, then even if they choose not to pursue college degrees, they will still have all they need for the ‘good life’. For in the end, education is about helping them grow up into becoming fully human. That process is happening now, and therefore education should look not only to what is coming down the road, whether college or a job, but also to what is present now.

Indeed, a school that does not embrace the formation of the whole student cannot even lay a sound foundation for intellectual achievement. As a society we try to make up for our continual decline in education by constantly renewing our emphasis on science, technology, engineering, and math (STEM), thinking that if they learn these subjects more intensely and sooner we can close the gap. But that is a dead end. Instead, we have to give students the momentum for a lifetime of learning. We must teach them to wonder, to seek, to think, to choose, and to love. We must help them to ask the right questions and give them the tools to find the answers. We must give them something to live for and something to die with.

As has been shown time and again, a student who receives such an education is not only well-equipped for any field of work, but he is also useful to himself in the whole sphere of life and to his fellows as well. In a society where truth and morality are increasingly marginalized, this becomes a matter of life and death for the individual, as well as for society. Make no mistake: societies do die, and often by the folly of those who make them up. Only citizens who are capable of addressing the questions at the heart of their existence will be able to resolve the perennial problems that face mankind. Do we not want our child to be one of those?