Lisa VanDamme, though an Objectivist opposed to classical Christian education, has some useful things to say about gaining knowledge in the (natural) sciences:
In the world of classical Christian education, some educators and theorists invoke Dorothy Sayers’s theory of the trivium. Miss Sayers held that the three parts of the trivium – grammar, logic, rhetoric – corresponded to three stages of child development: ‘Now it seems to me that the layout of the Trivium adapts itself with a singular appropriateness to these three ages: Grammar to the Poll-Parrot, Dialectic to the Pert, and Rhetoric to the Poetic age.’ She describes the first stage as follows:
The Poll-Parrot stage is the one in which learning by heart is easy and, on the whole, pleasurable; whereas reasoning is difficult and, on the whole, little relished. At this age, one readily memorizes the shapes and appearances of things; one likes to recite the number-plates of cars; one rejoices in the chanting of rhymes and the rumble and thunder of unintelligible polysyllables; one enjoys the mere accumulation of things.
In mathematical instruction, invoking the Sayers typology, educators may focus on dogmatic learning of mathematical algorithms, with quite unsatisfactory results. Sometimes, under the impression that young children, being in the ‘poll-parrot’ stage and thus needing to learn mathematical processes by rote, they decide to use the Saxon Math curriculum, whose incremental approach of repeating concepts, rather than building on them and so continuing their use, promotes a rigid learning without genuine understanding. As one parent says, ‘Saxon does a very poor job of teaching conceptually, and the procedural speed it produces hides a general lack of any but the shallowest understanding.’ (Not, by the way, that I am at all impressed with students’ mental arithmetic skills when they have any inclination to reach for the calculator, but mathematics without conceptual understanding is bad policy.) The children, then, by the time they have reached middle school, are woefully unprepared to understand mathematics logically, because their mathematical instruction has till then been most rigidly and irrationally short-circuited from memorization to application.
Some who follow Cornelius Van Til may say, of course, that knowledge must begin with the Holy Trinity, since it is from the Godhead that all in heaven and on earth has its being. I think this presupposition is negated by both the history of revelation and the way that most of us, at least, have come to hold a rationally defensible belief in the existence and the nature of God. The Old Testament saints did not know of the Trinity, yet they did indeed worship God as he had revealed himself till then. But Dr Van Til said, ‘Of course arithmetic must be taught in a Christian school. It cannot be taught anywhere else.’ But is it really to be expected that from a fideistic standpoint can come a sufficient accountability to the facts that God has written, or that an insistent presuppositionalist is likely to change his mind in any reasonable way, when he can write off what others say? Is it not rather to be supposed that, alienated from the very senses God has given, he will affirm what the magisterium says, be it that of Rome or of the secular bureaucrats? Or he will forever be tossed to and fro by his own whims and desires disguised as fundamenta, his own sensibilities disguised as facts.
No, right use of reason must remain. What business have we inculcating children with theories that they cannot possibly, even with guidance, infer from sensible facts? What is the point of telling them the dogma that the earth revolves around the sun, when just as easily, and to greater profit, we could hold off on that teaching till they could be taught to reason the same? Likewise Newton’s laws, atoms, and the complexities of evolutionary biology: none must be taught as mere doxa, as mere belief, if they can later be taught by right reason. For it is no godly catechesis that gives opinions as facts to be believed upon authority; even of theology St John Chrysostom says,
Let us not therefore carry about the notions of the many, but examine into the facts. For how is it not absurd that in respect to money, indeed, we do not trust to others, but refer this to figures and calculation; but in calculating upon facts we are lightly drawn aside by the notions of others; and that too, though we possess an exact balance, and square and rule for all things, the declaration of the divine laws?
It may be wondered, then, whether it be not doxa to believe the Bible, to take it as a given, rather than as opinion to be tested. Not so: for God has given us both the book of nature and the majestic and unerring book of his saving grace, and we cannot but take the one, as we do the other, as reality. Theology, indeed, is a science, though differing in kind from natural sciences. As Thomas Aquinas says (Summa Theologiae I, q. I, a. II),
Sacred doctrine is a science. We must bear in mind that there are two kinds of sciences. There are some which proceed from a principle known by the natural light of intelligence, such as arithmetic and geometry and the like. There are some which proceed from principles known by the light of a higher science: thus the science of perspective proceeds from principles established by geometry, and music from principles established by arithmetic. So it is that sacred doctrine is a science because it proceeds from principles established by the light of a higher science, namely, the science of God and the blessed. Hence, just as the musician accepts on authority the principles taught him by the mathematician, so sacred science is established on principles revealed by God.
And Charles Hodge, in the nineteenth century,
In every science there are two factors: facts and ideas; or, facts and the mind. Science is more than knowledge. Knowledge is the persuasion of what is true on adequate evidence. But the facts of astronomy, chemistry, or history do not constitute the science of those departments of knowledge. Nor does the mere orderly arrangement of facts amount to science. Historical facts arranged in chronological order, are mere annals. The philosophy of history supposes those facts to be understood in their causal relations. In every department the man of science is assumed to understand the laws by which the facts of experience are determined; so that he not only knows the past, but can predict the future. The astronomer can foretell the relative position of the heavenly bodies for centuries to come. The chemist can tell with certainty what will be the effect of certain chemical combinations. If, therefore, theology be a science, it must include something more than a mere knowledge of facts. It must embrace an exhibition of the internal relation of those facts, one to another, and each to all. It must be able to show that if one be admitted, others cannot be denied.
The Bible is no more a system of theology, than nature is a system of chemistry or of mechanics. We find in nature the facts which the chemist or the mechanical philosopher has to examine, and from them to ascertain the laws by which they are determined. So the Bible contains the truths which the theologian has to collect, authenticate, arrange, and exhibit in their internal relation to each other. This constitutes the difference between biblical and systematic theology. The office of the former is to ascertain and state the facts of Scripture. The office of the latter is to take those facts, determine their relation to each other and to other cognate truths, as well as to vindicate them and show their harmony and consistency. This is not an easy task, or one of slight importance.
Biblical skepticism can be discussed, as can Kant, but observation of the inspired Scriptures is as basic as – though perhaps more difficult than – observation of nature. As articulated by Dr Hodge especially, it is equally in theology, as it is in the other sciences, that we learn by drawing rational inferences from what we observe.
In both the natural sciences and the theological, it is key for younger learners to develop the skills of observation taught by Dr Agassiz. Look at that fish. Good; keep looking at that fish. Even in the catechisms, then, the answers should merely formulate what is seen in holy Scripture, making rational sense of what no less an authority than the Holy Ghost has infallibly expressed from the Wisdom of the Father. It is out of his word that we must receive sacred doctrine. For it will not do for a tradition – even a Protestant tradition – to stand reified as an authority practically equal to holy Scripture in the lives of young children, and for its dogmas to come down not de Scriptura, but de magisterio. For no man has ever, even in pontificating, spoken infallibly, no man but one, Jesus Christ himself. Therefore, even in sacred doctrine – or especially in sacred doctrine – it is important that learning proceed by persuasion, wherein folk are compelled by force of truth and nor of coercion.
Nor does such practice breed impiety in children, when they prefer sweet persuasion to hard coercion: for at home, by the same principles, they may articulate themselves, not as tyrants, but as citizens; and abroad they will have learnt, not to riot, but to remonstrate. It is obvious that such harmony cannot be impious, nor such instruction be hurtful to the common good. What is pursued, after all, is not the interest of one party but the truth which applies to all. And reason can surely demonstrate the wisdom of submitting to one’s superiors, that in all things there may be peace, as parents cherish their children, and children honour their parents.
Let truth be taught by demonstration, according to the ability of the learner. Though reasoning be hard, let it not be given up entirely in the early years, for man is a rational soul. Let the words of Pascal guide our plans for instruction: ‘A human being is only a reed, the weakest in nature, but he is a thinking reed. To crush him, the whole universe does not have to arm itself. A mist, a drop of water, is enough to kill him. But if the universe were to crush the reed, the man would be nobler than his killer, since he knows that he is dying, and that the universe has the advantage over him. The universe knows nothing about this.’