Whether studying math with Perdocere or pursuing other academic subjects, these writings by Quintilian (ancient Rome) on education are insightful and relevant for parents and students.

Quintilian Book 2, Chapter 3 – English Translation (Latin below)
Translation from Rev. John Selby Watson 1892 A.D.
Another translation by W. Guthrie, Esq. 1805 A.D.

A pupil should be put under an eminent teacher at first, not under an inferior one [1-3]. Mistakes of parents as to this point [3-4]. The best teacher can teach little things best, as well as great ones [5-9]. The pupils of eminent teachers will afford better examples to each other [10-12].

[1] Nor is the opinion of those to be passed in silence who, even when they think boys fit for the professor of rhetoric, imagine that he is not at once to be consigned to the most eminent, but detain him for some time under inferior teachers with the notion that moderate ability in a master is not only better adapted for beginning instruction in art, but easier for comprehension and imitation, as well as less disdainful of undertaking the trouble of the elements.

[2] On this head I think no long labor necessary to show how much better it is to be imbued with the best instructions and how much difficulty is attendant on eradicating faults which have once gained ground, as double duty falls on succeeding masters, and the task indeed of unteaching is heavier and more important than that of teaching at first.

[3] Accordingly, they say that Timotheus, a famous instructor in playing the flute, was accustomed to ask as much more pay from those whom another had taught as from those who presented themselves to him in a state of ignorance.

[4] The mistakes committed in the matter, however, are two: one, that people think inferior teachers sufficient for a time, and, from having an easily satisfied appetite, are content with their instructions (such supineness, though deserving of reprehension, would yet be in some degree endurable if teachers of that class taught only worse, and not less), the other, which is even more common, that people imagine that those who have attained eminent qualifications for speaking will not descend to inferior matters and that this is sometimes the case because they disdain to bestow attention on minuter points, and sometimes because they cannot give instruction in them.

[5] For my part, I do not consider him, who is unwilling to teach little things, in the number of preceptors; but I argue that the ablest teachers can teach little things best, if they will; first, because it is likely that he who excels others in eloquence has gained the most accurate knowledge of the means by which men attain eloquence;

[6] secondly, because method, which, with the best qualified instructors, is always plainest, is of great efficacy in teaching; and lastly, because no man rises to such a height in greater things that lesser fade entirely from his view. Unless indeed we believe that though Phidias made a Jupiter well, another might have wrought, in better style than he, the accessories to the decoration of the work; or that an orator may not know how to speak; or that an eminent physician may be unable to cure trifling ailments.

[7] Is there not then, it may be asked, a certain height of eloquence too elevated for the immaturity of boyhood to comprehend it? I readily confess that there is, but the eloquent professor must also be a man of sense, not ignorant of teaching, and lowering himself to the capacity of the learner; as any fast walker, if he should happen to walk with a child, would give him his hand, relax his pace, and not go on quicker than his companion could follow.

[8] What shall be said, too, if it generally happens that instructions given by the most learned are far more easy to be understood and more perspicuous than those of others? For perspicuity is the chief virtue of eloquence, and the less ability a man has, the more he tries to raise and swell himself out, as those of short stature exalt themselves on tip-toe, and the weak use most threats.

[9] As to those whose style is inflated, displaying a vitiated taste, and who are fond of sounding words, or faulty from any other mode of vicious affectation, I am convinced that they labour under the fault, not of strength, but of weakness, as bodies are swollen, not with health, but with disease, and as men who have erred from the straight road generally make stoppages. Accordingly, the less able a teacher is, the more obscure will he be.

[10] It has not escaped my memory that I said in the preceding book (when I observed that education in schools was preferable to that at home) that pupils commencing their studies, or but little advanced in them, devote themselves more readily to imitate their school-fellows than their master, such imitation being more easy to them. This remark may be understood by some in such a sense, that the opinion which I now advocate may appear inconsistent with that which I advanced before.

[11] But such inconsistency will be far from me; for what I then said is the very best of reasons why a boy should be consigned to the best possible instructor, because even the pupils under him, being better taught than those under inferior masters, will either speak in such a manner as it may not be objectionable to imitate, or, if they commit any faults, will be immediately corrected, whereas the less learned teacher will perhaps praise even what is wrong, and cause it, by his judgment, to recommend itself to those who listen to it.

[12] Let a master therefore be excellent as well in eloquence as in morals; one who, like Homer’s Phoenix, may teach his pupil at once to speak and to act.

Quintilian Book 2, Chapter 3 – original Latin

An protinus praeceptore optimo sit utendum.

[1] Ne illorum quidem persuasio silentio transeunda est, qui, etiam cum idoneos rhetori pueros putauerunt, non tamen continuo tradendos eminentissimo credunt, sed apud minores aliquamdiu detinent, tamquam instituendis artibus magis sit apta mediocritas praeceptoris cum ad intellectum atque imitationem facilior, tum ad suscipiendas elementorum

[2] molestias minus superba. Qua in re mihi non arbitror diu laborandum ut ostendam quanto sit melius optimis inbui, quanta in eluendis quae semel insederint uitiis difficultas consequatur, cum geminatum onus succedentis premat, et

[3] quidem dedocendi grauius ac prius quam docendi: propter quod Timotheum clarum in arte tibiarum ferunt duplices ab iis quos alius instituisset solitum exigere mercedes quam si rudes traderentur. Error tamen est in re duplex: unus, quod interim sufficere illos minores existimant et bono sane stomacho

[4] contenti sunt: quae quamquam est ipsa reprensione digna securitas, tamen esset utcumque tolerabilis si eius modi praeceptores minus docerent, non peius; alter ille etiam frequentior, quod eos qui ampliorem dicendi facultatem sint consecuti non putant ad minora descendere, idque interim fieri quia fastidiant praestare hanc inferioribus curam, interim

[5] quia omnino non possint. Ego porro eum qui nolit in numero praecipientium non habeo, posse autem maxime, si uelit, optimum quemque contendo: primum quod eum qui eloquentia ceteris praestet illa quoque per quae ad eloquentiam peruenitur diligentissime percepisse credibile est,

[6] deinde quia plurimum in praecipiendo ualet ratio, quae doctissimo cuique plenissima est, postremo quia nemo sic in maioribus eminet ut eum minora deficiant: nisi forte Iouem quidem Phidias optime fecit, illa autem quae in ornamentum operis eius accedunt alius melius elaborasset, aut orator loqui nesciet aut leuiores morbos curare non poterit praestantissimus medicus.

[7] Quid ergo? non est quaedam eloquentia maior quam ut eam intellectu consequi puerilis infirmitas possit? Ego uero confiteor: sed hunc disertum praeceptorem prudentem quoque et non ignarum docendi esse oportebit, summittentem se ad mensuram discentis, ut uelocissimus quoque, si forte iter cum paruolo faciat, det manum et gradum suum

[8] minuat nec procedat ultra quam comes possit. Quid si plerumque accidit ut faciliora sint ad intellegendum et lucidiora multo quae a doctissimo quoque dicuntur? Nam et prima est eloquentiae uirtus perspicuitas, et, quo quis ingenio minus ualet, hoc se magis attollere et dilatare conatur, ut statura

[9] breues in digitos eriguntur et plura infirmi minantur. Nam tumidos et corruptos et tinnulos et quocumque alio cacozeliae genere peccantes certum habeo non uirium sed infirmitatis uitio laborare, ut corpora non robore sed ualetudine inflantur, et recto itinere lassi plerumque deuertunt. Erit ergo etiam obscurior quo quisque deterior.

[10] Non excidit mihi scripsisse me in libro priore, cum potiorem in scholis eruditionem esse quam domi dicerem, libentius se prima studia tenerosque profectus ad imitationem condiscipulorum, quae facilior esset, erigere: quod a quibusdam sic accipi potest tamquam haec quam nunc tueor sententia

[11] priori diuersa sit. Id a me procul aberit; namque ea causa uel maxima est cur optimo cuique praeceptori sit tradendus puer, quod apud eum discipuli quoque melius instituti aut dicent quod inutile non sit imitari, aut, si quid errauerint, statim corrigentur: at indoctus ille etiam probabit fortasse

[12] uitiosa et placere audientibus iudicio suo coget. Sit ergo tam eloquentia quam moribus praestantissimus qui ad Phoenicis Homerici exemplum dicere ac facere doceat.