First, let's remember that a knight is not just an armoured soldier on horseback; he is a knight precisely because of being in receipt of a knight's fee under knight-Service, with military (and/or financial, see scutage) obligations to his lord in exchange for possession of land, a manor, deemed sufficient to support not only the knight and his family, but also his required retinue in war. This retinue would have included several horses (At least two full-grown war horses and a riding horse each for the knight himself, his sons if old enough, and perhaps for one or two senior men-at-arms.) and men-at-arms, squires, grooms for the horses, etc. As such, by the twelfth century, a knight was a gentleman farmer, small businessman, and junior military leader all in one. This makes the twelfth century knight (when not also a baron) as much a member of the emerging middle-class as of the aristocracy. Certain assumptions are reasonable to make about the prerequisites of success in these multiple endeavours.
An essential skill in warfare is identifying friend from foe. In Medieval Europe this science was heraldry, and was conducted in Latin. The descriptions of arms was in Latin, as were their oft-associated mottos. Note that the art-work of a coat-of-arms is, to an extent, arbitrary; provided that it satisfies the recorded description for the arms.
Survival in warfare frequently being dependent on split-second reflexes and decisions, thinking in Latin sufficiently well to recognize arms never seen before from their heraldic description is a survival skill. One can assume that, at a minimum, the knights with a tendency to survive in battle would be those with a solid (not necessarily fluent) knowledge of Latin vocabulary and grammar.
Further, the language of the Royal and baronial courts was still Anglo-Norman French in the twelfth century. Fulfilling the feudal obligation of providing counsel to his liege-lord would have required fluent knowledge of the court's language, making our successful knight at least marginally trilingual in Latin, Anglo-Norman French, and the vulgar tongue(s) (be it an English, Scottish, Welsh, or Irish dialect) of his own vassals.
The twelfth century is the great age of both cathedral- and castle-building; and the construction and besieging of such lies at the heart of todays Civil and Mechanical Engineering disciplines. Fundamental to both is geometry. While the advanced study of that is part of the quadrivium (of arithmetic, geometry, music and astronomy), a basic knowledge would have been immediately beneficial to our hypothetical knight; and easily recognized as such.
While the founding of Free Masonry still lies several hundred years in the future, the origins of speculative masonry lies in the admission of, paying, honourary members to masons guilds, from the middle- and upper-class, at about this time. In exchange for their contributions, these members received education in the geometric underpinnings to the mason's art and science.
Campaign planning further requires a basic understanding of where one is in the world. How many days march is it to London, Rouen, Paris and Jerusalem is useful knowledge for one's liege-lord, and makes one a more competent knight counselor. Perhaps not all knights have this education, but the more successful ones are learning it.
Business and Agricultural Requirements
To finance his military service obligations our knight had to run a successful manor. He holds a manorial court, adjudicating cases that are not violations of the King's Peace (ie civil and non-felony cases). Adoption of three-field rotation over two-field is occurring at this time, and decisions on specific crops for each phase need to be made. Smiths and tradesmen need to be located and hired for the village arising around the manor. Budgets need to be drawn up and adhered to. All of this requires management skills, fluency in the local vulgar tongue, and sound reasoning ability. An upwardly-mobile knight does well to at least ensure that his sons have this knowledge, even if he hasn't.
Medieval Education in General
The trivium of grammar, rhetoric, and logic was throughout Western Europe of this time taught in Latin, its Lingua Franca. By 1100 several (residential) grammar schools have already been established for sons of the elite, a number of which have survived to the present day. It is likely that every sizeable town also possessed one or more non-residential grammar schools. Increasing supply of education presupposes a matching increase in demand, at least some of which is likely to have been from upwardly mobile knights.