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Jews during the time of Jesus were educated. I cannot copy and post everything, but the following will provide everyone a glimpse of schools in Israel during the time of Christ.

Supposing, then, a child to be so far educated at home; suppose him, also, to be there continually taught the commandments and observances, and, as the Talmud expressly states, to be encouraged to repeat the prayers aloud, so as to accustom him to it. At six years of age he would be sent to school; not to an academy, or “beth hammedrash,” which he would only attend if he proved apt and promising; far less to the class-room of a great Rabbi, or the discussions of the Sanhedrim, which marked a very advanced stage of study. We are here speaking only of primary or elementary schools, such as even in the time of our Lord were attached to every synagogue in the land. Passing over the supposed or real Biblical notices of schools, and confining our attention strictly to the period ending with the destruction of the Temple, we have first a notice in the Talmud (Bab. B. 21, b), ascribing to Ezra an ordinance, that as many schoolmasters as chose should be allowed to establish themselves in any place, and that those who had formerly been settled there might not interfere with them. In all likelihood this notice should not be taken in its literal sense, but as an indication that the encouragement of schools and of education engaged the attention of Ezra and of his successors. Of the Grecianised academies which the wicked high-priest Jason tried to introduce in Jerusalem (2 Macc. 4:12, 13) we do not speak, because they were anti-Jewish in their spirit, and that to such extent, that the Rabbis, in order to “make a hedge,” forbade all gymnastic exercises. The farther history and progress of Jewish schools are traced in the following passage of the Talmud (Bab. B. 21, a): “If any one has merit, and deserves that his name should be kept in remembrance, it is Joshua, the son of Gamaliel. Without him the law would have fallen into oblivion in Israel. For they used to rest on this saying of the law (Deut. 11:19), ‘Ye shall teach them.’ Afterwards it was ordained that masters be appointed at Jerusalem for the instruction of youth, as it is written (Isa. 2:3), ‘Out of Zion Shall go forth the law.’ But even so the remedy was not effectual, only those who had fathers being sent to school, and the rest being neglected. Hence it was arranged that Rabbis should be appointed in every district, and that lads of sixteen or seventeen years should be sent to their academies. But this institution failed, since every lad ran away if he was chastised by his master. At last Joshua the son of Gamaliel arranged, that in every province and in every town schoolmasters be appointed, who should take charge of all boys from six or seven years of age.” We may add at once, that the Joshua here spoken of was probably the high-priest of that name who flourished before the destruction of the Temple, and that unquestionably this farther organisation implied at least the existence of elementary schools at an earlier period. Every place, then, which numbered twenty-five boys of a suitable age, or, according to Maimonides, one hundred and twenty families, was bound to appoint a schoolmaster. More than twenty-five pupils or thereabouts he was not allowed to teach in a class. If there were forty, he had to employ an assistant; if fifty, the synagogue authorities appointed two teachers. This will enable us to understand the statement, no doubt greatly exaggerated, that at the destruction of Jerusalem there were no fewer than four hundred and eighty schools in the metropolis. From another passage, which ascribes the fall of the Jewish state to the neglect of the education of children, we may infer what importance popular opinion attached to it. But indeed, to the Jew, child-life was something peculiarly holy, and the duty of filling it with thoughts of God specially sacred. It almost seems as if the people generally had retained among them the echo of our Lord’s saying, that their angels continually behold the face of our Father which is in heaven. Hence the religious care connected with education. The grand object of the teacher was moral as well as intellectual training. To keep children from all intercourse with the vicious; to suppress all feelings of bitterness, even though wrong had been done to one’s parents;1 to punish all real wrong-doing; not to prefer one child to another; rather to show sin in its repulsiveness than to predict what punishment would follow, either in this or the next world, so as not to “discourage” the child—such are some of the rules laid down.1 A teacher was not even to promise a child anything which he did not mean to perform, lest its mind be familiarised with falsehood. Everything that might call up disagreeable or indelicate thoughts was to be carefully avoided. The teacher must not lose patience if his pupil understood not readily, but rather make the lesson more plain. He might, indeed, and he should, punish when necessary, and, as one of the Rabbis put it, treat the child like a young heifer whose burden was daily increased. But excessive severity was to be avoided; and we are told of one teacher who was actually dismissed from office for this reason. Where possible, try kindness; and if punishment was to be administered, let the child be beaten with a strap, but never with a rod. At ten the child began to study the Mishnah; at fifteen he must be ready for the Talmud, which would be explained to him in a more advanced academy. If after three, or at most five, years of tuition the child had not made decided progress, there was little hope of his attaining to eminence. In the study of the Bible the pupil was to proceed from the book of Leviticus to the rest of the Pentateuch, thence to the Prophets, and lastly to the Hagiographa. This regulation was in accordance with the degree of value which the Rabbis attached to these divisions of the Bible.2 In the case of advanced pupils the day was portioned out—one part being devoted to the Bible, the other two to the Mishnah and the Talmud. Every parent was also advised to have his child taught swimming. It has already been stated that in general the school was held in the synagogue. Commonly its teacher was the “chazan,” or “minister” (Luke 4:20); by which expression we are to understand not a spiritual office, but something like that of a beadle. This officer was salaried by the congregation; nor was he allowed to receive fees from his pupils, lest he should show favour to the rich. The expenses were met by voluntary and charitable contributions; and in case of deficiency the most distinguished Rabbis did not hesitate to go about and collect aid from the wealthy. The number of hours during which the junior classes were kept in school was limited. As the close air of the school-room might prove injurious during the heat of the day, lessons were intermitted between ten A.M. and three P.M. For similar reasons, only four hours were allowed for instruction between the seventeenth of Thamuz and the ninth of Ab (about July and August), and teachers were forbidden to chastise their pupils during these months. The highest honour and distinction attached to the office of a teacher, if worthily discharged. Want of knowledge or of method was regarded as sufficient cause for removing a teacher; but experience was always deemed a better qualification than mere acquirements. No teacher was employed who was not a married man. To discourage unwholesome rivalry, and to raise the general educational standard, parents were prohibited from sending their children to other than the schools of their own towns. Edersheim, A. (2003). Sketches of Jewish social life in the days of Christ (pp. 133–137). Bellingham, WA: Logos Bible Software.

What was the literacy rate? I have posted estimates in the region ranging from 1.5% to 20%

When Jerusalem fell to the Romans in 70 AD there were 482 schools there.

EDUCATION — the transfer of knowledge, morals, and attitudes from one person to another, and usually from one generation to the next. For the Israelites, the goal of education was to prepare people to know God and to live peacefully with one another (Luke 2:52); education did not emphasize the “three R’s.” The method of education was different, too, although by New Testament times, it had changed significantly. In the Old Testament period education was rather informal. Children were taught in the home by the parents. However, by New Testament times schools had been established to assist parents in the teaching of their children.
God gave the responsibility of teaching to parents (Deut. 11:19). To be a parent meant to teach. Both parents were involved in the child’s education; however, the father was responsible to see that his children were properly educated (Prov. 1:8–9). A young son stayed with his mother when the father went to the fields to work. Therefore, a boy’s first significant instruction came from his mother (Prov. 31:1–9). As the boy grew, the father’s involvement in his son’s education increased, especially as they began to work together in the fields or in the father’s trade. A daughter stayed on with her mother and continued under her instruction. In the close-knit family structure of that day, as parents became grandparents they also became involved in teaching their grandchildren (Deut. 4:9; 2 Tim. 1:5; 3:14–15). A parent’s responsibility for instructing children continued until death.
The term “father” was applied to teachers outside the family, also, and teachers often called their students “sons.” God made Joseph a “father” to the PHARAOH (Gen. 45:8), which means that the Pharaoh listened to Joseph as a pupil listens to his teacher and receives instruction from him. Throughout Proverbs the term “my son” indicates the same teacher-pupil relationship (Prov. 1:8, 10, 15; 2:1; 3:1, 11). And in the New Testament Paul spoke of Timothy as his son (1 Tim. 1:18).
During the period between the Old and New Testaments, SYNAGOGUES and schools were established. Generally, each rabbi taught in a village school supported by the parents of the children who attended. The teacher, or rabbi, of the school helped the parents by instilling religious truths in the boys’ minds; however, the parents still were responsible for their children’s education. In choosing a rabbi as a village teacher, the parents were more concerned with his personal character than with his ability to teach. His example was more important than his teaching skills. The ideal rabbi was a married man who also was industrious and serious. He would never joke with the boys, nor would he tolerate any wrongdoing. However, it was considered important that he be a patient man. Both rabbi and parents took God as their model for proper teaching. God was the Master Teacher (Is. 30:20–21), who taught by word and example (Ps. 78:1; Deut. 8:2–3).
Every father was expected to teach his son a trade. A Jewish proverb reads, “He who does not teach his son a useful trade teaches him to be a thief.” Usually, a son followed in his father’s occupation, with the father passing on his skills and trade secrets.
Scholars do not agree on how many Israelites could read and write in Old Testament times. By the New Testament period, however, almost every village had its own school where reading and writing were taught to the boys. Parents sent their sons to school for the purpose of learning to read the Scriptures; they continued in school from the age of 6 or 7 until about 12 years of age. If the parents wanted their son to receive more training, he was sent to Jerusalem, where a number of notable rabbis had schools. Paul spent time there, studying under GAMALIEL (Acts 22:3), a famous rabbi. School was in session year-round, with the day beginning shortly after sunrise and continuing until about 10:00 A.M. On a hot day, the students would be dismissed for the remainder of the day. If the weather was more comfortable, classes reconvened about 3:00 P.M. for several more hours of study.
The school consisted of one classroom; all the students studied together. The teacher sat on a low platform (Luke 4:20); the students sat at his feet (Acts 22:3). Because the students were at different learning levels, the instruction had to be individualized. While the rabbi worked with one student or group, the others busied themselves with assignments. Because the rabbi believed that if the student did not voice his lessons they would be forgotten, students spoke out loud as they read and memorized.

Youngblood, R. F., Bruce, F. F., & Harrison, R. K., Thomas Nelson Publishers (Eds.). (1995). In Nelson’s new illustrated Bible dictionary. Nashville, TN: Thomas Nelson, Inc.