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For whose learning are we responsible?

ואמר רבא הני תרי מקרי דרדקי חד גריס ולא דייק וחד דייק ולא גריס מותבינן ההוא דגריס ולא דייק שבשתא ממילא נפקא רב דימי מנהרדעא אמר מותבינן דדייק ולא גריס שבשתא כיון דעל על דכתיב (מלכים א יא, טז) כי ששת חדשים ישב שם יואב וכל ישראל עד הכרית כל זכר באדום כי אתא לקמיה דדוד אמר ליה מאי טעמא עבדת הכי אמר ליה דכתיב (דברים כה, יט) תמחה את זכר עמלק אמר ליה והא אנן זכר קרינן א"ל אנא זכר אקריון אזל שייליה לרביה אמר ליה היאך אקריתן אמר ליה זכר שקל ספסירא למיקטליה אמר ליה אמאי א"ל דכתיב (ירמיהו מח, י) ארור עושה מלאכת ה' רמיה א"ל שבקיה לההוא גברא דליקום בארור א"ל כתיב (ירמיהו מח, י) וארור מונע חרבו מדם איכא דאמרי קטליה ואיכא דאמרי לא קטליה ואמר רבא מקרי ינוקא שתלא טבחא ואומנא וסופר מתא כולן כמותרין ועומדין נינהו כללא דמילתא כל פסידא דלא הדר מותרה ועומד הוא

Rava said: If there are two teachers of children, one who teaches a lot of material but is not precise in his statements, and one who is precise but does not teach a lot of material, one hires the one who teaches a lot of material but is not precise. Why is this? Errors will be corrected by themselves, and no lasting harm will be caused. By contrast, Rav Dimi of Neharde’a said: One hires the instructor who is precise and does not teach a lot of material, as once an error is taught, it is taught, and cannot be easily corrected. The Gemara cites a proof for the opinion of Rav Dimi of Neharde’a: This is as it is written: “For Joab and all Israel remained there six months until he had cut off every male in Edom” (I Kings 11:16). When Joab came before King David after this episode, David said to him: What is the reason that you did that? Why did you kill only the males? Joab said to him: As it is written: You shall blot out the males [zakhar] of Amalek, i.e., the male descendants of Amalek, who descend from Edom. David said to him: But we read the verse as stating: “You shall blot out the remembrance [zekher] of Amalek” (Deuteronomy 25:19). Joab said to him: I was taught to read it as zakhar. Joab went and asked his childhood Bible teacher. Joab said to him: How did you read this word to us? The teacher said to him: I read it as zekher. The teacher had read it the proper way, but he failed to notice that his student had learned it incorrectly. Joab took a sword to kill him. The teacher said to him: Why do you want to kill me? Joab said to him: As it is written: “Cursed is he who does the work of the Lord with a slack hand” (Jeremiah 48:10), and you taught me incorrectly. The teacher said to him: Leave that man to remain as cursed. This is a sufficient punishment; there is no need to kill me. Joab said to him: It is also written: “And cursed is he who keeps back his sword from blood” (Jeremiah 48:10). There are those who say that Joab killed him, and there are those who say that he did not kill him. In any event, this episode demonstrates that an error learned in one’s childhood stays with him his whole life. And Rava says: With regard to a teacher of children, a professional tree planter, a butcher, a bloodletter, and a town scribe, all these are considered forewarned. In other words, they need not be exhorted to perform their jobs correctly, as if they err in the performance of their duties they can be dismissed immediately. The principle of the matter is: With regard to any case where loss is irreversible, the individual is considered forewarned.

(א) הלכות תלמוד תורה
...הוא היה צריך ללמוד ויש לו בן ללמוד ואין ידו משגת להספיק לשניהם אם שניהם שוין הוא קודם לבנו ואם בנו נבון ומשכיל מה שילמוד יותר ממנו בנו קודמו ואע"פ שבנו קודם לא יבטל הוא שכשם שמצווה עליו ללמד לבנו כך הוא מצווה ללמוד לעצמו כשם שמצווה ללמד לבנו כך מצווה ללמד לבן בנו שנאמר והודעתם לבניך ולבני בניך ולא לבן בנו לבד אלא מצוה על כל חכם מישראל ללמד לתלמידים שגם הם נקראים בנים

If a man and his son both need to study, but the man only has means to support one of them: If they are both of equal aptitude, then he takes precedence over his son. But if his son is particularly bright, such that the son will learn more than the father, then the son takes precedence. However, even though the son takes precedence, he is not exempt from his own study, for just as it is a commandment upon him to instruct his son, it is likewise a commandment to study for himself. And just as he is commanded to teach his son, he is also commanded to teach his grandson, as it is said, "And you shall instruct your children, and your children's children." And this applies not only to his grandson, but it is a commandment on every sage of Israel to teach students, for they are also called "children."