Mr. Dictionary Disliked American Elementary Schools
According to this brief bio from the Noah Webster House and West Hartford Historical Society, the Word Man, unlike naively sentimental Americans, wasn't fond of the crammed one-room schoolhouse. And unlike celebrity-crazed Americans, No-Web was fond of learning.
His defintion of "education" reflects those biases and those preferences: “The bringing up, as of a child; instruction … To give children a good education in manners, arts and science, is important; to give them a religious education is indispensable; and an immense responsibility rests on parents and guardians who neglect these duties.”
Source: An American Dictionary of the English Language, 1828
Addition: Connecticut Girl - Judy Aron - supplied a bit of education history. She writes: "Noah must have gotten his ideas from the Ludlowe's code of 1620 (still in existence today as part of our CT education statutes) ... This first line is what gives us the right to home educate in CT."
Here's what she's referring to: "Sec. 10-184. Duties of parents. School attendance age requirements. All parents and those who have the care of children shall bring them up in some lawful and honest employment and instruct them or cause them to be instructed in reading, writing, spelling, English grammar, geography, arithmetic and United States history and in citizenship, including a study of the town, state and federal governments."
According to this brief 