There is an element of truth here, just as there is with whole language. A good reading teacher will have kids reading real books with a decent story line so they will want to read and have the interest to figure out words from context - but that good teacher will also teach kids to sound out words so they are not just guessing from context or from what makes sense. Similarly, we all learn better from doiing things than we do from passive listening. A good teacher uses that and puts students in a position to make those logical connections between the material and the real world - but a good teacher also provides plenty of direct instruction (lectures!) so the kids have some facts with which to make those connections.
... “there is simply too much knowledge in the world today for students to learn everything they need to know.”...
That sounds like a recipe for raising democrats: "There is too much to know, and you just don't have what it takes to understand. Don't worry. Aunt Nancy and Uncle Barack know what you need, and they'll take care of you."
***That sounds like a recipe for raising democrats: “There is too much to know, and you just don’t have what it takes to understand. Don’t worry. Aunt Nancy and Uncle Barack know what you need, and they’ll take care of you.” ***
Very good post, MathDoc.