From the comments at Tam’s:
I tutor children from our public schools and I, too, had a high-school senior who didn’t know that the Sun is a star around which the Earth revolves, that the Moon is a planet that revolves around the Earth, or that light travels very fast. This student had memorized the multiplication tables in elementary school but didn’t know what multiplication “means.”
Another example was with a high-school senior taking an “AP Chemistry” class. This student wanted help understanding how to calculate the molarity of a solution. I kept working “backwards” through the “things one needs to know” in search of the student’s baseline competence. At one point I posed the question “If you have two five pound bags of sugar, how much sugar do you have?” The student responded, “Twenty-five pounds. You multiply don’t you?”Several years ago, I had a third grade student who needed help with arithmetic. This student was very bright but didn’t seem to be retaining much from her class at school. I made an appointment with the teacher to try to get more information about what and how my student was being taught.
At one point in the conversation I mentioned that my student didn’t seem confident in even basic facts like knowing the “multiplication table.” The teacher said, “Well, we’re not as concerned about their knowing the exact answer as how they feel about that answer.”
At this point, I knew I had found the root of this student’s problem. I thanked the teacher for taking time to meet with me and backed slowly out of the office.
Again, all of the students in these examples were very bright and had managed to be very successful in their classes. They were all eager students and found their way to me because they really wanted to learn. They all came from homes where their parents were present, loving, dedicated, and involved in their lives. In every case, their performance improved quickly once we put some of the basics in place. All graduated from college and are successful in their careers. The first is now an accountant, the second is a nurse, and the third is a psychiatrist. In short, the only thing preventing them from getting a high quality education was the Educational System itself. – “Larry”