"Common sense beliefs about motion are generally incompatible with Newtonian theory. Consequently, there is a tendency for students to systematically misinterpret material in introductory physics courses."
"Common sense beliefs are very stable, and conventional physics instruction does little to change them."
"Conventional instruction has little effect on the students basic knowledge state."
"The small gain in basic knowledge under conventional instruction is all the more disturbing when one considers the uniformly low levels of the initial knowledge states shown in Table I. This means that throughout the course the students are operating with a seriously defective conceptual vocabulary, which implies that they continually misunderstand the material presented."
"Diagnostic test results show that a students initial knowledge has a large effect on his performance in physics, but conventional instruction produces comparatively small improvements in his basic knowledge. The implications of failure on the part of conventional instruction could hardly be more serious, for we are not talking about a few isolated facts that students failed to pick up. Ones basic physical knowledge provides the conceptual vocabulary one uses to understand physical phenomena. A low score on the physics diagnostic test does not mean simply that basic concepts of Newtonian mechanics are missing; it means that alternative misconceptions about mechanics are firmly in place. If such misconceptions are not corrected early in the course, the student will not only fail to understand much of the material, but worse, he is likely to dress up his misconceptions in scientific jargon, giving the false impression that he has learned something about science."
You are quite right about the inability to comprehend F=ma, but your personal language is similar to the "wrong" language of most people. You write:
"So many students (A & B included) don't connect the concept that you make your car go faster by increasing its acceleration (hence, the correct name of that pedal, the accelerator). Or that when you pedal your bike faster, you are increasing the acceleration on the bike. They don't get that the new increased speed is the result of a rebalance of the new acceleration and drag forces. They memorize F=ma, but don't actually know what it means. It is one of the toughest things to overcome -- learning that your instincts are wrong. This is true in the physics classroom, and this is true in golf. Higher speed is the result of increased acceleration, and longer drives are the rest of not using your hands, etc. You have to fight to overcome your first instincts of how position, velocity, and acceleration are related in physics and your first hit instincts in golf."
The Newtonian "correct" language is that "CONSTANT" acceleration leads to increasing velocity, not your language of "increasing acceleration". Your sense of "adding" acceleration in order to add velocity is not Newtonian, but "medieval" physics in conception.
And the phrase learning that your instincts are wrong confuses the "conscious misconceptions" with what the "instincts" represent. Actually, the implied "ignorance" of instincts about real physics is exactly backwards: the "instincts" get the real physics right, without language-based and concept-based misconceptions, and it is the "conscious" mind that does NOT get the physics right. The conscious mind is indeed "ignorant" in the usual sense of the word, but the instincts are brilliant compared to the misconceptions of the conscious mind. This is especially relevant to how the body and instincts perform the physics of motion -- by instincts, without the interference of the "dumb" conscious mind.