Below is a rather normal textbook example for Newton's 2nd Law:
A person pushes a box, mass xx kg on a frictionless surface with force yy N, determine the resultant force and acceleration of the box.
Very few teachers will spend their time to discuss about the person pushing the box since identifying the forces on the box is sufficient to illustrate the use of F = ma. However if one is to take a closer look at the forces on the person pushing the box, there will be plenty of inconsistencies. This is the kind of textbook problems that plague physics teaching which are the source of confusion among students because it cannot exist in real life. There is no way the person standing on a frictionless floor to push the box for more than an instant! There is a contradiction between actual experience and physics principles. To deal with the discrepancy, students resorted to assimilate the solutions of this kind of problems through mental accommodation rather than through a consistent mental model. Many researches have pointed out that such laymen's preconceptions of how the world functions continue to persist in learners even after years of high quality science education.
What Newton's 3rd Law claims and how we perceive how forces work in the real world can be poles apart. To master it, learners have to stop relying on personal perceptions and use the laws which are unbias and self-consistent. Learners should start to build a consistent mental model from ground up rather than accomodate Newton's Laws with pre-existing perceptions. For the record, it took the ancients (from Aristotle to Newton's) almost 2000 years to realise that over-reliance on the senses lead to inconsistent scientific model. To master Newton's Laws of motion, we may want to take a leaf from a small part in a famous martial art novel 《倚天屠龙记》.
Finally I appeal to all teachers and anxious parents to allow students the time to struggle with Newton's Laws. The more they struggle, the more they can distil the essence of the laws. Trying to shorten the 2000 years' of journey taken by scientists is not practical. If a teacher can teach the laws [in the textbooks] and the students can understand them with a few examples and assignments, why do we need teachers? We can easily replace teachers with DVDs of lectures and demonstrations (Hewitt or Walter Lewin just to name a few)!
The following conversation may shed some light on the struggle of learners have in order to reconcile real world experience with Physics model.
Student - If I am pushing a box on a frictionless surface, then the box should push back at me with the same amount of force. But if the box is moving in the direction i am pushing it, doesnt that mean that i am exerting a larger force on it?
Teacher - Why do you think you need a larger force to move the box in the direction of motion? Maybe you want to break down the question into the forces acting on the box and the man. Maybe sketch and drop me a pic?
Student - Because there needs to be a resultant force for the box to move? But if that's so then newtons third law doesn't apply... So it only applies for stationary objects?
Teacher - Newton's third law applies 100% of the time! Looking at what you have drawn, the box will accelerate to the right but the person will accelerate to the left! Do you think there is something missing on the person? Can you walk on a frictionless ground?
Student - Then the person should have a force by muscles letting him walk?
Teacher - Nope. No one can walk on a frictionless floor! To walk, you need to be able to exert a force on the floor backward relative to you which gives rise to a force on you by the floor (see diagram). In fact you need to be able to exert a force by your legs larger than what you apply to the box in order for the situation to be possible in real life! Your question is the kind of textbook problems that plague physics teaching which led to confusion among students (You have brought up an excellent problem). If you look at the box alone, no problem, most students will be able to work out the acceleration of the box easily. However contradiction arises because the person can't accelerate forward with the box unless the floor under him miraculously turn into a rough floor for him to exert a force on it backward!
Student - But then if we use your first question of two boxes as an example, when box A pushes on box B, by N3L box B should push back with the same amount of force. But box B will move, which means its pushing back with less force. then how does N3L apply then? Or rather, why is there even resultant force in the world?
Question that is referred to by student
Student - Oh. Is it cause the amount of force with which B pushes back on A doesn't affect the resultant force of B itself cause it's on A, not B?
Teacher - Yes! Well done!