How to avoid adding concepts to our thinking This question is mere practical: how a practitioner avoids that his mind wanders away into stories and dramas. There are moments that "noting" does not help.
The short answer is: by not adding concepts to the thinking, by not feeding it.


  There are moments that "noting" does not help.


Sometimes the mind is more quiet, sometimes it is more uneasy. Don't expect that in meditation you will always progress, or that the progress will be steady. Don't create the expectation that the mind will always settle when meditating, because it can be unsatisfying. Don't fight your mind and don't force it to calm down, it can be frustrating.

Instead, when you notice your mind is wandering, bring your awareness back to the object of meditation. The practice of meditation is not to stop adding concepts to the thinking actively, or to learn to interrupt the process of thought. But it is more like weakening the impulse and momentum of thought. Thinking will never completely cease as it inherent to the human being. But with practice you get less overwhelmed and blinded by it, thinking becomes subtle and calm. Then, don't be anxious about being peaceful or settling the mind, because this anxiety defeats the purpose of meditation, it just would feed the eager to think.

You can also practice to perceive the thoughts in a distanced manner. When someone is wandering on the thoughts, it is like he/she is immersed on them, being carried away by them. Then instead of being in the flow of the thinking, try to watch the thinking from outside. Be aware of the process of thought, perceive how it moves and watch it go away by itself. Instead of trying to block the chain of thoughts, something that is usually ineffective, try to stop feeding it and let it go.

There is also shamata, a practice to improve the stability of awareness. Begin by keeping the focus on the breath as long as you can. It seems that shamata is commonly disregarded for its simplicity, but it is very important. How can you meditate on something if you your awareness isn't stable? If you are really into it, I suggest you to read the book "The Attention Revolution: Unlocking the Power of the Focused Mind" by Alan Wallace.

And last, vipassana can be helpful to perceive that it makes no sense to "feed the trains of thought". From one side, thinking usually tries to fight the impermanent and unfulfilling marks of existence, and asserts the identity (the concept of self). From other side, thinking itself is impermanent (it is mostly random in the long run), is unfulfilling (its desires and aversions are never completely met) and have no self (it is not absolute, nor apart from everything else). Although thought is produced, you don't need to get overwhelmed and blinded by it, you don't have to be driven by it.

EDIT:

Adding some more explanation on second paragraph after the quote, regarding interrupting the thought or stopping adding concepts to it.

And adding a bit more info to shamata and vipassana part.