Is this mindfulness? 

A mistake frequently made by practitioners is that the fourfold practice of satipaṭṭhāna is today translated as: “the four establishments of mindfulness.” But the English term mindfulness refers to being aware of or recognizing what is going on outside. Satipaṭṭhāna, however, means: focusing attention within (sati = attention + upaṭṭhāna = placing within. A more appropriate English term to translate the Pali term satipaṭṭhāna would be “introspection.” It is looking within in order to observe the experience (sampajañña) that is going on quite unconsciously within. What is going on within is the emotional reaction to circumstances outside. The emotion aroused is dependent on the interpretation made by the cognitive process. 
In one of the Suttas the Buddha has given a very interesting analogy to explain satipaṭṭhāna (as introspection). Let us suppose there is a musical show, along with dancing, going on before an audience. A person is given a bowl full of oil, filled to the brim, and asked to walk between the front row of the audience and the stage on which the show is going on. A ferocious man carrying a sword is following him saying, “If you drop one drop of oil on the floor I will cut off your neck.” Imagine you are the one walking with the bowl of oil in your hand. What would you be doing? Will you be looking at the show, or looking at the bowl? No doubt your attention will be on the bowl. That is how the introspection (satipaṭṭhāna) has to be practiced. This will help you to understand the difference between “mindful awareness” and the “intensive introspection” that has to be carried out throughout the day, while walking, standing, sitting, and lying down. 
Sigmund Freud, the father of psychoanalysis, recognised the need to eliminate emotions. He saw that the emotions were responsible, not only for all neuroses and psychoses, but also for all the crimes, wars and terrorism in the world. He saw that although emotions helped some animals to preserve their lives and even propagate, human beings have begun to use emotions even for destructive purposes that often harm themselves as well as others. Human beings, however, have something better than emotions, which can be used more constructively, and that is the ability to think rationally. This was why Freud said, “In place of the id there shall be the ego,” where id referred to the emotions, and the ego referred to the rational faculty. Erich Fromm, the Neo-Freudian quotes this passage often. Freud thought, however, that the emotions could not be rooted out, because they were inborn instincts that were built into the system. The only solution to this problem that he saw was sublimation, which was to direct the energy of the emotions into socially acceptable good channels. He also pointed out, however that to be civilized is to be discontented, because when civilized, the emotions are not adequately gratified. 
The main concern of Sigmund Freud was the conflict between the id and the ego, but the modern day Neo-Freudians have begun to ignore this conflict and focus on a conflict between the ego and its object. They have begun to call the psychology of Freud an id psychology, and the modern psychology of the Neo-Freudians an ego psychology that emphasises the relation between the ego and its object. This ego psychology was really an idea introduced by Alfred Adler during the time of Freud. It appears that the Neo-Freudians have gone through a paradigm shift from the partly experiential mode of Sigmund Freud to the fully existential mode of Alfred Adler. 
Modern cognitive psychologists, however, seem to have solved the problem between ego and the id by pointing out that emotions can be eliminated, by changing the way we interpret our circumstances (cognition). They are aware that the emotion that is aroused is dependent on how the cognitive process interprets the external circumstances. In cognitive psychotherapy, they attempt to remove the aroused emotion, by changing this cognitive interpretation. 
The Buddha recognized this fact about the relationship between the cognitive and the affective processes more than twenty-six centuries ago. In the first verse in the book of verses called Dhammapada, he points out that “Cognition precedes all experience” (mano pubbangamā dhammā). He even made use of this fact to absolutely eliminate all self-centered emotions within him, and even taught his disciples to follow suit.