As clearly explained by Hammer in his 1994 article ( and by Jorge Grave in the brilliant account of such article gave during the first formation we organized) we can identify three main distinctive features in the most constructive approach to learning science. We are going to discuss them here by giving a personal interpretation of the Hammer paper.

What one wants to encourage in pupils who are learning science, is:

1) the search for the meaning underlying each concept;

2) a view of knowledge which is integral, consistent, and systemic;

3) the will to question and reformulate autonomously the academic content.

In the specific case of physics, these three elements are equivalent to the mastery of a mathematical formalism which models an aspect of reality, and the ability to translate any element of the formalism to its counterpart in the real world, back and forth.

The opposite approach, which, unfortunately, is much more popular, is the view of learning as storing in our memory a bunch of meaningless concepts unrelated to one another, in which we believe because we are told to by the teacher or because they are declared by some other official source, and use them to solve stereotyped problems whose relevance is limited to a very narrow context: pass a test or answer a question posed by the teacher.

Teaching science is useful, important and meaningful, only to the extent that it manages to overcome the approach to learning described in the previous paragraph and promote instead the three so called epistemological believes of the list above. There exist indications in the literature that intelligence or a specific talent for science, are not as related to the capacity of engaging with the right epistemological believes as we might think. Such indications include case studies reported in the same paper cited above (Hammer 1994) and the very same fact that discussion among peers make a huge difference in this respect for the majority of learners.

The three aforementioned features of good learning , are clearly dependent one on another. This will become clearer through an example. A student thinking on the meaning of pressure, the "p" symbol present in some physics equation, will be willing to learn more than the mere numerical value that she has to substitute to the symbol "p" in order to get the result of the test right. Pressure is an abstract concept that applies to a huge variety of situations. Understanding the meaning of "p" leads necessarily to understand that the pressure that we feel when we dive, is stronger in the bottom of a swimming pool than it is closer to the surface. Inquiring about the meaning of pressure, makes one relate an everyday experience outside school with a physics problem in a text book. More, in order for the meaning of pressure not to get lost, the relations that one builds among notions involving pressure, have to be compatible with one another, must form an integrated and consistent system. It will be thus necessary to use the words said by the teachers and written in a textbook without explicit, step-by-step directions.

We tentatively suggest the hypothesis that this process has a lot to do with commitment to ethical coherence. Those who see the link between their claimed believes and their real-life choices, are obliged to either behave ethically, or gain awareness of their flaws in this respect. Such flaws are inherent to human condition, but the capacity to detect them has a great impact on our behavior. We are not proposing a correlation between acting upon the constructive epistemological believes in the scientific field and being committed to ethical integrity in the social domain. What we do conjecture, is a similarity between the processes that have the two conditions as outcome, both based on the ability to integrate pieces of information otherwise thought as unrelated. Reflecting on the process of learning as it unfolds, increases the chances to make the most of it in a broader set of contexts.

The quest for an integrated, consistent system of notions, lead us to make the most of our intuitions. By intuition we mean the "thinking fast" that Daniel Kahneman describes in his excellent book "Thinking, fast and slow". Thinking slow is deliberated, aware, and effortful, thinking fast is effortless and quite independent of will. Intuitions are fast. Intuitions in physics are as important as in any other field of human ingenuity. But they might also be a hurdle. A fundamental trait of scientific knowledge, is its surprising rebuttal of deep, strongly held intuitions. Earth is not flat. Earth is not eternally immovable. A heavy object does not drop faster than a lighter one, no matter how lighter, provided that they both undergo the same friction. Humans and dogs belong to a common lineage ... Learning science, also means question a lot of intuitions that  were obvious truths at some point of anybody's life. Newton himself, when he formulated the theory of gravitation, were uncomfortable with the idea of an action at distance. Force can only be applied through direct contact. This was Newton's intuition and it was most probably our own, or still is, before learning in a physics class the concepet of field. But Newton did not stop paying attention to his intuitions at any time in his life. His intuitions simply grew more sophisticated as he picked up a new element and stored it in his intellectual toolbox: action at distance. Without the possibility of refining intuitions, the only possible conceivable physics is Aristotle's, who is also a consistent organized system of intertwined and meaningful cincept, but it did not undergo centuries of revisions guided by  systematic collection of empirical data. We are not aware of our intuitions, but we feed them constantly with everything we consciously and deliberately learn, when we do it deeply enough. This process happens at the individual level, but also at the social and historical one. Students, as soon as they go to high-school, have the possibility to develop physics intuitions which are more accurate than Aristotle's, without necessary being more engaged and talented for it than Aristotle was.

Learning that an intuition is wrong, is a transforming experience. Once again we suggest that this aspect of science learning has an everyday-life counterpart. It is the following: if we stubbornly stick to our initial intuitions, possibly out of fear of loosing something of ourselves very intimate, we miss an important opportunity of refining such intuition. Relaxing the instinctive assumption that "the stronger I feel about it, the truer must it be", for instance, helps developing the much wiser and more fertile insight that "reality tends to be much more complex than the opinions we initially form". One might call it openness to change. Science requires in the intellectual sphere, the meaningful life requires it in the social sphere.

We would like to leave a last note on questioning. It's the single most important mental habit, but we do not advocate here a radical and over-simplified version of it. Trust is a necessary ingredient for any social process, positive or negative, to take place. The building up of scientific knowledge is no exception. It is not possible for an isolated individual to measure the average annual size of a glaciers, for instance. To do that, one needs definitely more than a self-made meter stick. In order to have any knowledge on climate science (to name a field that suffers the attacks from people who misinterpret skepticism) it is necessary to trust the social process that allow scientific institutions to elaborate and share information. Einstein did not perform independently all physics experiments that had been done since Galileo's time until the beginning of the 20th century. Had he engaged in such a nonsensical enterprise, he would not have had the time and energy to bring forth a revolution in physics. Einstein, like any other human being that wants to achieve something as trivial as drinking a beer, had to have trust. He trusted physics textbooks available to him, he assumed the validity of the physics knowledge of his time, while at the same time radically reformulated such knowledge.

Knowing when to trust and when to be skeptic is a crucial skill, especially in the internet era. I do not believe everything that people tell me, but when I am for the first time in a place, I ask for indications, I believe what I am told, and I have never regretted it in more than 30 years of adult life. My trust in the indications that local people give me, is validated by my personal experience, despite the inevitable errors that occur now and then. Similarly, my trust in the scientific knowledge, as presented in textbooks, articles, educational videos and so on, is supported by my every-day experience, although I am aware of the incomplete and imperfect nature of such knowledge.  Those who reject any scientific authority on the ground of skepticism towards any official truth, will be faced with two possible alternatives: accept some other authority, for instance a dodgy website, as it usually happens, or limit their knowledge to that ridiculously tiny part of it that we acquire by direct personal experience. Questioning does not mean rejecting unconditionally.

Giancarlo Pace P.I. of the team KEY 1.0.