1) Describe the phenomenon or the phenomena that seem to need an explanation -- the phenomena that seem puzzling in some way.  If possible explain or describe what seems puzzling or odd or worth exploring about the phenomenon or phenomena in question.  Try to foster curiosity in the students about it.

2) Let the students suggest ideas and explanations to explain the phenomenon or phenomena.  And insofar as possible, either pursue those ideas with some sort of experiment, or explain what was done historically to pursue them and what the result was.  If you can do either of these things, ask the students what they think the results show.

3) Describe the (most interesting or instructive) explanations which were given historically and tell which one became accepted, and why.  Explain what the confirming evidence was for that theory or explanation.  This evidence will often also be the disconfirming evidence for the rival theories.

4) Explain the ramifications of the theory and what new phenomena, if any, were discovered because of it.

5) If there are any problems with the theory, anything relevant the theory does not seem to account for or that seem to possibly contradict the theory, describe them; or if you are teaching science in historical order of discoveries, explain the problems or the newly discovered phenomena that seemed to cause a problem for the theory.

6) Repeat steps 2 - 5 with regard to the phenomena that seems unaccounted for or contradictory.

The point of teaching science in this way is not just to spark curiosity and teach experimental research methodology, but primarily to help students distinguish between phenomena and theory about it; to help them distinguish between the questions of science and the answers of science, and to see why those answers have been accepted or rejected or still debated; and to see to what new discoveries or phenomena they have led.  Too often students tend to memorize "facts" and formulas as though everything is somehow known or is known in the same way.  Too often students try to calculate or predict a phenomena that should simply be known to occur -- that does not need "predicting" or calculating.  Teaching science whenever possible as outlined above should give students better understanding of the material itself and make it make more sense to them.  Too often students learn scientific material without really having any understanding of it. So even when they do satisfactorily on tests that ask for recall answers or rote calculations of formulas they have practiced, they do not really have any understanding of that material, or they have insufficient understanding to apply it in situations other than the ones they have practiced.

The math and calculations of science are often difficult, but that should not get in the way of showing and describing to students what phenomena actually happen.  Even if students cannot understand why or how basic physical phenomena occur, there is no good excuse for not trying at least to show them what kinds of basic and important things occur in the universe.  There are many wonders of nature, often very simple ones, that could stir the imagination of children who would otherwise never experience having their imaginations stirred or their curiosity aroused.

And more importantly, this would help students understand science in general better, particularly if they are not able to understand math that might be involved.  Everyone with normal intelligence should be able to know what the phenomena are that prompt the questions in chemistry, physics, astronomy, biology, geology, economics, psychology, sociology, etc.  They should have some understanding, even if not mathematically precise, about the answers that have been given and why those answers have either so far held up or have failed.  One does not have to understand relativity or quantum mechanics or string theory in order to be aware of what the amazing phenomena are that prompted those theories to be propounded and accepted or modified or still questioned for further exploration.

The theory of relativity is nearly 100 years old (as of this writing), and it explains phenomena known by the late 1800's.  It was written at a time airplanes were just getting off the ground, the electric light and electric power were just coming into common usage in cities, automobiles were just getting started, and movies and sound recordings were in their earliest stages.  By modern standards, it was a primitive era, and yet it was the time that science made many of the strides that are not known today by most people, about phenomena most people today do not yet even know occur -- but whose study have led to many of the things we take for granted and would find it difficult or uncomfortable to live without. 

Perhaps even more astounding, Newton's Laws were first published more than 300 years ago to explain phenomena already known by educated people of that time, and yet most people today neither understand those laws or know why they are important or know much about the phenomena they describe and explain, even though we have access now to weightless conditions in space and can see many of the things that only 50 years ago were difficult to imagine or describe because we could only have verbal descriptions of them, and because it took a special kind of imagination to translate that verbal description into the accurate idea of what was being described.

While I do not expect everyone to be a gifted scientist or mathematician, it seems to me to be a terrible thing that children today are not taught about many of the phenomena of the universe that have been known for at least 100 years and many of which have been known since the time of the Greeks and others, twenty five hundred years ago.  It is terrible because these phenomena are surprising and interesting, and, more importantly, because the understanding of them shows us how limited, egocentric, and narrow our perceptions are, not to mention the ideas we develop about those perceptions.  Almost every child is taught today that though it looks like the sun goes around the earth by moving across the sky, the same appearance would be given by the earth's rotating while the sun stands still. Those are two ways to explain the same phenomenon -- the motion of the sun across the sky.  Science and philosophy and mathematics, however, have discovered there are many other phenomena that can be understood in ways far more general and far better, and far differently, from how we typically tend to think of them based on their appearance to us.  It would be good for people to understand that even in the objective world of factual experience, all is not the way it seems. Even if knowing that led to no other practical and scientific discoveries, it might help more of us realize that perhaps we should not be so arrogantly and destructively defiantly confident in some of our less objective ideas about how the world is or ought to be.

This is not an argument for teaching "classics".  Much that is in the classics is too difficult for students to digest for any of a number of causes that are difficult for teachers to overcome.  But it is an argument for teaching relevant elements, portions, and ideas of the classics in artistically and intellectually honest ways so that much of the best of what has come before will at least be introduced to students in ways they can digest and appreciate. At the very least it will show students some of what is possible to produce besides action movies, provincial  political polemics, simplistic news reports, and gangster rap.  There are successful and useful ways to introduce the best of the past, some of which I have suggested at The Power and Purpose of Poetry in Prose, Teaching Literary Style, The Theban Plays of Sophocles, Selected Passages from Jane Austen, A Loose Introduction to Reading Plato, and The Socratic Method: Teaching by Questions (this last being a modern example, with some explanation, of how Socrates' teaching method works).  Other teachers have worked out ways to successfully show students the power of important past works and authors, composers, and artists. 

It is possible to teach students the best of what the past has produced in science, language, literature, philosophy, and the arts. It is a shame not to do it.