Let me change your question a bit (hope this is no dirty trick on my side!): "What is my attitude towards teaching any science starting with concrete experiments, and making abstraction on the basis of your findings?" I consider this way the only viable one in teaching and in research as well. Gamow writes in his Biography of Physics (referring to Faraday) that in certain cases higher mathematics is not only superfluous, but explicitly harmful for a researcher in physics. The researcher loses the way in the mist of complicated formulas, and cannot perceive "the forest from the tree". Strange as it may sound, but I, a lover of both math and physics, begin any research in math with "qualitative math" (quoting your experession), and turn to math abstraction only when I feel solid ground of direct experience under my feet. I am convinced that the same method should be followed in teaching, adapted to the needs and expectations of our students.

I think physics without mathematics is nearly useless (and I am saying this as a trained experimentalist). There are so many advantages in the mathematical formulation of physical concepts, for example:

• Mathematics ensures that your models and theories are logical consistent.
• Mathematics is an universal language that can be understood by all humans regardless of their mother tongue.
• Even the concept of pure experiments, which implies measurement of physical entities, relies on numbers and thus maths (you cannot measure things without comparing them).
• ...

So every natural science should be based on mathematics - you can also see this when you compare the advances in physics from the ancient greeks up to Galileo and Newton and the progress after these two "mathemized" physics. The progress after connecting physics with maths has been tremendous compared to the progress before...

Probably, I was too brief, for only István Lénárt understood my point hidden in the last sentence: "solving an experimental problem begins with a qualitative approach and ends in a quantitative one"

Let us suppose we investigate Oersted's effect using his apparatus: a circuit with a long straight wire and a movable magnetic needle. We know that eventually the magnetic deviation became a measure of the intensity of electric current, but how was this established.  If we had an independent method of measuring the intensity of current, we could have determined the magnetic deviation as a function of the intensity.  Before the concept of current was solidly established it had been presumed that some effects of current (heat and chemical, for instance) increase with the number of cells in the circuit.  Thus, it makes sense to accept the number of cells as a measure of intensity of current. 

Now we do the first part of the experiment (the qualitative part): we change the number of cells and observe the needle.  We see that in a certain range an increase of the number of cells leads to a greater magnetic deviation. With this the first part ends: we established our function quasi-quantitatively, that is in terms of "ïncrease-decrease", "greater-smaller" and the like.  The purpose of the second (quantitative) part will be to determine our mathematical function precisely.  This can be achieve if proper instruments are available in this particular school (my general presumption is that most schools are poor).  In this particular case it is enough to have ammeters of any type (analog are preferable) and a graduated magnetic compass.  Incidentally, to make myself clear, whenever I speak of lab experiments I mean that all student groups do the same experiment, which implies a need in up to 10 sets of equipment, which in turn implies that the equipment must be cheap.

In the next message I'll explain the advantage of dividing an experiment into two parts. For  more details on the subjects discussed above, see A Law of Physics in the Classroom: The Case of Ohm’s Law   and Qualitative Physics in High School.

The merit of starting solving a problem qualitatively is a possibility to focus on the physical meaning of the problem.  Students do preliminary observations and experiments to figure out a few potential variables and a good procedure to deal with them.  The variables are investigated one by one and their connections are expressed quasi-quantitatively, that is in such terms as "greater", "farther", etc.  As shown in the previous post, if the proper instruments are available, the qualitative part may be followed by a quantitative one in which we obtain a mathematical law of the phenomenon.

Sometimes, this is not possible, as for instance, with electrostatic experiments.  Instruments for measuring potentials across capacitors are too expensive for laboratory experiments of the type I described above.  This is not  a good reason, however,  for avoiding electrostatic experiments, because  all other  necessary materials are cheap and readily available.  Students can do a number of qualitative investigations, such as discovering which materials conduct electricity or proving the existence of two kinds of electricity. Other problems may have both qualitative and quantitative parts. 

For instance, when solving the problem of making an effective Leyden jar,  students start with materials of the jar itself and those adjacent to its walls from inside and outside.  Having found materials which guarantee a working Leyden jar, they may proceed with a quantitative investigation of the size of the coated  surface and the distance between the coats.  By changing these variables they may try to maximize either the potential difference across the jar or a power of its discharge. Moreover, they may discover using a simplest electrometer  that potential of a jar increases when the size of its surface decreases, and that increasing the charge inside a given jar increases the potential.  From these results Volta deduced the proportionality between the charge and potential and inverse proportionality between capacitance and potential.  Students cannot prove these functions as well as Volta, because their electrometers are less precise, however, even with the conclusions they reached themselves they can solve a number of problems with capacitors.

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