Difficult Concepts in Science

Learning scientific concepts has an inherent difficulty that arises from the fact that they are expressed in common language terminology but with a specific meaning. For example the word 'difference' that the dictionary definition would state as: "not equal", in mathematics is specific to the idea of a quantitative value 'A - B' "the result of arithmetic subtraction" (Mac's dictionary). In particular chemistry uses symbolism to express these differences, a capital Greek letter Δ (delta) for major differences like the difference in temperature, between two physical states; and lower case δ (delta) for minor/slight differences like the one encountered in electromagnetic polarities within the atom. These major differences are of extreme importance when looking at energy changes during physical and chemical reactions, and they can be expressed as difference in enthalpy, entropy, volume, or any other variable of state that only depends on the values at the end and beginning of the process not on the path that the change followed from initial to final state. Of course we can also apply the idea of big difference when dealing with non conservative phenomena that is dependent on the path followed, such as when dealing with friction generated loss of energy during a process.

It sure become critical in the discussion of these phenomena to keep in mind the definition of all variables and parameters in the process, and these is what makes these concepts difficult to understand.

So, I think, I have to start with the definition of definition!
From my Mac's Dictionary:
 Quote
"definition |ˌdefəˈni sh ən|noun1 a statement of the exact meaning of a word, esp. in a dictionary.• an exact statement or description of the nature, scope, or meaningof something : our definition of what constitutes poetry.• the action or process of defining something.2 the degree of distinctness in outline of an object, image, or sound, esp. of an image in a photograph or on a screen.• the capacity of an instrument or device for making images distinct in outline : [in combination ] high-definition television.PHRASESby definition by its very nature; intrinsically : underachievement, by definition, is not due to lack of talent.

A definition is astatement of the meaning of a term (aword, phrase, or other set of symbols).^[a] The term to be defined is the definiendum. The term may have many different senses and multiple meanings. For each meaning, a definiens is a cluster of words that defines that term (and clarifies the speaker's intention).

A definition will vary in aspects like precision or popularity. There are also different types of definitions with different purposes and focuses (e.g. intensional, extensional, descriptive, stipulative, and so on).

A chief difficulty in the management of definitions is the necessity of using other terms that are already understood or whose definitions are easily obtainable or demonstrable (e.g. a need, sometimes, for ostensive definitions).

A dictionary definition typically contains additional details about a word, such as an etymology and the language or languages of its origin, or obsolete meanings. "

As a noun definition is a statement of the exact meaning of the word. Exact in the sense of providing meaning that not only is accurate but precise so one can use the meaning repetitively within different contexts. But as 2 above: provides a degree of distinctness characterized by its relationship to the topic. Within a metaphor the words "atomic view" and "microscopic view" can be interchanged without changing the intent of those words, while in the description of an item, atom and microscope are completely different.

With this in mind let's retake the idea of 'atom' for an initial analysis of what constitute a difficult concept in science. The last sentence in our definition of definition it is stated that additional details about etymology should be given, so atom mean without a parts from the Greek, so we infer it is the smallest part of the world, but we now know that the atom has parts, protons, neutrons, electrons, that themselves are made of smaller parts (subatomic) components such as muons, mesons, quarks, bosons, and others with a variable set of colors and flavors as you find out in Wikipedia.

So the question about understanding what an atom is becomes inherently complicated and a simple explanation of what an atom is becomes elusive. One can of course simplify with models or analogies but it must be understood that the simplification will undoubtedly produce inaccuracies and misinterpretations that can, if magnified lead to critical errors of understanding. One example of this could be the lack of understanding many people have regarding the significance of 'orbital' as a 'mathematical' description of the probable localization of the electron around the nucleus within the atom. An electron that is modeled as a small particle (dot in the drawing) but mathematically is represented by a wave or probability function as stated by the Schrödinger equation http://en.wikipedia.org/wiki/Schrödinger_equation.

As an educator I have to make sure that the student understand the complexities of nature as well as the difficulties of concepts describing the behavior and properties of phenomena within nature while at the same time providing students with mechanisms, formulas, and procedures that will permit them apply their skill to the solution of basic problems, even without a full understanding of the deep meaning of the phenomena.

This is the art of making difficult concepts easy to understand.