A puzzling problem of science education
Science has revolutionized human thought through some profound insights that began to become effectively used about three or four centuries ago.  When understood, they empower.  When learned, but not understood, they are empty shells of words.

Much teaching and learning of today is of empty shells. . . . . . LOOK AGAIN!

Three criteria currently used to test for competency in science at the 10th and 12th grade levels:

  • explain the principle that energy can be transferred and matter can be changed, but the sum of energy and matter in systems, and  therefore in the universe, remains the same.  (10th grade)
  • apply the law of conservation of mass to analyze chemical reactions.  (10th grade)
  • apply unifying scientific concepts in projects, investigations, and further learning (within the sciences and other disciplines).  (12th grade)
The first two statements have hints of some of the "pervasive, persistent, predictable, and pre-scientific" misconceptions that plague public understanding of science.

Einstein's energy-mass equivalence, E = mc², is an equivalence in the sense of formal logic.  It is very often mistakenly seen as a mutual exclusion in which we observe mass vanishing and energy taking its place, or vice versa.

"Mass," "weight," "matter" (and sometimes even "volume") are pervasively and persistently confused with each other.  They are seen as being, vaguely, quantity-of-substance, but without differentiating between the more abstract (read "subtle," perhaps) concepts the terms mean in science.

Before we can apply those unifying scientific concepts we must first understand them.

Let's look at something from Einstein, something from Piaget, and something from Feynman.

"...therefore energy and mass are merely different expressions of the same thing."
It's a summarizing statement in Einstein's explanation of E = mc² in his The Meaning of Relativity.  He starts by noting that whenever we increase the energy of an object, for example increasing the kinetic energy of a baseball by hitting it with a bat, we also  increase it's mass.  The ball is going faster (with respect to our observations) and special  relativity calls for a corresponding small mass increase.  Einstein showed that the increase in mass is proportional to the increase in energy, and the constant of proportionality is the speed of light squared. 

It's very general, Einstein suggested.  Anything that increases an object's energy also increases its mass.  He took a small step of reasoning that made a giant leap in concept:  The mass we observe at rest also has associated with it an appropriate amount of energy.  Rest mass has a rest energy associated with it.  That's the small step.

The giant leap is the conclusion: mass and energy are different ways of observing some  mysterious "thing," some characteristic of all matter.  Depending on how we query that matter we might see mass or we might see energy—but it's the same thing.  Mass and energy are related by an equivalence relationship, not a mutual exclusion.

"...Energy and mass are merely different expressions of the same thing."


Piaget asked the question, 

"Where has evolution been taking us in our abilities to know the world and how does it go about it?"

He sought answers by watching infants mature into adults and observing their ever more subtle information processing the older they get.  One concept that gets subtler and subtler, as the conceptualizer gets older, is "conservation."  Piaget dissolved some sugar in some water and asked his maturing subjects some questions about taste, weight, volume, etc.  The youngest expected no sugar taste after the sugar had dissolved.  Slightly older children expected the taste of sugar, but did not expect the weight or the volume of the contents of the glass to increase from the addition of the sugar.  Somewhat older yet and weight was expected to increase, but not volume. 

Volume conservation is shown to be understood when children recognize that a piece of clay dropped in a glass of water will raise the water level the same amount whether the clay is flattened or not.  When Jan Smedslund squashed the clay and surreptitiously removed a piece at the same time, only the older children jumped off their stools and  insisted that the experimenter open his hands and turn out his pockets.  They hadn't simply learned, they understood. The younger children reverted to the "pre-understanding" reasoning; such as, "It's flatter so it doesn't push the water up as far."

We use very different elements of information processing to recognize conservation of matter, of weight, and of volume. These are very different concepts in physics, and differentiating between them gets better and better as our skills at handling information develop further and further. 

But the skills needed to differentiate mass from weight are right at the edges of human comprehension.  Piaget and his colleagues themselves incorrectly analyzed one of their physics puzzles in The Growth of Logical Thinking, from childhood to adolescence:  they confused weight and mass in much the same way as do most college students when they take a course in elementary physics.


Richard Feynman once evaluated all the K-12 science textbooks submitted to the California State Curriculum Commission.  Seventeen shelf-feet of textbooks!  He was the only one assigned the task who discovered that one of the books had all blank pages. That is, he appears to have been the only one who actually looked inside the covers.

What did he find? 

All of the authors "were teaching something they didn't understand  ... didn't know what the hell [they were] talking about, so it was a little bit wrong, always!"  The entire group of texts submitted were "UNIVERSALLY LOUSY!"  "Perpetual absurdity."  "That's the way all the books were: They said things that were useless, mixed-up, ambiguous, confusing, and partially incorrect. How anybody can learn science from these books, I don't know, because it's not science. "  ("Judging Books by their Covers," in Surely, You're Joking, Mr. Feynman, Bantam Books, pp 262 - 276.)

These authors were not teaching sophisticated science or complex science.  What they were not seeing were some of the simplest concepts of science.  But they had come up against the reason for the saying, well-known in physics, "Physics is simple, but subtle."  They were butting their heads against the edges of human comprehension.

That's a lot of textbook writers and a lot of remarkably inadequate understanding.  This collection of writers and understandings is a good sampling of teaching professionals outside the actual disciplines being taught.

The implications of this observation are "obvious."

Three outstanding "seers" of the twentieth century.  Each saw a different piece of the puzzle.


observed something "obvious" that goes widely unobserved:  the science discovered during the past several centuries is almost always not what it at first seems.  Furthermore, those who learn it often don't go beyond those first impressions.  They retain beliefs now recognized as being "misconceptions." Holding a degree, even a doctorate, does not guarantee understanding of even the simplest of principles.  Especially when that degree has not led to actual use of the principles in the real world. 


observed something "obvious," too: we can see a little further into the edges of human comprehension by developing new ways of looking.  But Piaget did not find the right way of looking at weight and mass.  He joined the majority in failing to see weight and mass as opposites in the sense that weight is a force and mass is a resistance to force.  (One changes if we go to the moon, and the other doesn't.)  Piaget's two doctorates were in philosophy and biology; he obviously did not find need to use the physics principles for solving actual physical problems. 


observed energy and mass with some of the developments that Piaget explicitly described as being at the furthest limits of human intellectual development: specifically, distinguishing between the abstract relationships of formal (Boolean) logic—such as is the distinction between an equivalence and a mutual exclusion—and then recognizing which ones actually apply to which real-world relationships. 

explain the principle that energy can be transferred and matter can be changed, but the sum of energy and matter in systems, and  therefore in the universe, remains the same. 
This statement is the sort that Feynman described as "a little bit wrong, always!"  The sum of energy and mass in the universe does indeed remain constant.  But not because energy might be "converted to" mass, or mass to energy.  It's because the total energy remains constant and the total mass remains constant.  They are just different aspects of the same thing, and that thing is conserved.  Energy remains constant.  Mass remains constant. 

However, "matter" is a different matter. 

The writer seems to be using "matter" as a substitute for "mass" and has in mind Einstein's energy-mass equivalence.  Some textbook authors so speak of the "sum of energy and mass" remaining constant, because energy and mass get "converted" one to the other.  While it can be correct to say "matter gets converted to energy in a nuclear explosion," it is correct only if terms are very carefully defined—and those definitions won't be the meanings used in colloquial speech.  Otherwise, the statement is "a little bit wrong, always!"  It misses those meanings from modern science.

Energy, the thing that's conserved, is not the "energy" of common usage, which is a concept from the days of Aristotle and the thing related to food and fuel which keeps us alive and keeps our engines running.  [See the science of silt.]  Mass is not weight, is not quantity of substance, and is certainly not volume (recall, we do determine the quantity of gasoline and ice cream by volume). 

Both mass and energy are rather abstract quantities that we know how to calculate in a variety of situations and something that, when everything affected is taken into account, has the same value when all the little pieces are added up—no matter what.  That's "something" not "some things" because they are the same "thing."  (This description of energy comes from The Feynman Lectures on Physics and is virtually unique to that physics text.) 


Quantity of substance
could mean:
It then refers to:
A list of numbers of elementary particles, such as electrons, protons, neutrons, neutrinos, gravitons, photons, Higgs bosons...or whatever.  Also, perhaps, hydrogen atoms or ions, alpha particles, uranium atoms, etc.  This might be called "matter."  The number of atoms and particles could remain the same even though the mass changes: promoting electron levels in an atom would add to the mass without changing this "quantity of substance," for example.  This number-of-particles quantity is the "mass" meant in "apply the law of conservation of mass to analyze chemical reactions," the second principle listed above.
mass of a particle or collection of particles This, not the above, is the mass in the law of conservation of mass.  It does not change when we place the object on the moon. 
weight of a particle or collection of  particles This is almost universally thought of as "quantity of substance"—and also the meaning of "mass."  It does change when we place the object on the moon.  This is among the most salient of the pervasive and persistent misconceptions. 
volume of ice cream or gasoline  "Quantity of substance" to a gas stations attendant or ice cream parlor employee.

These are the kind of distinctions that distinguish modern science from prescientific thinking.  They need "insights."  We see the distinctions developing as Piaget asks older and older children what they expect of sugar dissolved in water.  Piaget observes "insights" developing.   Copious learning usually substitutes for the insights needed for distinguishing between mass, weight, and quantity of substance.  That doesn't empower the learner.  "Seeing" does.

We need science teaching, testing, and textbooks that would have pleased Feynman:  That implies:

These all are parts of applying "unifying scientific concepts in projects, investigations, and further learning (within the sciences and other disciplines.")