[Contents]

Copyright © 2010 jsd

Principles of Teaching and Learning
John Denker

*   Contents

1  Overview
2  Dealing with Misconceptions
2.1  Emphasize Correct Conceptions
2.2  Confronting Misconceptions
2.3  Outright Ambiguity
2.4  Insufficient Specificity
2.5  Recurring Misconceptions
3  Terminology
4  A Few Prevalent Misconceptions
5  Next Generation Science Standards
6  References

1  Overview

1.
Emphasize motivation. This includes encouraging curiosity and the love of learning for its own sake. It also includes explaining the practical value of what is being learned.

2.
Emphasize learning as opposed to mere teaching. It doesn’t directly matter what you teach; it matters what the students learn.

3.
Emphasize personal responsibility. Learning is the students’ responsibility; you cannot do it for them. Your job is to inspire them and help them to fulfill their responsibilities.

Responsibility can be taught, bit by bit, over the long haul. The topic of responsibility should be addressed directly. It should be discussed early and often. There should be clear rewards for responsible behavior.

I tell students that more than 90% of what they need to know, they need to learn on their own. All I can do is help get them started in the right direction.

4.
It helps to know where the students are coming from. A useful proverb is:

Learning proceeds
from the known
to the unknown.
     

To say the same thing the other way, you cannot explain idea X in terms of idea A unless the students already understand idea A.

5.
Accentuate the positive, and emphasize constructive suggestions. In particular, start by teaching the correct ideas, as opposed to starting by confronting misconceptions. For details on this, see section 2.

6.
Students can’t learn everything at once, but they have to start somewhere.

That is: If the long-term goal is for the students to have a comprehensive, detailed, sophisticated, rigorous understanding of the subject, they can’t learn that on the first day.

Typically the students start by learning some examples, analogies, and approximations. This should include explicit disclaimers emphasizing that the examples are not entirely representative and the approximations are not exactly accurate. Next the students should learn some math and some theoretical principles, which they can apply to the examples. Also they should always make every effort to see the connections between the new information and everything else they know. Then they should spiral back and learn a wider range of examples, better approximations, more math, more theory, and more connections. And so forth, iteratively.

7.
Explicitly teach students how to learn, and how to remember what they have learned.

There are a number of standard techniques to help with memory, some of which date back 2500 years.

Memory should not be thought of as a substitute for critical thinking, or vice versa. Indeed, memory itself is a thought process. Being able to recall relevant information is a necessary ingredient for critical thinking.

8.
If you want to improve your memory, it is far from sufficient to think “harder” about something at the time it must be recalled. Instead, one must make the effort to form useful memories at the time the memory is laid down, days or months or years before it is needed. It takes time and effort to lay down such memories. As mentioned in item 6, thinking about the connections (aka associations) between ideas is important. More than 100 years ago, in reference 1, William James wrote this about each remembered idea:
Each of the associates is a hook to which it hangs, a means to fish it up when sunk below the surface. Together they form a network of attachments by which it is woven into the entire tissue of our thought. The ‘secret of a good memory’ is thus the secret of forming diverse and multiple associations with every fact we care to retain.

Thinking about the connections between a newly-learned idea and older ideas is first of all a check on the correctness and consistency of the ideas, and secondly serves to reinforce the memory of both the new and old ideas.

To say the same thing another way: A rote memory can be recalled in one way, so technically it counts as a memory, but it is not a very useful memory. In contrast, a well-constructed memory can be recalled in 100 different ways, which makes it 100 times more useful.

9.
There is a fine line between an approximation and a misconception.

In teaching, as in every other facet of life, approximations are necessary. On the other hand, any approximation can be abused.

This topic needs to be taught – directly, emphatically, early, and often. Students need to learn to think clearly about approximations in general, not just this-or-that approximation du jour. Things they need to know include:

10.
Preservice and novice teachers beware: the space of misconceptions is larger than you can possibly imagine. Just because you were never confused about this-or-that doesn’t mean your students won’t be confused about it. That’s one of the N reasons why you give tests: to find out what you didn’t cover sufficiently well.

11.
Don’t become part of the problem. Don’t teach misconceptions, and don’t teach nonsense.

That advice is harder to follow than it might seem, because we are constantly besieged by misconceptions and nonsense. This includes the misconceptions we grew up with. The misconceptions and nonsense are particularly pernicious when they appear in textbooks and in state-mandated “standards” and tests.

Almost any topic can be taught in N different ways, most of which will cause trouble later, and only a few of which form a good foundation for further work.

Just because it was badly taught to you doesn’t dictate that it must be badly taught by you.

12.
If a student seems confused or hesitant, don’t be shy about asking the student what the problem is. Sometimes they don’t know what the problem is ... but sometimes they do.

13.
Learn from other teachers. Whenever possible, drop in on other teachers, to see how they handle things.

14.
Learn from your students. I have a long list of nifty ideas I learned from my students.

15.
Do not tolerate cheating.

It is sometimes claimed that in the long run, the cheaters harm only themselves, but it is not true. Sometimes jobs, scholarships, and even the privilege of staying in school are awarded partly on the basis of grades, and unfair grades can cause serious harm to innocent students and third parties.

In particular, you must not tolerate any situation where students who are not predisposed to cheat feel obliged to cheat just to keep up.

I don’t want to live in a culture where cheating is considered normal. School should not train people to think that cheating is normal.

16.
Do not tolerate plagiarism, since it is a form of cheating.

17.
More generally, do not tolerate anything that gives an unfair advantage to some students over others.

For example, you should assume that some students will have access to the questions and answers to tests given in previous years, filed away in fraternities, private homes, et cetera. I mention this because even if such files are not against the rules, they are unfair, because not all students have equal access to the files. Making a rule against such files is not helpful, because it is more-or-less unenforceable.

Therefore: do not re-use previous years’ questions, unless you have made sure that all students have equal access to the questions and answers.

Constructive suggestion: If you want to re-use any questions from previous years, you can level the playing field by making previous years’ questions and answers available, on the web or otherwise.

By way of example, consider the tests given by the Federal Aviation Administration. For each test, there is a pool of approximately 1000 possible questions, of which a few dozen appear on any given instance of the test. The questions are a matter of public record, but the large size of the pool discourages rote memorization, since most people find it easier to to learn the underlying principles than to memorize specific answers to specific questions.

If you want to re-use a question from a previous year, another way to encourage understanding (as opposed to mere rote regurgitation) is to rejigger the question so that even though the idea is the same, the answer is not literally the same.

2  Dealing with Misconceptions

2.1  Emphasize Correct Conceptions

Whenever the topic of misconceptions comes up, there is an important contrast that needs to be made:

Explaining the correct conceptions should always come first.   Confronting misconceptions can come later, if at all.

“The light shines in the darkness, and the darkness cannot overcome it.”   “You cannot beat something with nothing.”

By way of analogy: If you have a healthy lawn, you won’t have much trouble with weeds. They can’t compete.   If the lawn is weak and sparse, due to insufficient water and fertilizer or otherwise, weeds will invade.

  In an unhealthy lawn, if you just cut off the top of a weed, it will grow back. Even if you manage to kill the weed, it is likely to be replaced by some other weed. See figure 1.

Correct ideas need to be linked to each other, and supported by evidence.   Misconceptions do not exist in a vacuum; they are supported by their own evidence. If you simply contradict a misconception, it will grow back, sooner or later, probably sooner. Furthermore, often an imperfect notion contains a germ of truth, so if you flatly contradict the whole notion you’re not even correct.

On this web site, there are hundreds of documents that try to explain correct ideas.   On this site, there is only one part of one document – section 4 – that has focuses on misconceptions, and it should not be the starting point.

If you are tempted to search the PER literature for a list of misconceptions, my advice is: Don’t go there! Reasons for not going there include:

  1. The literature will tell you that students have more misconceptions than you could possibly imagine ... but if you have any teaching experience at all, you already know that.
  2. There are so many misconceptions that it would be impossible to list them all, let alone analyze them.
  3. It is OK for teachers to talk amongst themselves about this-or-that misconception, but talking about it in front of students is at least as likely to reinforce the misconception as to dispel it.
  4. This brings us back to the main point: To a first approximation, with isolated exceptions, the best policy is to teach the correct concepts and move on.

    Figure 1 is one way of visualizing the situation. If students move randomly away from any given bad idea (shown in red), they are more likely to settle onto a new bad idea than onto a good idea (shown in blue). You need to attract them to the good idea, not merely push them away from this-or-that bad idea.

    good-from-bad
    Figure 1: Lead Toward Good, Not Merely From Bad

    We now turn to figure 2, which is another way of visualizing the situation. Imagine a very narrow path through a vast swamp. The path is safe, and everywhere else is unsafe. If you pick a random point in the swamp, there is a 99.99999% chance you don’t want to visit that place, or even talk about that place.

    One valid path from A to B is shown in black. (There may be more than one valid path, but even taken together, the valid paths are a subset of measure zero in the overall space.)

    truth-sparse
    Figure 2: Stay On (or Near) the Valid Path

    On rare occasions, as you lead students along the path, you might want to point out something nasty that is just next to the path, so they can recognize it and avoid it (as indicated by the yellow places in the diagram). Still, even so, it is usually easier to recognize the path than to recognize the nasties. This is the Anna Karenina principle: All happy students are alike, but every unhappy student is unhappy in his own way. In more detail: Every student who understands the material understands it in more-or-less the same way, but every student who is confused is confused in his own way.

    In a one-on-one teaching situation, you can sometimes afford to deal with misconceptions as they come up. However, this is tricky and hard to plan, because students often come up with weird misconceptions that you never dreamed of. Meanwhile, in a classroom situation, things are even worse, because each student is going to have a different set of misconceptions.

  5. The misconceptions most worth worrying about are the ones that are exceptionally prevalent and exceptionally pernicious. The classic example concerns the washed-out bridge. As discussed in section 2.2, it is well worth confronting misconceptions of this kind.

    Section 4 contains a list of misconceptions that seem particularly prevalent. Please keep in mind that compiling and/or studying such lists is usually not a good use of resources.

  6. I’m not so much worried about the misconceptions that the students bring to class as the misconceptions that the teacher and the textbook author bring to class. When a misconception is passed on from teacher to student, it can cause tremendous difficulties for the students in later courses, and in later life.

    Remember that it is proverbially difficult to unlearn something.

    Some textbooks contain large numbers of misconceptions. For an example – not even the worst example – see reference 2.

  7. Most of the people who collect lists of misconceptions don’t understand the subject well enough to know what’s a misconception and what’s not.

    On top of that, even though statistics will tell you what’s common and what’s not, that is nowhere near sufficient; it takes serious judgment to decide what’s important and what’s not.

  8. Reading the PER literature is definitely a source of misconceptions. I don’t mean you will get a tidy list of avoidable misconceptions labeled as such; I mean that after reading the literature, if you believe what it says, you will suffer from more misconceptions than you started with.

    For example, the book by Arons, Teaching Introductory Physics is — unintentionally — an extensive compendium of bad pedagogy and wrong physics. For a detailed review, including a list of some of the misconceptions propagated and/or introduced by this book, see reference 3.

2.2  Confronting Misconceptions

In many cases, when confronting a misconception, the first step is to recognize that you are dealing with a notion that probably contains a germ of truth. Indeed, the most dangerous ideas are the ones that are usually mostly true, but then betray you at some critical moment.

The classic example concerns a washed-out bridge. Most people take it for granted that it is OK to drive across the bridge, and this is usually true. However, if the bridge has been washed out this becomes a misconception, and could have fatal consequences. Therefore it is worth putting up some “Bridge Out” signs and barriers, and possibly even some flashing lights.

As always, it is better to make constructive suggestions, as opposed to merely pointing out a problem. In this case, it would be silly to put up a “Bridge Out” sign just at the edge of the washout, because by the time drivers could see the sign it would be too late to do anything about it. Instead the proper procedure is to go back to the previous intersection and block off the approaches to the bridge. This includes putting up signs directing traffic to a suitable detour.

There are very few life-critical misconceptions that show up in the introductory-level physics classroom. In the case of misconceptions that are not acutely dangerous, you have the option of confronting them or not.   By way of contrast, in the research lab you might have high-power invisible lasers, high voltages, toxic chemicals, et cetera. Safety-related misconceptions must be confronted.

As an example of a classroom misconception that might be worth confronting, consider the first law of motion. Practically everybody starts out with the Aristotelian notion that objects at rest tend to remain at rest, and objects in motion tend to come to rest. This directly conflicts with the Newtonian principle that objects in motion tend to remain in motion.

As is so often the case, we are dealing with a notion that contains a germ of truth: In situations where friction is overwhelmingly important and taken for granted, objects do tend to come to rest. That’s fine. It is OK for students to retain that idea, provided they learn to distinguish it from situations where friction is not so important. In physics we start by considering situations where friction is completely negligible. Later we consider cases where there is a moderate amount of friction, but even then we do not take friction for granted, but instead account for it as one of the forces that change the state of motion.

Again, we want to do this in a constructive way. That requires:

It must be emphasized that it is pointless (or worse) to contradict the old idea before the new idea has been presented. It is not helpful to push students away from a bad idea unless/until they have a good idea to latch onto.

The same principle applies to everyone you deal with, not just students. It applies at every age, from infancy on up. For example, if a young child is banging a Wedgwood teacup against the tile floor, it is better to give the kid something else to play with, rather than simply taking the teacup away. A small plastic bottle with a few dried beans inside makes a much better toy, from everyone’s point of view.

2.3  Outright Ambiguity

It is quite common to find the same term being used to describe two or more ideas. This is a perennial source of misconceptions. For example:

2.4  Insufficient Specificity

Consider the assertion that “cows are brown”. Is that a misconception? I don’t know, because I can’t figure out what is being asserted. Possibilities include:

  1. Some cows are brown.
  2. All cows are brown.

Statement (A) is entirely correct, whereas statement (B) is entirely incorrect.

Many ideas that are a good approximation in one context are a bad approximation in other contexts. The goal is to formulate a more-specific version of the idea, containing enough provisos so that you know which is which.

Here is another example that touches on the notion of specificity:

a2 + b2 = c2             
always  
             (1)

 

In Euclidean geometry,        
a2 + b2 = c2                                
where abc is a right triangle        
and c is the hypotenuse
             (2)

If you are going to teach people that a2+b2=c2, you have an obligation to tell them that the result is valid for Euclidean right triangles only. This is important, because there are lots of triangles in this world that are not right triangles ... and lots that are not Euclidean.1

2.5  Recurring Misconceptions

While some misconceptions are only lightly held, others are quite deeply held, based on the student’s lifetime of experience (in school and otherwise). As mentioned in reference 5, when you confront a deeply-held misconception, students may become wary, defensive, or even angry. It is likely that the students will pretend to discard the misconception, but then re-adopt it at the first opportunity.

If a misconception keeps coming back, there are several possible explanations, and correspondingly several ways of dealing with the situation. These include:

  1. Consider the first law of motion: an object in motion tends to remain in motion. Contrast that with the widely-held opinion that objects in motion tend to come to rest. This directly contradicts the first law of motion. It is a notorious misconception, widely and deeply held.

    There is however another way of looking at this situation.

    1. If you are a flagellate bacterium, then you live in a world with a verrrry low Reynolds number. Friction is dominant, and inertia is an utterly negligible correction.
    2. If you are an aircraft, your Reynolds number is much higher. Inertia is dominant, and friction is a relatively minor correction term.

    In the introductory physics class, we choose to start from the low-friction case. Students’ intuition about the high-friction case is not wrong; it’s just incompatible with our chosen starting point.

    A direct attack on the idea that objects in motion tend to come to rest will never be successful, because the idea has too much supporting evidence. The best you can hope for is to place limits on the validity of the idea, to restrict it to tiny objects moving slowly through a sticky medium.

  2. I take a similarly tolerant attitude toward scalar acceleration: It’s not crazy wrong; it’s just ambiguous, as mentioned in section 2.3.
  3. The same attitude works for notions of “heat content” aka “caloric”. Such ideas are not crazy wrong, and indeed it is easy to find supporting data. However, such ideas apply only cramped thermodynamics, i.e. to situations so heavily restrictricted that it is impossible to build any kind of heat engine. Such ideas greatly interfere with any attempt to understand uncramped thermodynamics.

There is a pedagogical / psychological dimension to this. There is a mountain of evidence suggesting that established ideas are virtually never truly unlearned, not on any pedagogically relevant timescale anyway. Instead the best you can hope for is to hide the bad ideas behind a wall of better ideas, so that in any given context the right idea is more likely to be recalled. The wrong (or merely inapplicable!) ideas are still there; they just won’t be the first things that come to mind. So, rather than figure 1, the picture is more like figure 3.

good-surrounding-bad
Figure 3: Good Surrounding Bad

By telling students their ideas are not crazy wrong – just restricted – they are less likely to get defensive. It enhances the teacher’s credibility. It gives students a framework that accounts for all the data. This upholds one of the core principles of critical reasoning: account for all the data.

3  Terminology

Some people use the word “misconception” in very narrow ways, or avoid it altogether. One teacher sent me a list of thirty different terms intended to describe different types of misconceptions, preconceptions, and related ideas.

I am not interested in such fine distinctions. I use words like “idea” and “notion” in a broad sense, including ideas that are completely correct, completely incorrect, and everything in between. Almost all ideas are imperfect in some way. I use the term “misconception” to apply to whatever part of the idea is incorrect.

4  A Few Prevalent Misconceptions

The following list is restricted to misconceptions that afflict professionals in the field. (There is of course a far wider class of misconceptions that afflict naïve students.)

Some related issues of weird terminology are discussed in reference 6.

Keep in mind that you should always start by emphasizing correct conceptions, as discussed in section 2.1. To say the same thing the other way: creating and/or studying lists of misconceptions is usually not a good idea, and should never be a starting point.

1.
Far and away the biggest problem is an overall lack of critical thinking skills. See reference 7.

This includes, far too often, accepting a “rule” without differentiating between a “rule of thumb” and a “rule in all generality”.

This includes learning a “rule” without reconciling it with other experimental and theoretical things they know.

This includes learning the headline of a rule without learning the provisos, without learning the limitations on the range of validity of the rule.

2.
Chronic and pervasive inability to tell the difference between a good approximation and a bad approximation ... and even unawareness that this is even an issue. See reference 8.

3.
Multiple misconceptions about scientific methods. For example, fixating during the planning stage on a single hypothesis. Common sense and basic scientific principles demand considering all the plausible hypotheses. Indeed this is required for safety if nothing else. See reference 8.

4.
Multiple misconceptions about “significant figures” and/or how to handle uncertainties. See reference 9. See also item 6.

It is easy to find examples of professors being completely confident about the wrong answer.

5.
That includes pervasive misunderstanding of what “error” means in the context of “error analysis”. See reference 9.

6.
Innumerable misconceptions about probability. For example, suppose I toss a coin 100 times. On every “heads”, I take one step to the north. On every “tails”, I take one step to the south. After the 100th step, how far away am I, on average, from where I started? (Most kids – and more than a few teachers – say “zero” ... which is not the right answer.)

7.
Widespread misconceptions about the fundamental principles of quantum mechanics. The fact is that even in fully quantum mechanical systems, not everything is quantized, not all waves are quantized, not all states are discrete, et cetera. See reference 10.

8.
Innumerable misconceptions and/or archaic conceptions about special relativity.

This includes velocity-dependent mass, rulers that can’t be trusted, clocks that can’t be trusted, et cetera. It is a misconception to think those are a good idea (even if they are not provably wrong). Certainly they must be unlearned as a prerequisite to any modern (post-1908) understanding of special relativity, spacetime geometry, and 4-vectors ... not to mention general relativity. See reference 11.

9.
Misunderstanding of the famous equation E=mc2. Hint: this E is the rest energy. If the mass is moving, we need a more complicated formula. Mass is the invariant norm of the [energy, momentum] 4-vector. See reference 11.

10.
Misunderstanding of general relativity, especially as to what is curved, and in what direction it is curved. A marble rolling around inside a bowl does not illustrate general relativity. See reference 12.

11.
The idea that «Kirchoff’s laws are fundamental, and can be directly derived from Maxwell’s equations».

A previous version of the wikipedia article said exactly that (before I changed it). In fact, for AC circuits, both of Kirchhoff’s laws are flatly contradicted by the Maxwell equations.

Also note that both of Kirchhoff’s laws are routinely violated in practice. There are tremendous misconceptions about this.

12.
Assuming that every voltage must be a potential, and every electric field must be the gradient of some potential. This assumption is embodied in Kirchhoff’s laws. We know it can’t be true when there are time-varying magnetic fields running around.

13.
Misconception that thermal energy (whatever that means) is random kinetic energy to the exclusion of potential energy. See also item 19. For details, see reference 13.

14.
There are some who try to define energy as “capacity to do work”. This formulation is fairly common in nonscientific books. It appeals to those who know nothing about thermodynamics. See reference 13.

15.
Entropy as “disorder”.

16.
Entropy as “spreading of energy”.

17.
Misconception that expansion of the universe correlates with thermodynamic irreversibility i.e. entropy production

18.
Innumerable other misconceptions regarding entropy. See reference 13.

19.
Trying to think of thermodynamics in terms of a “heat content” or “thermal energy” state function. See reference 13.

20.
Writing d(something) for ungrady one-forms, e.g. dQ = T dS. (This is somewhat related to item 19.) See reference 14.

21.
Terminology and thought patterns that confuse “heat” with “enthalpy”, e.g. tables of the “heat of reaction”. Counterexample: reversible reactions such as electrochemical cells. Similarly, misconception that heat is conserved (e.g. in the typical statement of Hess’s law). See reference 13.

22.
Holy wars about the various definitions of “heat”. Example: adding heat to something “surely” raises its temperature. See reference 13.

23.
Confusion about the relationship between energy and temperature, e.g. Define temperature as the measure of thermal energy

24.
Confusion about the meaning of “intensive” versus “extensive”. (Possibly confused with intrinsic versus extrinsic?)

25.
Conflict over whether the rate constant for the reaction x A → y B + z C should depend on the stoichiometric coefficient x. In particular, deciding to scale the rate constant by a factor of x without regard to the order of the reaction. I claim that for an Mth order reaction, the normalization factor is x(M−1). I claim you want to define the rate constant per unit of “→” not per unit of [A].

26.
Misconception that electrons must “jump” from stationary state to stationary state. To say the same thing in NMR terminology, the misconception is that π/2 or π/10 tipping pulses are impossible.

27.
Misconception that electrons “like” to pair up, like Siegfried and Roy. In fact, physics says they hate each other. Spectroscopy (as summarized by Hund’s rule) says that in the ground state, they pair up only as a last resort.

28.
Misconception that breaking a chemical bond releases energy, the way that breaking an eggshell releases what’s inside.

29.
Misconception that during changes of state the temperature remains constant.

30.
Multiple inconsistent definitions of “molecule”.

molecules = “stable particles of matter” is a non-starter, because water molecules are not stable in aqueous solution.

molecules are “covalently bonded” is a non-starter, because many things that ought to be considered molecules are not covalently bonded.

molecules obey the “law of definite proportions” is a non-starter, because many macromolecules do not uphold it.

31.
Uncertainty about the definition of “compound”.

32.
Related minor point: There seem to be widespread misconceptions about the definition of “dimer”. Also note that the IUPAC definition of polymer is very broad, and does not parallel the definition of dimer.

33.
The alleged dichotomy between “ionic compounds” and “molecular compounds”.

34.
The whole notion of “physical change” as distinct from “chemical change” is disconnected from reality. There are multiple inconsistent definitions of the terms. All the usual definitions conflict with the usual examples. See reference 15 .

35.
In most chemistry texts, there is some kind of a flowchart that uses various crude criteria to classify substances as elements, compounds or mixtures. This incorrectly implies that it is impossible for any substance to simultaneously be an element and a mixture. In particular, it gets you into trouble with an element that is a mixture of isotopes. The right way to think about this is in terms of equivalence classes. Things that are “pure” w.r.t one property may not be “pure” w.r.t to another.

36.
Misconception that “Like Dissolves Like”.

37.
Le Chatelier’s principle is highly problematic. LeChatelier in his lifetime gave two inconsistent statements of the “principle”. One is trivially tautological, and the other is false. See reference 16.

38.
Widespread deep-seated misconceptions about osmosis and osmotic pressure. This includes using glycerin or other hygroscopic substances as pedagogical examples of osmosis. See reference 17.

39.
Way too much emphasis on the Bohr model of the atom, i.e. electrons following Keplerian orbits within atoms.

40.
There are profound problems with Lewis dot diagrams in general, and the idea of filled Lewis octets in molecules in particular. These ideas are are fundamentally inconsistent with all the spectroscopic data ... and other data. The paramagnetism of O2 makes for a nice, graphic, in-class demonstration. See reference 18.

It’s particularly comical when they arrange Lewis dots (falsely representing electrons) onto little Keplerian circles (falsely representing orbitals) to make molecules (falsely suggesting that there are filled “Lewis octets” in molecules).

41.
Talking about “position” of the electron within a “p orbital”. (These are incompatible variables, incompatible in the Heisenberg sense.)

42.
Uncertainty about “orbitals”. Does the term refer to wavefunctions describing actual electrons, or does it refer to basis wavefunctions that are purely mathematical?

43.
The whole idea of oxidation numbers in redox reactions is grossly abused. When balancing redox reactions, it is simpler and better to just use conservation of charge, directly. See reference 19.

44.
Arons asserts there are two kinds of electrical charge. He says the two-fluid model is right, and the one-component model is wrong. See reference 20 for a refutation.

45.
Arons also suggests teaching students the difference between “passive forces” and “active forces”.

46.
Questions about where the lanthanoids and actinoids belong in the periodic table. There should not be any questions. These are basically elementary fencepost errors. See reference 21.

Also, a related bundle of misconceptions revolve around the ill-conceived notion of p-block, d-block, and f-block elements ... and the corresponding “block structured” periodic table. See reference 21.

47.
Numerous misconceptions concerning absolute zero, degeneracy, zero-point motion, et cetera.

48.
Teaching Boyle’s law, Charles’s law, and Gay-Lussac’s law separately, on the theory that in each case “the” variables not mentioned are held constant. This is an OTBE fallacy. For example, T1/P1=T2/P2 is not valid if we hold N and S constant. See reference 17.

49.
Allegedly “Temperature is not a state function.” (I’m not kidding. A professor vehemently asserted that.)

50.
Wild misconceptions about the shape of the H2O molecule. In fact, contrary to what several chemistry professors have said:

Fussing with the terminology will not change these facts. See reference 22.

51.
Attempts to build a classical ball-and-stick model of the isolated ammonia molecule.

Fact: The isolated gas-phase ammonia molecule in its ground state has D3h symmetry. See reference 23. (It has a much lower symmetry, C3v, in liquid ammonia or in aqueous solution.)

52.
You can allegedly determine the temperature of a flame by looking at its color. (Not just a black body, but a flame!)

53.
Confusion regarding negative temperature coefficient versus negative activation energy. These are not the same.

54.
Persistent failure to understand (even after being told) that dimensional analysis can sometimes give the wrong answer, both false positives and false negatives. That is, arrested development at the level of dimensional analysis when a scaling analysis is called for. See reference 24 and reference 25.

55.
Teaching the “density triangle” as described at e.g. reference 26.

This approach has many weaknesses, but we should not overreact. You can solve the problem by converting this to an equation M/(D V) = 1 and then forgetting the triangle.

If you don’t convert, and stick with the “cover up” rule, it is not just opaque to the underlying math, it is actively misleading. The problem becomes obvious if/when the underlying equation has more than one variable in the numerator.

The triangle is a crutch. Normal students should not need any such crutch.

56.
Allegedly, the term “algorithmic” is synonymous with rote, i.e. turning the crank without thinking. This is crazy wrong. Algorithms are good for you. Do not confuse the presence of one thing with the absence of another.

57.
I once heard a professor talking about a «adiabatic calorimeter .... “Adiabatic” means no heat.» In other words, we’re talking about a no-heat heat-capacity experiment. This is what comes from restricting the definition of “heat” (“flow across a boundary”) without checking the consequences for consistency.

58.
True or False? – There is no such thing as centrifugal force. See reference 27.

59.
True or False? – As part of the recovery from a severe spiral dive, it is important to roll the wings level and then pull back on the yoke.

Hint: John-John Kennedy probably didn’t know the right answer to this one.

60.
True or False? – The airplane’s stability depends on the fact that the tail is producing a downward force.

61.
True or False? – In a Cessna 172, starting from normal flight, if you increase the throttle setting (without moving any of the other controls) the airplane will speed up.

62.
True or False? – If two parcels of air flow past a wing, they move from the front to the back in essentially equal amounts of time, even if one passes above and the other passes below the wing.

63.
True or False? – To work properly, an airplane wing must be curved on top and relatively flat on the bottom.

64.
True or False? – Blowing a jet of air across the top of a piece of paper is a good way to demonstrate the principle that “faster-moving air has lower pressure”.

65.
True or False? – Bernoulli’s principle is only valid for incompressible fluids, which means it cannot be trusted for something as obviously compressible as air.

66.
True or False? – As suggested by the saying “power plus attitude equals performance”, if you put the airplane into a particular attitude with a particular power setting, the airplane will give you the corresponding performance (airspeed, rate of climb, et cetera) and if you maintain this attitude and power setting you will continue to get that performance.

67.
True or False? – To perform an ordinary steady roll to the right, the upgoing wing must produce a greater amount of lift (compared to the other wing), and therefore a greater amount of drag, which is why you need to apply steady right rudder during the roll.

68.
True or False? – During flight at very low airspeeds, some sections of the wing are unstalled, while other sections are stalled and contributing practically nothing to the lift.

69.
True or False? – During a normal steady climb, lift is necessarily greater than weight.

70.
True or False? – During a steady, coordinated turn to the left, dihedral creates a tendency for the airplane to roll back toward level, and you generally need to apply steady left aileron to overcome this.

71.
True or False? – P-factor (i.e. asymmetric disk loading) explains why, early in the takeoff roll in a Cessna 172, you must apply right rudder to keep it going straight.

72.
True or False? – On approach, you should never retract the flaps to correct for undershooting, since that will suddenly decrease the lift and cause the airplane to sink even more rapidly.

73.
True or False? – When properly performing turns on a pylon in the presence of wind, the airplane will remain at the pivotal altitude, and the pattern will be shifted somewhat downwind relative to where it would be in no-wind conditions.

74.
True or False? – To model the earth’s magnetic field, take a globe and skewer it with an ordinary bar magnet, putting the bar’s “N” pole in northern Canada, and its “S” pole in Antarctica.

I emphasize that the foregoing list is restricted to misconceptions that afflict professionals in the field. There is of course a far wider class of misconceptions that afflict naïve students.

I have seen collections of student misconceptions, but they all seem so incomplete as to be virtually useless. Furthermore some of them tend to replace old misconceptions with new ones; see e.g. reference 3.

5  Next Generation Science Standards

A great many misconceptions are being spread by the NGSS, as discussed in reference 28.

6  References

1.
William James,
Talks to Teachers On Psychology; and to Students on Some of Life’s Ideals (1899).
http://books.google.com/books?id=XYSsCLlF_mkCprintsec=frontcover
Chapter XII deals specifically with memory.
http://ebooks.adelaide.edu.au/j/james/william/talks/chapter12.html

2.
John Denker,
“Review of Hewitt, Conceptual Physics
http://www.av8n.com/physics/hewitt.htm

3.
John Denker,
“Review of Arons, Teaching Introductory Physics
http://www.av8n.com/physics/arons-1996.htm

4.
John Denker,
“Definition of Weight, Gravitational Force, Gravity, g, Latitude, et cetera”
http://www.av8n.com/physics/weight.htm

5.
Christopher Horton,
“Student Alternative Conceptions in Chemistry”
http://www.daisley.net/hellevator/misconceptions/misconceptions.pdf

6.
John Denker,
“Weird Terminology”
http://www.av8n.com/physics/weird-terminology.htm

7.
John Denker,
“Learning, Remembering, and Thinking”
http://www.av8n.com/physics/thinking.htm

8.
John Denker,
“Scientific Methods”
http://www.av8n.com/physics/scientific-methods.htm

9.
John Denker,
“Measurements and Uncertainties versus Significant Digits”
http://www.av8n.com/physics/uncertainty.htm

10.
John Denker,
“Coherent States”
http://www.av8n.com/physics/coherent-states.htm

11.
John Denker,
“Welcome to Spacetime”
http://www.av8n.com/physics/spacetime-welcome.htm

12.
John Denker,
“Tabletop Geodesics, General Relativity, and Embedding Diagrams”
http://www.av8n.com/physics/geodesics.htm

13.
John Denker,
“Modern Thermodynamics”
http://www.av8n.com/physics/thermo-laws.htm

14.
John Denker,
“Thermodynamics and Differential Forms”
http://www.av8n.com/physics/thermo-forms.htm

15.
John Denker,
“Chemical versus Physical Change?” http://www.av8n.com/physics/chemical-physical.htm

16.
John Denker,
“Spontaneity, Reversibility, and Equilibrium”
http://www.av8n.com/physics/spontaneous.htm

17.
John Denker,
“Gas Laws”
http://www.av8n.com/physics/gas-laws.htm

18.
John Denker,
“How to Draw Molecules ... Just Like Lewis Dot Diagrams, Only Easier & Better”
http://www.av8n.com/physics/draw-molecules.htm

19.
John Denker,
“Balancing Reaction Equations w.r.t Charge and Atoms”
http://www.av8n.com/physics/balance-charge-atom.htm

20.
John Denker,
“One Kind of Charge”
http://www.av8n.com/physics/one-kind-of-charge.htm

21.
John Denker,
“Periodic Table of the Elements – Cylinder with Bulges”
http://www.av8n.com/physics/periodic-table.htm

22.
Martin Chaplin,
“Water Molecule Structure”
http://www.lsbu.ac.uk/water/molecule.html

23.
Feynman, Leighton, and Sands
The Feynman Lectures on Physics volume III chapter 9
(“The Ammonia Maser”).

24.
John Denker,
“Dimensional Analysis”
./dimensional-analysis.htm

25.
John Denker,
“Scaling Laws”
http://www.av8n.com/physics/scaling.htm

26.
Wendy Boomer,
“Density Triangle”
http://westirondequoit.org/ihs/Science/EarthScience/density.htm

27.
John Denker,
“Motion in a Rotating Frame”
http://www.av8n.com/physics/rotating-frame.htm

28.
John Denker,
“Next Generation Science Standards”
http://www.av8n.com/physics/ngss.htm

1
As the name suggests, geometry was initially the science of surveying the surface of the earth. However, the formula a2+b2=c2 does not reliably apply to the surface of the earth, because the surface is curved, not planar. If you carefully survey a moderately large triangle, you will notice the curvature. Indeed, if you make the triangle large enough, you can construct on the surface of a sphere a triangle with three right angles.
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