Suppose I'm teaching out of a textbook and it makes some blanket statement that is almost always true, but has some limited exceptions. Examples:
- All living things get their energy directly or indirectly from the Sun. (Deep-sea hydrothermal vent ecosystems exist.)
Do I point out these exceptions to the students, or does that just cause unnecessary confusion?
Somewhat related: How should one handle a flawed question in a textbook? which asks about some other flaw that can also cause confusion.
At the university level, it is important to convey that statements you make have a limited validity. However, most of the time, it is not useful to go into exactly what those limits are. Instead, it is usually enough to use careful phrasing that avoids making unwarranted blanket statements. On some occasions, the easiest way of conveying the limited validity of a statement may be by providing a counter example, but most of the time that would be distracting.
Making unwarranted blanket statements that students have to repeatedly "unlearn" later, can lead to an erosion of trust, which is detrimental to the overall learning process.
In Biology, if you spent your time on every exception you'd never get through a course.
It would also be pretty irresponsible for a textbook to contain such blanket statements as your example, though textbooks are rarely perfect. Instead, you might expect the statement to be "living things need oxygen to survive", which is at least ambiguous about whether it applies to some or all members of that group. It sort of scaffolds the material, though, where you start by learning one concept and later branch out into the details.
A real example from my field would be that neuroscience textbooks teach the sodium/potassium action potential where cells have high internal potassium and low internal sodium. There are some cells that use different ions or have different relative concentrations, but we start with the "representative" example in a basic neuroscience or physiology textbook and likely not every student will even get to the exceptions; they're not important for understanding the underlying biological concepts, and using concrete "sodium" and "potassium" ions is easier to learn than some arbitrary ion example ("ion 1" and "ion 2", say).
For that purpose, I don't think a blanket statement is possible to make about whether the exceptions are within or outside of the confines of a given lesson. Those decisions should be made based on the learning goals of the lesson/course, not rote rules about blanket statements.
You have to distinguish between things that are seriously wrong and will lead to important and enduring misconceptions and things that only nitpicking junior faculty talk about to show how smart they are. EVERY introductory book I have seen contains a number of convenient simplifications.
Now if one were to digress...to talk about some statement that is not quite true and why it is not quite true...you can be sure to have the discussion end with the invariable question "will this be on the test?"
Ask yourself: Why are you giving the exceptions?
Be honest, is it because there is really some lesson to be learned for your students? Or is it mostly because you want to show off that you know some edge cases, where the general rule has an exception?
Teaching, well good teaching, is a lot of reading the room. You can't give a blanket statement that is true and useful on exceptions from blanket statements.
It would likely be more useful to instruct the students to think about possible counterexamples whenever they come across a blanket statement, and to possibly discuss part of these as part of the course depending on what the course's goals are. Instilling the habit of doubting generalizations is also useful for fostering critical thinking for the students.
If OTOH your main goal is to pound testable knowledge/processes into the students, muddling the waters is of course counterproductive.
I am surprised that no one has pointed out that the statement can simply be amended to
Almost all living things get their energy directly or indirectly from the Sun.
and this is (1) 100% correct, (2) avoids any subtlety/ambiguity in the previous version, (3) uses only a single extra word, and (4) avoids the trap of requiring you to explain the specific exception in detail.
Teaching is often about what the instructor chooses to focus on (a difficult task), as much as it is about precision in language and learning to state the simple truth. I doubt that explaining an exception in detail is going to help, especially when one can simply not make the blanket statement in the first place.
I think you're assuming the premise that if you are teaching out of a textbook then you are endorsing all of its contents. Therefore if the book says something wrong or misleading then it's your responsibility to correct it.
There may be a partial truth to this premise, but the full truth is a bit more nuanced. First, you are clearly responsible for things that you say to your students, so take care not to mislead them and to carefully scope your statements. There's not always the time to go into depth on any topic and spell out all the exceptions, so with your biology example a good way to handle this may be:
With a small number of exceptions that we will not discuss right now, all living things get their energy directly or indirectly from the Sun.
Second, as for the textbook and whether it's worthwhile to comment on the accuracy of problems you find there, that depends on how closely you are following it and how many inaccuracies it contains. If the book contains a large number of inaccuracies, it will become tedious and impractical to comment on each and every issue. At that point, ideally you would switch to using a better textbook, but if that's not an option then I would simply make a blanket statement(!) to the class along the lines of:
Unfortunately the textbook we are using in this class has a fair number of inaccuracies. I may let you know if I spot any particularly egregious mistakes, but I won't have the time to discuss each and every issue, so I'd advise you to take anything you read in the book that we haven't discussed in detail in class with a grain of salt. I've also set up a channel on the course [name of web-based discussion forum, e.g., Piazza, Discord etc] where you all can discuss such issues among yourselves.
Ultimately, while I can see how it would bother you at a personal level to read something wrong in a textbook and to worry that your students might be misled by it, it's good to keep in mind that, unfortunately, the textbook is only one of many sources that your students are exposed to that give out information of poor quality. We simply don't have the time to go around and correct all the bad information that's out there. So the main thing that you can do is to resolve to doing your own small part to increase the signal-to-noise ratio in the world, by making sure the information that you yourself put out there is of high quality. And accept that beyond that, you will sometimes have to let your students figure things out for themselves.
It depends on:
Exceptions can be more tangible/simple to think of than the rule itself. This is a common issue in complicated/non-intuitive systems/topics. E.g.,
"Rule: Numbers are perfectly/accurately representable in Base 10 (within a finite number of place values)" + "Exception: Transcendental numbers like Pi and e, and Irrational numbers like sqrt(2), aren't."
=> Student reinterpreting the rule by framing it wrt the exception so that they can memorize the rule, where the exception and/or rule is oversimplified: "Aside from two specific numbers, Pi and e, any number can be represented in the typical number format like 123.4 or -5.7."
=> Student's final re-interpretation: "If the number isn't Pi nor e, then it can be represented."
What happened? The exception mentioned two counterexamples and the student internalized the two given counterexamples as the only exceptions to the rule, despite infinitely many other counterexamples existing, like sqrt(2).
This is a major component of where mentioning exceptions can become misleading/confusing to the student, hence the importance of saying:
Here are a few exceptions to this rule, but make sure to internalize that these exceptions I'm telling you about right now are by no means the only exceptions!
A student not knowing any of the exceptions (whether the mere existence or the specifics) can lead to a student's perception of the too-common bad teacher ideology
"This is a rule, it is fact because A) I have tenure B) I am intrinsically smarter than you as a human C) You are too dumb to be able to understand this equation D) I have researched this for longer than you've been alive E) etc"
, which leads to the student mentally giving up for the entire remaining semester/year/period with that teacher, the student assuming that it's futile to listen to the teacher because the teacher can't explain anything in a useful/practical/meaningful manner, and, in my experience (from Junior High to Masters), pretty much guaranteeing the student starts skipping class for almost every single day/occurrence of the specific course, meaning the teacher has lost all their ability to teach the student any valuable info in the future. From the student's PoV, it is a waste of time to attend a class in which the teacher does not explain things (to them) in an understandable manner, meaning skipping class is the obvious choice.
The student's perception of unexplained/unmentioned exceptions in non-trivial cases (which is the vast majority of noticeable cases in an educational setting) would be "The teacher just did a 'proof by Magic', so I'm going to stop attending this useless class".
Please be aware that no matter how many times you tell students to "read the textbook", some students absolutely never will, even including the curious/creative ones.
It may be beneficial to explicitly mention the exception to get the student to try to come up with a better, more-accurate rule where that exception doesn't occur. That helps them try to think of examples that the rule is designed to model, which can often be difficult, especially in math classes with complicated-looking equations. Personally, I learn far more about an equation (whether in math, chemistry, physics) by learning where it fails thanks to a teacher's explanation than I ever learn from where the equation succeeds in a teacher's explanation, because that lets me know where I made erroneous fundamental assumptions.
If the student comes up with a more accurate rule, it may show the student that a rule that is more generalized (true in all (or merely more) cases) may be so generalized that it has abstracted away the usefulness of that rule. E.g.,
In general, if there are tons of exceptions to a rule (e.g., periodic table elements' Name-to-Symbol naming conventions like Hydrogen->H and Oxygen->O but Gold->Au but Tungsten->W but Calcium->Ca and Barium->Ba but Chlorine->Cl), then there will be no apparent pattern (the rule) to students who are listening to the teacher rattle off a dozen exceptions with the specific rule embedded somewhere in there. See what I did? You just lost your train of thought, didn't you? The student will hear "case1 is exception. case2 is exception. case3 (is probably another exception, so I stopped paying attention). (repeat for all remaining cases). rule (already zoned out, so completely/mostly ignored this rule the teacher just said because I didn't notice when the teacher switched from exceptions to the rule)".
The student may also think "I can ignore this rule because this many exceptions implies this rule is obviously pointless and that we're learning the rule for no actual reason."
If you're teaching an overview course (e.g., history of mathematics, history of the world, physics 1, survey of literature, intro to business, intro to biology, intro to computing), chances are that you have many topics to cover, and therefore you can't spend much time on each individual topic, meaning you definitely can't spend much time on the exceptions to each rule in each topic.
As a teacher, you need to mentally weigh:
1A) the value of a student knowing only the rule (limited knowledge of how it can be applied)
1B) how much time it takes to teach the rule
,
2A) the value of a student knowing the rule with the exception(s)
2B) how much extra time (on top of time to teach the rule) it takes to teach the exception(s)
,
3A) the intellectual value lost by the student knowing neither the rule nor the exception(s)
3B) how much time was saved by not discussing the rule and not discussing its specifics
, and compare 1), 2), and 3).
Examples:
Ex 1)
5 minutes to teach the rule, likely 20 minutes to teach the exceptions, narrow-scoped (not broad) course (there's time to cover details, whether of rules, exceptions, both):
Ex 2)
20 minutes to teach the rule, likely 5 minutes to teach the exceptions, broad/survey-scoped (not nitty-gritty details) course (there's not enough time to cover details, whether of rules, exceptions, both):
Pi and e?