Here is an innocuous thought: in order for me to be able to make use of, or understand in any but the most etiolated sense, a bit of information, I must already be able to situate myself with respect to it. If I ask who put the bop in the bop-sheb-bop and am told "Kevin", this is helpful insofar as I can tell that it's the name of a person, but if that's all I know, it would be very curious to say that I know who did it. It's slightly better than a shorthand for "person who …" because the name "Kevin" might be intelligible to others as well, but as yet it functions, for me, as such a shorthand. If, emerging from the train station in a foreign city, I can see that I am at the intersection of Rue Georges Perec and Odos Ermou, and know that my hotel is 11 Hegelallee (cosmopolitan city), but am otherwise disoriented, then while I'm better off than if I knew only that I am "here" and my hotel is "there" (especially if I know that "11 Hegelallee" decomposes into a street number and a street name, but even if I don't, I might suspect that other people will recognize the unit as the stable name of a place, which they wouldn't for "there"), but it would be a stretch to say that I know where the hotel is in any robust sense (rather than that I know the name of where the hotel is, say).
So, comes now Ted Poston, in "Know How to Transmit Knowledge?", arguing that knowledge-that and knowledge-wh can be transmitted by testimony but knowledge-how cannot, in a series of examples that one wished confronted that innocuous thought a bit more full-on. He does give it a few sidelong glances, admittedly. In the first glance, he wishes to set aside examples of know-how apparently being transmitted via testimony such as the following: Sam knows how to tie the Bimini Twist, and tells John (an experienced fisherman) how to do so; John now knows how to tie it, too. The reason he gives is that "it is a general skill being applied to a specific novel case" (6) rather than a new skill cut from whole cloth. It is a case "in which a subject has preexisting practical knowledge that is then applied to a new case" (6). One might rather characterize it this way: it is a case in which the subject is prepared to make use of the testimony given. A good instance of knowledge-that being imparted by testimony, on Poston's view, is "(4) Bill knows how Obama will govern. (5) Bill tells Hannah how Obama will govern. So, (6) Hannah knows how Obama will govern" (5), yet anyone would think that Hannah had better be bringing an awful lot of background knowledge about the United States and its politics to bear in order to get anywhere with Bill's speech; that, in other words, she has some general knowledge about the subject matter being brought to bear on this one particular president.
Another possibility, perhaps, is simply that Bill is very patient, and takes a great deal of time to explain things to Hannah, essentially giving her the preparation as well as the information about Obama. Poston's glance in this direction is concerned not with preparation per se but with the complexity of the subject matter; he gives two (similar) examples. In the first, Terence Tao, who knows (all about) topology, tells Smith "all about" it (the "all about" is there because it doesn't count for Smith just to know "that topology concerns the mathematical study of spaces" (7)); then "if Tao tells smith all about topology then Smith will come to know topology, but Smith will not know as well as Tao. Once we control for this fact, the inference is good." (8; remember that control!). Or suppose "Sam knows that all non-trivial zeros of the zeta function have as real part 1/2. Sam tells Jones this. Assuming that Jones understands what is said (he understands the concepts expressed) Jones comes to know this. So the difference in learning is not a result of complexity" (8). If Jones the mathematician is in a position to just hear the words "all the non-trivial zeros of the zeta function have as real part 1/2" and get it, he seems to me to be in the same position as John the fisherman (it also seems to make the example remarkably bad if it's supposed to be about the complexity of the knowledge imparted—recall the mathematical joke that "trivial" is whatever you know the answer to. If Jones is that prepared, it can't be that complex for him). Suppose he isn't, though; suppose he's like Smith with respect to topology, or suppose he's, I don't know, an average fifth-grader; he doesn't even know about trigonometric functions. It would seem to be Poston's belief, which I hope is not his actual pedagogical practice, that fifth-grade Jones, if Sam just talks to him long enough (I suppose Sam can also make use of a blackboard, etc.), will come to understand about the zeta function. That is, Poston would seem to believe that the preparation necessary to understand "all the non-trivial zeros of the zeta function have as real part 1/2" can be imparted via testimony, with the testified-to party not needing to do anything.
How liberating!: if someone just talked to us skillfully enough, we would have no need of problem sets, homework, asking questions, any of that. Advanced mathematics can be learned entirely passively! Poston doesn't say that explicitly, of course, because it sounds absolutely bats, but I don't see how he can avoid it. If he acknowledges that in learning something, the learner too must act, then his argument would seem to fall apart: it would divide into cases where the learner is either already adequately prepared to simply hear something described or discussed, in which case testimony (without audience participation) suffices, and cases where the learner must take part in her learning. In those cases, sometimes the participation will amount to asking for clarification, asking about connections, mental reconstructions, and practicing; in others, it will amount to, er, asking for clarification, asking about connections, mental reconstructions, and practicing. The practice might be completing the square (and learning how to tell when to complete the square, which is something that someone learning all about high school algebra would seem to be learning, but which would also seem to be difficult to impart solely by testimony—lots of know-how (however theorized) goes into acquiring knowledge-that, or is implicitly present in what's characterized as knowledge-that) or it might be mounting the bicycle, whatever.
Recall Smith's inferior knowledge of topology, after being told all about it by Terence Tao. Two things come to mind here. First, if he can count as knowing topology even though he doesn't know it as well as his instructor, why should we be so quick to deny the validity of the inference "(7) Bill knows how to ride a bike. (8) Bill tells Hannah how to ride a bike. So, (9) Hannah knows how to ride a bike" (5)? She probably doesn't know how to ride a bike as well as Bill, but she might be better at it than someone who hadn't benefited from Bill's instruction. If Bill knows what he's talking about and is a good instructor (let's not lose sight of the fact that knowing something, whether it's -that or -how, is not the same as knowing how to impart that knowledge) who knows what pitfalls a beginner might encounter and can talk through them in advance, etc., she might fare a lot better than her uninstructed counterpart. She might not win any races, but I wouldn't put a lot of money on Smith passing topology exams, either. (You might think that with performing a triple Axel, someone with no experience ice skating will derive approximately no benefit from testimony. Seems plausible to me. But I also am very skeptical that someone with no experience of high school math will be able to be brought to an understanding of the zeta function solely from testimony.) Second, Poston says, plausibly, that Tao "knows because he has accumulated knowledge of many truths about topology but also has keen insight and skill" (8). Where did that skill come from? Possibly some of it is down to Tao's being super smart (but on the topic of raw mathematical genius, bear in mind the words of Tao himself), but probably a lot of it comes from hard work, deep immersion, and practice practice practice. Smith can work hard and practice, too; he might get better! But, again, the notion of practice here, and for that matter skill, in the realm of the transmission (or mastery) of knowledge-that, seems dangerous to Poston. Tao doesn't know better because he received better testimony.
One reason I buy that one doesn't count as knowing about topology for just knowing that it's the mathematical study of spaces is that one can be able to say that, even knowing what "spaces" means in this context, without having the first idea what a practicing topologist actually does. Of course, something similar is true of the sentence "all the non-trivial zeros of the zeta function have as real part 1/2"; someone could say that and be like Aristotle's drunkard reciting scientific proofs or Empedocles, or, more aptly, like Aristotle's students "who have just begun to learn a science can string together its phrases, but do not yet know it; for it has to become part of themselves" (in EN 7.3; sadly the Internet Classics Archive allows for no more exact citation). (Or like the Brazilian physics student Feynman encountered who could rattle off equations but not apply them to simple word problems.) So there's a lot of unacknowledged work going into the parenthetical about Jones "understand[ing] the concepts expressed", by my lights; it can't just be that Jones knows about the zeta function the way I know where my hotel at 11 Hegelallee is. But the beefier sort of understanding Jones must have strikes me as being intimately intertwined with Jones' knowing how to do things. And even without that, Poston already refers to Tao's knowledge of topology in ways that implicate skill. Poston quotes Noë on the fact that skills aren't acquired all at once but come gradually with practice; the same is true of knowledge-that, because … it implicates skills. Which suggests that if you can't transmit novel knowledge-how by testimony, then you also can't transmit novel knowledge-that by testimony, either. Which again suggests the breakdown of the argument into the two cases mentioned above: the subject is adequately prepared to receive the testimony, in which case testimony works, or isn't, in which case activity on the subject's part is required. So I'm unmoved: Poston seems unduly glib about the powers of testimony to impart knowledge in the knowledge-that case, in the very kinds of examples that concern him in the knowledge-how case.