First of three parts. Summary:  Benjamin Bloom and his taxonomy team were more modern than most people realise.  But there is little help in being domain specific.  Part 2 will introduce a domain specific structure for physics Part 3 will be an attempt to use this structure.
Before you start reading, how many times does Bloom mention “challenge” in his taxonomy?
When I was an NQT I looked at Blooms taxonomy to help me with increasing the challenge of my lessons. The conventional wisdom of the time suggested that challenge was deeply tied to the verb attached to the prompt. For example: did the question ask students to evaluate or create? If the question did ask that then it was a higher-order thinking question. Well meaning middle leaders or consultants repeatedly push for this shortcut. Bloom and his committee were well aware of that this could happen very early on in their discussions:
[t]here was some concern expressed in the early meeting that the availability of the taxonomy might tend to abort the thinking and planning of teachers with regard to curriculum, particularly if teachers merely selected what they believed to be desirable objectives from the list provided in the taxonomy.(Bloom et al. 1956, p5)
Furthermore, the committee recognised that teachers would misconstrue classification for order. They likened the misconstrual to a reader that thought a library, with “nonfiction” and “fiction” categories, made a claim about the order of books:
Thus, the Dewey decimal classification system for libraries describes all the classes of books. lt does not indicate the value or quality of one class as compared with another, nor does it specify the number and kind of books any particular library should possess.(Bloom et al. 1956, p14)
Even as they said this, they did call their classification scheme a taxonomy. Two things which are, as far as I know, mutually exclusive. A strict taxonomy is validated by the empirical agreement of its proposed order, a classification scheme is validated by its usefulness and communicatibility. Bloom and his committee settled on a half-way house:
(Bloom et al. 1956, p18)
They conjectured that this was suggestive of a hierarchical order of complexity where the probability of answering questions of class 1 was, on the whole, greater than answering questions that combined class 1 and 2. But this was a conjecture, a conjecture which did not fully appear to be corroborated by contact with the real world:
…evidence on this is not entirely satisfactory, but there is an unmistakable trend pointing toward a hierarchy of classes of behavior which is in accordance with our present tentative classification of these behaviors.(Bloom et al. 1956, p19)
We have to remember that simple should not be substituted with “less worthwhile” – a point made by countless edu-tweeters including Adam Boxer, Ruth Ashbee, Christine Counsell and Daisy Christodoulou. Indeed that is what Bloom and his committee stressed when they provided the common defence of traditionalist pedagogy:
Another justification for the teaching of knowledge is that it is quite frequently regarded as basic to all the other ends or purposes of education. Problem solving or thinking cannot be carried on in a vacuum, but must be based upon knowledge of some of the “realities”(Bloom et al. 1956, p33)
As I carefully read the original work I was impressed by how modern it sounded. For example, they were fully aware that remembering lots of things is far more difficult than remembering a few things (p35), generalisations were better than isolated facts but harder to learn (p36), and that starting from the concrete to the abstract was probably a useful strategy (p36). All of these have graced a researchED presentation more than once and have been, in some way shape or form, earth-shattering enough for attendees to take a picture on their mobile phones. Even the regular refrain of “you need something to think about to be critical!” is something anticipated by Bloom:
Thus, it is expected that when the student encounters a new problem or situation, he will select an appropriate technique for attacking it and will bring to bear the necessary information, both facts and principles. This has been labeled “critical thinking” by some, …
This requires some analysis or understanding of the new situation; it requires a background of knowledge or methods which can be readily utilized; and it also requires some facility in discerning the appropriate relations between previous experience and the new situation…
Clearly it is impossible to give the individual all the knowledge he will ever need for every new situation he will encounter. It is possible however, to help him. acquire that knowledge which has been found most useful in the past, and to help him develop those intellectual abilities and skills which will enable him to adapt that knowledge to the new situations.(Bloom et al. 1956, p38,41)
The conclusions Bloom makes, if you adjust for the sexist language, could easily be inserted into a modern conference and no-one would recognise it (they have, and no one did). This is all well and good. But, for me, this does not help me as much as Bloom thinks it does. The hypothetical theorising which has run rampant through traditional circles and many conferences has lost contact with hard reality.
So the next part will of this three part series will try to find something concrete and useful for the case of structuring physics problems. After that, the third part will try and apply to a particular unit.
Answer to the question at the top: Once. Bloom and his team say that synthesising activities might challenge a student to do similar work. Oh, and this synthesising activity is probably best left much later — maybe postgraduate level…
Bloom, B. S. (1956). Taxonomy of educational objectives. Vol. 1: Cognitive domain. New York: McKay, 20, 24.