I am starting out as a teacher and I'm confused about the verbs that we use in Bloom's taxonomy.

I was looking at a lot of websites that provide verbs for Bloom's level that describe the skill associated at that level. For example, this chart

But I need more clarity.

The verb 'identify' is given in the Comprehension level and the Analysis level.

  1. How is that possible?
  2. Why is it there in both levels?
  3. What is the difference in the skill if it's there in both the levels?
  • $\begingroup$ It's also on the "Knowledge" level. $\endgroup$ Dec 24 '16 at 6:49
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    $\begingroup$ I'm voting to close this question as off-topic because it's not specific to mathematics teaching. Perhaps SE Academia would be better better? $\endgroup$ Dec 24 '16 at 6:53
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    $\begingroup$ @DanielR.Collins: That said, an on-topic version of this question could be made regarding Bloom's taxonomy verbs in mathematics. For instance, certain verbs are used differently in mathematical English (e.g. evaluate). $\endgroup$
    – J W
    Dec 24 '16 at 7:28

Bloom's taxonomy is not very helpful for maths, as many of the verbs don't make much sense, and ones that do have meanings occur in the wrong order. There are a couple of people (at least) who have written versions more adapted to maths, with more understandable verbs. I don't have the references to hand though.

Edit to add some references:

  • Anderson & Krathwohl, 2001, A taxonomy for learning, teaching and assessing (Two dimensional version) (see also a summary here)
  • Pointon & Sangwin, 2003, An analysis of undergraduate core material in the light of hand held computer algebra systems (found here)
  • Darlington, 2013, The use of Bloom's taxonomy in advanced mathematics questions
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    $\begingroup$ I was not the downvoter, but perhaps Thompson's article would be worth including in your answer: iejme.com/makale_indir/314 $\endgroup$
    – J W
    Dec 24 '16 at 11:30
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    $\begingroup$ @DanielR.Collins: If I understand you correctly, the first "it" in your comment refers to a mathematics problem and the second "it" refers to the level in Bloom's taxonomy. (Please correct me if I've misunderstood.) For example, solving $ax+b=cx+d$ for $x$ may be somewhat challenging to a complete newcomer to linear equations who has only solved equations of the form $ax=b$ so far, but straightforward after practising many similar problems. So familiarity could drop solving $ax+b=cx+d$ from the application level to the comprehension level in Bloom's taxonomy, ... $\endgroup$
    – J W
    Dec 27 '16 at 8:37
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    $\begingroup$ ... Regarding difficulty, this does not seem to be clearly defined, but I quote the following passage: "Several teachers wrote that LOT problems are easier than HOT problems (e.g., “Higher order thinking involves solving difficult or challenging math problems.”) However, there are many mathematics tasks that are computational / algorithmic in nature that are quite difficult or challenging; therefore, although HOT items tend to be more difficult, level of difficulty is not a characterization in the literature on HOT and LOT (de Lange, 1987). ... $\endgroup$
    – J W
    Dec 27 '16 at 8:42
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    $\begingroup$ @DanielR.Collins Without looking, I believe 'difficulty' refers to the content of the maths. You can have a question about polygons in the plane that requires high-level thinking, or one about sheaves that requires only algorithmic computation. $\endgroup$
    – Jessica B
    Dec 27 '16 at 8:50
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    $\begingroup$ @DanielR.Collins One of the versions I've seen draws things on a square - with two different scales of difficulty. Does that help you understand? The whole point of the taxonomy, as I understand it, is that it measures a different type of difficulty to the one we usually notice. $\endgroup$
    – Jessica B
    Dec 28 '16 at 8:49

Not to directly address the question per se, but to get at how I view the thing in the context of mathematics.

One good thing about Bloom's taxonomy is the idea that not all forms of "knowing" are the same, and you can get a lot of leverage by addressing different aspects of the thing in your math classes. But looking at particular versions or phrasings of the thing don't seem very useful for me.

But I do like the idea of knowledge building on itself, and I like the different flavors of questions students can explore. For example, I like questions like:

Alice thinks X, but Bob thinks Y. Who's right and why? What's wrong with either argument?

Or another I might ask on a calculus exam.

What is the fundamental theorem of calculus? Explain this as if to a friend, and include several diagrams.

By encouraging students to these "deeper" levels of understanding (whatever you may feel like calling them), I find it's quite effective and a lot more fun to boot.


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