Difficulty has two dimensions: Easy vs. Hard, but also Simple vs. Complex. And almost every exam is based on it.

In 1956 a researcher named Benjamin Bloom came up with a model to classify different cognitive domains. In 2001 it was revised into The “Bloom’s revised taxonomy” with six levels, the most complex at the top and the simplest at the bottom. This is what is usually meant when talking about Bloom’s taxonomy.

Before talking in detail about what Bloom’s taxonomy is, lets first see why it is useful.

What is it good for?

Almost all schoolwork is based on levels 1-4, and some level 5.

Every exam, assessment, exercise set, and essay will directly or indirectly correspond to one (or more) levels of Bloom’s taxonomy. To understand the taxonomy means to understand what guided the making of an exam.

Even better, most LLM-AIs today are trained on Bloom’s taxonomy and will produce practice problems of different levels if the prompt mentions Bloom’s revised taxonomy. This is one of the ideas behind using AI to teach, not to cheat

But, more importantly: To practice for one level means to automatically also practice for the levels below it.

This is not necessarily a shortcut however. Practice problems at level 4 (Analysing) will be much more complex than those at level 2 (Understanding). One hour of practice at level 4 will be much more tiresome than at level 2. On top of that, progress will feel slower. This can lead to Misattribution of Effort , believing that just because practice is tiresome and slow it must be bad.

The levels

Typically those domains are arranged in a pyramid from least complex at the bottom to most complex at the top. The levels are:

    1. Creating
    1. Evaluating
    1. Analysing
    1. Applying
    1. Understanding
    1. Remembering

Remembering

This one is at the bottom for a reason: It is possible to remember everything, even nonsensical information. And yet, without remembering anything, the upper levels are impossible. Take this vocabulary list for example:

  1. wu
  2. em
  3. oci
  4. lu
  5. hum
  6. yew
  7. xuh
  8. vez
  9. zuq
  10. wo

There is no meaning behind any of these words because they are all randomly generated. And yet it is possible to learn them by heart.

Understanding

Still not all that useful, but better than just remembering. At this level application is still impossible. But at least the meaning is clear.

  1. mountain
  2. tree
  3. water
  4. car
  5. human
  6. animal
  7. moon
  8. sun
  9. good
  10. bad

Assuming that you are fluent in English, you should understand all of those words. Yet what would you do with this information?

Exactly!

This is why we need the next level

Applying

It is only here, after remembering information and understanding information, that we can finally do something with the information. Not necessarily understand why we can do, but we at least can do.

To give an example of knowing how without knowing why, suppose that the following facts are given:

  1. To estimate the circumference of a circle, you must measure its diameter, multiply it by 3, then add 10% to it
  2. The measured diameter of this circle is 10 cm

Now we can combine Information 1 and 2 in the following way:

10⋅3=3010 \cdot 3 = 30

10% of 30 = 3

30+3=3330 + 3 = 33

The circumference of a circle of diameter 10cm should therefore be roughly 33cm. Even though this is not (fully) wrong, this leaves a lot to be desired. Hence we need the next level.

Analysing

The meaning of the root of the greek word behind Analyse means to dissolve. And this is exactly what analysing does. An idea is broken down into its components to be used in different context. Or, new connections to existing information are made.

Returning to the example of the circle above: We can now see that this information is nothing but a badly rounded formula for the actual circumference of a circle:

C=d⋅πC = d \cdot \pi

Since π=3.141...\pi = 3.141... the formula before was just calculating C=d⋅3.1C = d \cdot 3.1

To analyse I must know how to apply, to do that I must understand, and for that in turn I must remember.

Evaluating

The world is a complicated place and this level takes it into account. At the level of evaluate we are dealing with several different complex information, opinions, theories, etc. and we must chose one over the other with rational reasons and arguments.

Suppose that an argument should be written about the merits of Theory-A compared to Theory-B.

To judge A over B I must first fully analyse both. Only then can I give my judgement.

Creating

The last level. So far we have dealt with already existing chunks of information. Theories, formulas, lists of vocabularies, …

Creating deals with existing information only inasmuch as they are necessary for the creation of new things.

Evaluating the pros and cons of existing algorithms is necessary to be able to come up with new ones.

The flaws of old cars guide the development of new models.

This level does not appear in the context of schoolwork. Only once we get to university doctoral theses does it become relevant.