Complexity and Difficulty

David Sousa
How the Brain Learns
Pg. 258-260
Complexity and Difficulty
Complexity and difficulty describe two completely different mental operations, but
are often used synonymously. This error, resulting in the two factors being treated
as one, limits the use of the taxonomy to enhance the thinking of all students. By
recognizing how these concepts are different, the teacher can gain valuable insight
into the connection between the taxonomy and student ability. Complexity
describes the thought process that the brain uses to deal with information. In
Bloom’s Taxonomy, it can be described by any of the six words representing the six
levels. The question What is the capital of Rhode Island? is at the knowledge level,
while the question Tell me in your own words what is meant by a state capital is at
the comprehension level. The second question is more complex than the first
because it is at a higher level in Bloom’s Taxonomy.
Difficulty, on the other hand, refers to the amount of effort that the
learner must expend within a level of complexity to accomplish a learning objective.
It is possible for a learning activity to become increasingly difficult without
becoming more complex. For example, the question Name the states of the Union is
at the knowledge level of complexity because it involves simple recall (semantic
memory) for most students. The question Name the states of the Union and their
capitals is also at the knowledge level but is more difficult than the prior question
because it involves more effort to recall more information. Similarly, the question
Name the states and their capitals in order of their admission to the Union is still
at the knowledge level, but is considerably more difficult than the first two. It
requires gathering more information and then sequencing it by chronological order.
These are examples of how a student can exert a great effort to achieve a
learning task while processing at the lowest level of thinking. When seeking to
challenge students, classroom teachers are more likely (perhaps unwittingly) to
increase difficulty rather than complexity as the challenge mode. This may be
because they do not recognize the difference between these concepts or that they
believe that difficulty is the method for achieving higher-order thinking.
CONNECTING COMPLEXITY AND DIFFICULTY TO ABILITY
When teachers are asked whether complexity or difficulty is more closely
linked to student ability, they more often choose complexity. Some explain their
belief that only students of higher ability can carry out the processes indicated in

analysis, synthesis, and evaluation. Others say that whenever they have tried to
bring slower students up the taxonomy, the lesson got bogged down. Yet I will
argue, along with Bloom, that the real connection to ability is difficulty, not
complexity.
The mistaken link between complexity and ability is the result of an
unintended but very real self-fulfilling prophecy. Here’s how it works. Teachers
allot a certain amount of time for the class to learn a concept, usually based on how
long they think it will take the average student to learn it. The fast learners learn
the concept in less than the allotted time. During the remaining time, their brains
often sort the concept’s sublearnings into important and unimportant categories,
that is, they select the critical attributes for storage and discard what they decide
is unimportant. This explains why fast learners are usually fast retrievers: They
have not cluttered their memory networks with trivia.
Meanwhile, the slower learners need more than the allotted time to learn
the concept. If that time is not given to them, not only do they lose part of the
sublearnings but they also do not have time to do any sorting. If the teacher
attempts to move up the taxonomy, the fast learners have the concept’s more
important attributes in working memory to use appropriately and successfully at
the higher level of complexity. The slow learners, on the other hand, have not had
time to sort, have cluttered their working memory with all the sublearnings
(important and unimportant), and do not recognize the parts needed for more
complex processing. For them, it is like taking five big suitcases on an overnight
trip, whereas the fast learners have taken just a small bag packed with the
essentials. As a result, teachers become convinced that higher-order thinking is
for the fast learners and that ability is linked to complexity.
Bloom reported on studies that included slower students for whom the
unimportant material was not even taught. The curriculum was sorted from the
start, and the focus was on critical attributes and other vital information. When
the teacher moved up the taxonomy, these students in some cases demonstrated
better achievement than the control groups! When teachers differentiate between
complexity and difficulty, a new view of Bloom’s Taxonomy emerges, one which
promises more success for more students.
EVALUATION
SYNTHESIS
ANALYSIS
APPLICATION
COMPREHENSION
KNOWLEDGE