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3.4 Conceptual frameworks for cognition 99

reminding them of what to do (e.g., to buy a card)
reminding them of when to do something (send it by a certain date)

2. Computational offloading
Computational offloading occurs when we use a tool or device in conjunction with
an external representation to help us carry out a computation. An example is using
pen and paper to solve a math problem.

(a) Multiply 2 by 3 in your head. Easy. Now try multiplying 234 by 456 in your head.
Not as easy. Try doing the sum using a pen and paper. Then try again with a calcula-
tor. Why is it easier to do the calculation with pen and paper and even easier with a
calculator?
(b) Try doing the same two sums using Roman numerals.

Comment (a) Carrying out the sum using pen and the paper is easier than doing it in your head be-
cause you "offload" some of the computation by writing down partial results and
using them to continue with the calculation. Doing the same sum with a calculator is
even easier, because it requires only eight simple key presses. Even more of the com-
putation has been offloaded onto the tool. You need only follow a simple internal-
ized procedure (key in first number, then the multiplier sign, then next number and
finally the equals sign) and then read of the result from the external display.
(b) Using roman numerals to do the same sum is much harder. 2 by 3 becomes 11 x 111,
and 234 by 456 becomes CCXXXllll X CCCCXXXXXVI. The first calculation may
be possible to do in your head or on a bit of paper, but the second is incredibly diffi-
cult to do in your head or even on a piece of paper (unless you are an expert in using
Roman numerals or you "cheat" and transform it into Arabic numerals). Calculators
do not have Roman numerals so it would be impossible to do on a calculator.
Hence, it is much harder to perform the calculations using Roman numerals than alge-
braic numerals-even though the problem is equivalent in both conditions. The reason for
this is the two kinds of representation transform the task into one that is easy and more diffi-
cult, respectively. The kind of tool used also can change the nature of the task to being more
or less easy.

3. Annotating and cognitive tracing
Another way in which we externalize our cognition is by modifying representations
to reflect changes that are taking place that we wish to mark. For example, people
often cross things off in a to-do list to show that they have been completed. They
may also reorder objects in the environment, say by creating different piles as the
nature of the work to be done changes. These two kinds of modification are called
annotating and cognitive tracing:

Annotating involves modifying external representations, such as crossing off
or underlining items.