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As described in Section 2, ACT-R is a theory and computational model of
human cognitive architecture. As a theory, it proposes the systematical hypoth-
esis on the basic structure of human cognitive system and functions of these
structures in information processing to generate the human cognitive behavior;
as a computational model, it offers a computer software system for the develop-
ment of computational models to quantitatively simulate and predict the human
behavior for a wide range of cognitive tasks. It consists of a set of modules with
their own buffers, each devoted to processing a different kind of information.
These modules include a declarative memory module, a visual module for iden-
tifying objects in the visual field, a manual module for controlling the hands, a
goal module for keeping track of current goals and intentions, and other modules.
Furthermore, there are two kinds of knowledge represented in ACT-R, declar-
ative knowledge and procedural knowledge. Declarative knowledge is represented
in structures called chunks with chunk-types as categories and slots as category
attributes, whereas procedural knowledge is represented as rules (if-then rules)
called productions. Thus chunks and productions are the basic building blocks
of an ACT-R model. A production rule as in the core production system can
be fired based on the chunks in these buffers and then it changes the chunks in
the buffer of the related modules or the state of the related modules, which may
leads to fire a new production rule and so on to generate the cognitive behavior.
In cognitive psychology, human problem solving can be modeled as operat-
ing on the human heart symbol (the form of information representation in the
mind), and retrieving memory and managing states of the goal. Based on the
observation, the following chunks were defined in the present study.
- Chunk that shows addition knowledge of one digit
- Chunk for carrying cognition
- Chunk for controlling states of a goal
- Chunk that maintains mental representation.
Furthermore, production rules were defined by dividing the visual perception
process and the computing process. In each step of operations, states of the goal
are managed, the mental representation is operated, the memory is retrieved,
and it demands from the buffer of an intellectual module. The visual perception
process was divided into the following steps.
- Position tracking for the displayed number
- Movement of attention to the detected position
- The number is recognized and maintained as a mental representation.
The computation process was divided into the following steps.
- Addition of units digit
- Determination of carrying
- Addition of tens digit
- Processing at the case of carrying
- Collation and input of results.
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