Why study models of arithmetic?

An example of a cognitive skill: an ability learned through conscious practice. Others include: solving well-dened, knowledge-lean problemsdriving (vs. walking)reading/writing (vs. understanding/speaking)Cognitive skills are interesting because anyone can, with sufficient practice and dedication become highly proficient in most cognitive skills. Kolers and Perkins (1975) reading mirror writing: after reading 200 pages, almost as fast as their reading of standard text

Skill acquisition shows that cognitive apparatus is highly flexible. It is able to adapt to a variety of complex tasks, although adaptation can require substantial practice. It is common to assume that adaptation involves a change to the knowledge or information used by the cognitive apparatus rather than a fundamental change to the way in which the cognitive apparatus functions.

Anyone of normal intelligence can acquire the skills required to perform large addition, subtraction, multiplication or division problems. These skills take the form of procedures or rules that should be followed in order to solve different types of arithmetic problems. Someone skilled at arithmetic must know how and when to apply these rules, and it is the rules and a facility with their use that constitutes the skill. Cognitive skills therefore engender a division between knowledge and a system that applies that knowledge. 

Production systems are particularly suited to the modelling of cognitive skills because they are general purpose processing systems.

Focus on multi-column subtraction; Cooper also covers addition. Both models illustrate how cognitive skills can be modeled using a production system.humans perform a task correctly by integrating many smaller sub-skills;failure of individual sub-skills may help explain systematic failures in main skill.

Cognitive Skills

Mental Arithmetic