The Dialectic of Arithmetic in Grocery Shopping

Key Words and Definitions

1. Dialectic: The art or practice of logical discussion as employed in investigating the truth of a theory or opinion.

2. Arithmetic Problem Solving:

• Basically, the past experiences and beliefs of the problem solver and what the individual is doing, what should happen in the course of doing it, and what the setting is in which it is taking place.

• Shaped by the broader activity in which it occurs

• What are the general characteristics of problem solving when something happens in the course of shopping that appears problematic to the shopper? And how does the character of problem solving within grocery shopping specifically affect the nature of arithmetic activity?

1. The integral nature of activity in relation with contexts

2. Mutual interdependence of mental and physical activity

3. Arena: A physically, economically, politically, and socially organized space-in-time. It is outside of, yet encompasses the individual, providing a higher-order institutional framework within which the setting is organized. Not context dependent!

4. Setting: A repeatedly ordered and edited version of the arena. Not simply a mental map of the individual, but also has an independent, physical character and a potential for realization only in activity.

• Barker says, the environment is seen to consist of highly structured, improbable arrangement of objects and events which coerce behavior in accordance with their own dynamic patterning. The environment dictates a certain type of behavior, and that the environment sets a behavior setting, called synomorphy (rules of the game). Activity is reduced to a passive response to the setting.

• Lave says, settings are not an objective phenomenon. Experienced differently by individual.

5. Activity: Dialectically constituted with the setting (is generated out of, and generates, the setting).

• They don’t exist in realized form except in relation to each other

6. Rationalization: Maintaining the contradiction between choice and the necessity of choosing. It structures the arithmetic activity.

• In the shopping context, it is a routine, and the shopper is faced with an abundant amount of choices. This routine and contradictory quality of the routine choices, and the dialectical form of activity in setting, together shape the rationalizing character of arithmetic calculation in the supermarket.

7. Gap-Closing: A dialectical movement between the expected shape of the solution and the information between the expected shape of the solution and the information and calculation devices at hand, all in pursuit of a solution that is germane to the activity that gave it shape to the first place.

• The solution shape is generated out of the decision process up to an interruption or snag. The act of identifying a problem changes the salience of setting characteristics.

• Eg: When I am working in the kitchen, and realize that I don’t have a pot. What will I do instead? How do I work around this problem?

• An ongoing process of comparing the current state of knowledge of the problem and the current definition of the solution.