A theory of Algebra-Word-Problem Comprehension and its Implications for the Design of Learning Environments
Nathan, Kintsch & Young (1992)
1. A psychological model of Word-Problem solving and comprehension
2. Theory of learning: making formalisms situationnaly meaningfull
3. A strategy for tutor design: discourse comprehension theory and instructional principles
4. The animate learning environment
5. Empirical system evaluation
A psychological Model of Word-Problem Solving and Comprehension (Kintsch & Greeno):
The process of understanding and solving word problems involves three mutually constraining levels of representation:
the textbase: a representation of the textual input itself
the situation model: conveyed by the text in everyday terms (text comprehension)
the problem model: the formalization of the situation
Exemple 1 : Distance-Rate-Time Word Problem
A plane leaves Denvers and travels east at two hundred miles per hour. Three hours later, a second plane leaves Denver on a parallel course and travels east at two hundred and fifty miles per hour. How long will it take the second plane to overtake the first plane ?
Because of the added cognitive demands of inference marking, readers will make inferences only when they seem necessary. Poor problem solvers will tend to omit them from their representations, and so they will omit the associated equations (supporting relations) from their solutions to story problems. Problem solvers who reason situationally will tend to include these inference-based equations.
Intitially poor problem solvers who have subsequently learned to make an adequate situation model of the cover story and to link this representation to their mathematical understanding will exhibit in their solution protocols a marked decline in their misspecification of supporting relations.
Students encouraged to interpret story situations mathematically by relating the caracters, events, and relations in a given cover story to their knowledge of formal symbols and expressions needed for a quantitative solution will be more competent in generating solution-enabling equations for word problems tha their counterparts who use a straight translation-based approach of mapping story phrases to equations.
Students encouraged to interpret algebraic equations situationally by relating the formal symbols and expressions to their knowledge of characters, events, and relations in the given cover story will be more competent in the generation of situational descriptions of algebraic equations than their counterparts who use a straight translation-based approach of mapping story phrases to equations.
Problem solvers who reason situationally are better equipped than their phrase-oriented couterparts to recognize to recognize the situational appropriateness or inappropriateness of a set of equations that may accompagny a cover story.
1. Animate Group (Network + Set-up Situation + Animation)
2. Stopping condition group (Network + Set-up Situation)
3. Network Only
4. Control Group
1. Pretest (4 problems: 2 solve, debug, story)
2. Training with Animate suivant les 4 traitements
3. Postest (comparable au pretest)
DRT and Supporting relation
Form or Omit