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

6. Method

7. Results

8. Discussion

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 situationExemple 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 ?*

Hypothesis

Prediction 1a:

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.

Prediction 1b

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.

Prediction 2

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.

Prediction 3

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.

Prediction 4

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.

Experimental Design

4 traitements:

1. Animate Group (Network + Set-up Situation + Animation)

2. Stopping condition group (Network + Set-up Situation)

3. Network Only

4. Control Group

Procedure

1. Pretest (4 problems: 2 solve, debug, story)

2. Training with Animate suivant les 4 traitements

3. Postest (comparable au pretest)

Scoring

DRT and Supporting relation

Form or Omit

unclassified