Intelligent tutoring of elementary arithmetic skills and concepts
Akhtar Lodgher, Henry Hamburger · 1990
The objective of this dissertation is to demonstrate and assess the integration of principles of cognitive science, education, artificial intelligence, curriculum design, and interface design for building an effective computer-based instructional system. Through this system, the student can effectively learn the procedures for carrying out a particular skill, especially for the domain of elementary arithmetic. This system is unique in the combination of the following features: (1) the problem is presented in an interactive real-world environment that makes it possible to monitor every step of the student; (2) semantic constraints are applied to prevent illogical wandering; (3) transfer of learning from real-world to actual problem is achieved by presenting the same problem in a paper and pencil environment, using identical move sequences in both environments, and providing the facility to flip between the two environments; (4) the next problem is generated by evaluating the performance of the student on the characteristics of the current problem. The student is then placed in the curriculum which is designed depending upon the characteristics of the problem; (5) the student is tutored whenever he is found to be lacking a skill; (6) a set of beginners' games are provided to help the student become familiar with the environments. In this research, a system with the above features is implemented and tested for the domain of written place-value subtraction. In the real-world environment, the student plays the role of a cashier in a store, and the process of subtraction is induced by the physical process of giving change to a customer who buys a product. The subtraction system, called Changers, in its entirety and during its various stages of development, has been tested on students at an elementary school, and the results have indicated a marked improvement in their performance. The general techniques developed and explored can be readily modified beyond the current model of subtraction to teach the procedures and concepts for different topics in arithmetic, such as counting, addition, multiplication, etc. More generally, the approach is relevant to other procedural skills in which the curriculum can be designed in a similar way, and global constraints can be enforced.