T-Algebra: Adding Input Stage to Rule-Based Interface for Expression Manipulation (original) (raw)

Rule dialogue in problem solving environment T-Algebra

This article presents the T-Algebra environment that allows step-by-step solving of algebraic problems in four fields of mathematics. An essential moment in the solving process is the solution step dialogue between the environment and the user. The so-called Action-Object-Input scheme is used for that purpose. Each solution step in T-Algebra consists of three stages: selection of the transformation rule, marking the parts of expression, entering the result of the application of the rule. The last stage can proceed in three different modes: direct entering of the result, structured entering of the result and construction of the result using different components. The presented scheme improves the ability of the program to check the student's solution and respond to the errors made by the student.

Designing Next-Generation Training and Testing Environment for Expression Manipulation

Computational Science – ICCS 2006, 2006

T-algebra is a project for creating an interactive learning environment for basic school algebra. Our main didactical principle has been that all the necessary decisions and calculations at each solution step should be made by the student, and the program should be able to understand the mistakes. This paper describes the design of our Action-Object-Input dialogue and different input modes as an instrument to communicate three natural attributes of the step: choice of conversion rule, operands and result.

A General Model of Algebraic Problem Solving for the Design of Interactive Learning Environments

Mathematical Problem Solving and New Information Technologies, 1992

The design of Interactive Learning Environments (ILE) in problem solving requires the modelling of the knowledge domain for the production of examples and explanations and for the control and guiding of the student's activity. Many problems are met in this work: some of them, like finding precise definitions of words, objects and concepts of the domain, are classic problems in Artificial Intelligence (AI) but need a didactic approach in this context; others, like taking into account an evolution of the reference knowledge (objects, concepts, strategies, etc.) are more specific to learning contexts. In this paper, we consider problems that are solved by successive transformations of algebraic expressions, like simplification of expressions, factorization of polynomials, equation solving, calculus of derivatives, calculus of primitives, etc. We propose a general model for this class of problems as a framework for the design of ILEs in algebra. The APLUSIX system, an ILE in the domain of factorization of polynomials, is described as an example of development within that framework.

A User Friendly Intelligent Algebra Tutor

Proceedings of the 5th International …, 2005

We present a new intelligent tutoring system, "Equation Guru" (EG), which is designed to help high school students at the grade 8 level with equation solving with one unknown. EG consists of two parts. The first is the "Tutorial" part where students are taught interactively, through the usage of an animated agent and visually stimulating graphics, how to solve equations with one unknown. In the second, "Drill and Practice" part, they practice their skills in equation solving by attempting to solve equations automatically generated by EG, which constantly monitors the student's performance and adjusts the difficulty level of the equations accordingly.

Integrating Rule-Based and Input-Based Approaches for Better Error Diagnosis in Expression Manipulation Tasks

Symbolic Computation and Education, 2007

T-algebra is a project for creating interactive problem solving environment for basic school expression manipulation exercises: calculation of the values of numerical expressions; operations with fractions; solving of linear equations, inequalities and linear equation systems; operations with monomials and polynomials. This article describes and motivates solution step interface and error diagnostics developed in T-algebra.

Implementation Strategies for “equation Guru,” a User Friendly Intelligent Algebra Tutor

Citeseer

We describe the implementation strategies of an intelligent algebra tutor, the "Equation Guru" (EG), which is designed to help students learn the concepts of equation solving with one unknown. EG provides a highly interactive and entertaining learning environment through the use of Microsoft Agents. It consists of two main parts. The first is the "Tutorial" part where students guided through the steps of solving equations with one unknown. The second, "Drill and Practice" part gives them a chance to practice their skills in equation solving. In this part, equations are automatically generated by EG, and presented to the student. EG monitors the student's performance and adjusts the difficulty level of the equations accordingly.

A Step-by-Step Solution Methodology for Mathematical Expressions

Symmetry, 2018

In this paper, we propose a methodology for the step-by-step solution of problems, which can be incorporated into a computer algebra system. Our main aim is to show all the intermediate evaluation steps of mathematical expressions from the start to the end of the solution. The first stage of the methodology covers the development of a formal grammar that describes the syntax and semantics of mathematical expressions. Using a compiler generation tool, the second stage produces a parser from the grammar description. The parser is used to convert a particular mathematical expression into an Abstract Syntax Tree (AST), which is evaluated in the third stage by traversing al its nodes. After every evaluation of some nodes, which corresponds to an intermediate solution step of the related expression, the resulting AST is transformed into the corresponding mathematical expression and then displayed. Many other algebra-related issues such as simplification, factorization, distribution and substitution can be covered by the solution methodology. We currently focuses on the solutions of various problems associated with the subject of derivative, equations, single variable polynomials, and operations on functions. However, it can easily be extended to cover the other subjects of general mathematics.

A Survey of User Interfaces for Computer Algebra Systems

Journal of Symbolic Computation, 1998

This paper surveys work within the Computer Algebra community (and elsewhere) directed towards improving user interfaces for scientific computation during the period 1963-1994. It is intended to be useful to two groups of people: those who wish to know what work has been done and those who would like to do work in the field. It contains an extensive bibliography to assist readers in exploring the field in more depth. Work related to improving human interaction with computer algebra systems is the main focus of the paper. However, the paper includes additional materials on some closely related issues such as structured document editing, graphics, and communication protocols.

Expanding the model-tracing architecture: A 3rd generation intelligent tutor for Algebra symbolization

2008

are intelligent tutoring systems that have been very successful at aiding student learning, but have not reached the level of performance of experienced human tutors. To that end, this paper presents a new architecture called ATM (for "Adding a Tutorial Model") which is an extension to the model-tracing architecture that allows these tutors to engage in a dialog that is more like what experienced human tutors do. Specifically, while MTTs provide hints toward doing the next problemsolving step, the ATM architecture adds the capability to ask questions towards thinking about the knowledge behind the next problem-solving step. We present a new tutor built in ATM, called Ms. Lindquist, which is designed to carry on a tutorial dialog about algebra symbolization. The difference between ATM and MTT is the separate tutorial model that encodes pedagogical content knowledge in the form of different tutorial strategies, which were partially developed by observing an experienced human tutor. Ms. Lindquist has tutored thousands of students at www.AlgerbaTutor.org. Future work will reveal if Ms. Lindquist is a better tutor because of the addition of her tutorial model.

Some human interaction issues in computer algebra

ACM SIGSAM Bulletin, 1994

This paper addresses some of the current issues concerning the improvement of user interfaces for computer algebra systems. Some state of the art commercial software as well as research prototypes are presented, followed by a description of present research directions.