Integrating Rule-Based and Input-Based Approaches for Better Error Diagnosis in Expression Manipulation Tasks (original) (raw)
Related papers
T-Algebra: Adding Input Stage to Rule-Based Interface for Expression Manipulation
International Journal for Technology in Mathematics Education
T-algebra is a project for creating an interactive learning environment for expression manipulation tasks of elementary 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 steps: choice of conversion rule, operands and result.
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 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.
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.
Automatic Equation Solver - A Technology Enhancement For Instructional Automation
SSRN Electronic Journal, 2019
Mathematics plays an important role in everybody's life. We mainly depend on calculators available in our electronic gadgets to solve mathematical equations. Calculators available in these gadgets are so advanced that it can solve most complex mathematical equations. Remembering the fact that almost all electronic gadgets are touch screen based now-a-days, developing a system that recognizes and solves mathematical equations from handwriting is a potential area of research. This work develops an automatic equation solver, which solves the mathematical equations written by different persons. Neural network approach is used for recognition of the symbols and alphabets. The system is able to recognise alphabets, all the numbers, mathematical symbols and some special symbols. The system is successful in solving polynomial equations of power up to degree 9, system of linear equations with 2 and 3 variables having finite, infinite and no solutions. The system gives a recognition accuracy of 90% out of the 60 equations tested.
Expert Systems with Applications, 2013
i In order for an Intelligent Tutoring System (ITS) to correct students' exercises, it must know how to solve the same type of problems that students do and the related knowledge components. It can, thereby, compare the desirable solution with the student's answer. This task can be accomplished by an expert system. However, it has some drawbacks, such as an exponential complexity time, which impairs the desirable real-time response. In this paper we describe the expert system (ES) module of an Algebra ITS, called PAT2Math. The ES is responsible for correcting student steps and modeling student knowledge components during equations problem solving. Another important function of this module is to demonstrate to students how to solve a problem. In this paper, we focus mainly on the implementation of this module as a rule-based expert system. We also describe how we reduced the complexity of this module from O(n d ) to O(d), where n is the number of rules in the knowledge base, by implementing some meta-rules that aim at inferring the operations students applied in order to produce a step. We evaluated our approach through a user study with forty-three seventh grade students. The students who interacted with our tool showed statistically higher scores on equation solving tests, after solving algebra exercises with PAT2Math during an approximately two-hour session, than students who solved the same exercises using only paper and pencil.
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.
2018
The article describes systems of computer mathematics for educational purposes with intelligent properties oriented to support practical activities of users students and teachers. Systems of computer mathematics for educational purposes are oriented, first of all, in support of practical activity of users students and teachers for solving educational mathematical tasks. The article presents mathematical models and methods for solving algebra tasks in systems of computer mathematics for educational purposes. In the work: functional requirements for activity environments supporting the solving of learning tasks in algebra in systems of computer mathematics for educational purposes are developed; the mathematical model of learning mathematical task is defined within the framework of the mathematical model of the training module and the construction of the corresponding algorithms of computer algebra; mathematical models of methods for supporting the solving of learning mathematical tas...