Conceptualizing a Pedagogical CAS for Algebraic Manipulation of Expression
AbstractIn this paper we define Pedagogical CAS as an exercise and assessment environment for exercises on numeric, fractional and algebraic expressions, equations, inequalities and equation systems. We assume that the student solves tasks step by step, performing arithmetic and algebraic operations. The system checks correctness of the student’s steps, provides feedback about errors and requires correction, records the student’s solutions and information about errors, is able to provide hints, has tools for visualizing recorded information and for automated assessment.
The paper describes our ideas on the following issues:
• Solution interface and working modes for students,
• Error diagnostics,
• Features and role of an automated Solver,
• Using random generation of expressions,
• Features and user interface of a Teacher Program for preparing tasks, analyzing the work of one student and groups of students, preparing tests with automated grading,
• Database and server architecture of the system, integration with course administration systems (like Moodle).
The paper is based on our experience with the programming and use of the interactive exercise environment T-algebra together with some supplementary programs but also on experience with a package for computerized exercises for an introductory course in Mathematical Logic.