xyAlgebra7

Description

XyAlgebra is a highly interactive first algebra course, including many brief explanatory sections and extensive practice problem sets for each major topic of a standard Algebra I syllabus.  All problems have randomly-generated coefficients and variables.  All multiple-step problems accept step-by-step solutions. XyAlgebra encourages the student to enter as many steps as necessary.  XyAlgebra responds to each student step as an instructor would, providing that student with helpful feedback appropriate to that step of that solution method.  Any equivalent step is accepted, regardless of method.  When xyAlgebra detects an incorrect step, it immediately shows the student either a hint (a suggested type of step to do next) or a complete appropriate next step suitable at that point of that student’s solution.

See the Comparison page for an example.

This contrasts dramatically with typical commercial software.  Most such programs accept only a completely simplified final answer to most problems.  If the short answer is incorrect, they show one possible way of finding the correct answer, often using a method totally different from that of the student.  Students have often been taught various methods.  XyAlgebra intelligently supports all correct methods.

The History/Future page includes a description of new features in the latest version, xyAlgebra 7.01, released in December, 2012.

How xyAlgebra does it:

The “intelligence” displayed by xyAlgebra results from two algorithms not normally available in software of this type:

• Equivalence Checker:
• Translates all expressions and equations into a notation ideal for both recursive expression analysis and program debugging.
• Checks algebraic equivalence of arbitrary rational expressions in n variables with real coefficients using standard algebraic techniques.
• Verifies equivalence of solution sets by solving equations and systems using the Next Step Generator, including a provision for extraneous roots.
• Verifies variable declarations and intermediate step descriptions in setting up verbal problems using text analysis with synonym lists.
   
• Next Step Generator:
• Accepts numerous parameters controlling type of solution sought and level of ambition and sophistication desired.
• Analyzs rational expressions, equations and systems of equations, identifies the appropriate next operation and generates the result thereof.
• Iterates this next step generation procedure as required to produce complete solutions..
   

For more information on these algorithms, please contact the Author.