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XyAlgebra is a highly interactive first algebra course, with many brief explanatory sections and extensive practice problem sets for a standard Algebra I syllabus.  All problems have randomly-generated coefficients and variables. When posing a problem, xyAlgebra encourages the student to enter as many steps as necessary, and responds to each step as an instructor would.  Any equivalent step is accepted, regardless of method, and the Next Step Generator can suggest a reasonable next step at any point.  When the Equivalence Checker detects an incorrect step the Next Step Generator suggests how to continue correctly. For an executable demo of the xyAlgebra Equivalence Checker and Next Step Generator, see the bottom of the Download Page.

The Comparison (Pearson) and Hawkes pages show typical examples from top-selling commercial programs that accept only a short final answer.  If it’s incorrect, they show just one possible way of finding the correct answer, often not even using the student’s method.

The “intelligence” of xyAlgebra requires two critical algorithms not available in most programs:

Equivalence Checker

  • Translates all expressions and equations into a notation ideal for both recursive expression analysis and program debugging.
  • Checks algebraic equivalence of  rational expressions in n variables with real coefficients using standard algebraic techniques.
  • Verifies equivalence of solution sets by solving using the Next Step Generator, with provision for extraneous roots.
  • Supports verbal problem solutions by verifying variable and intermediate step descriptions using text analysis and synonyms.

Next Step Generator

  • Accepts numerous parameters controlling type of solution sought and level of ambition and sophistication desired.
  • Analyzs rational expressions, equations and systems, identifies the appropriate next operation and generates the result thereof.
  • Iterates this next step generation procedure as required to produce complete solutions.

For a demo of these algorithms, see the bottom of the Download Page.

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