Abstract: Architecture for a word processing application that facilitates operating on mathematical symbols, expressions, and/or equations input to a word processing document, and returning results back to the document. User input to the document in the form of math symbols, expressions or equations is transformed into a format for processing by a math engine. The engine returns one or more operations to the user that can be performed on the input, including calculating mathematical solutions, graphing equations and viewing steps to solving math problems. A user interface allows the user choose from the possible operations and to interactively manipulate input and graphs in the word application. The results can be inserted directly into the document and also be graded automatically.

Abstract: A problem checker architecture that monitors user progress during a problem-solving process and assists the user through the process (e.g., when requested) using common human methods of solving the problem. Assistance can be in the form of detecting errors during the process, and providing context-sensitive help information when the user gets stuck or makes a mistake. The problem checker can walk the user through the process of solving a math problem one step at a time allowing the user to learn to solve math problems according to a number of different methods. Rather than simply calculating and displaying the answer, the problem checker allows the user to attempt to solve math problems, providing direction only when asked and correction only when required. The problem checker can recognize multiple solution methods for many common math problems and guide the user to the solution via any of the methods.

Abstract: Mathematical expressions and functions are graphed using a computer implemented method that automatically determines an appropriate graph range. One implementation of the method begins with determining an initial variable seed range. A number of points within this seed range are randomly selected. The method determines whether the selected points correspond to the mathematical expression (i.e., whether they produce valid results when the expression is evaluated at each point). When the selected points produce valid results, the points can be used to generate and display a graph of the mathematical expression on a user display device, with a graph range based on the seed range. If not, the variable seed range can be expanded until a predetermined number of the selected points correspond to the mathematical expression, so that a graph of the mathematical expression can be generated and displayed.

Abstract: A problem checker architecture that monitors user progress during a problem-solving process and assists the user through the process (e.g., when requested) using common human methods of solving the problem. Assistance can be in the form of detecting errors during the process, and providing context-sensitive help information when the user gets stuck or makes a mistake. The problem checker can walk the user through the process of solving a math problem one step at a time allowing the user to learn to solve math problems according to a number of different methods. Rather than simply calculating and displaying the answer, the problem checker allows the user to attempt to solve math problems, providing direction only when asked and correction only when required. The problem checker can recognize multiple solution methods for many common math problems and guide the user to the solution via any of the methods.

Abstract: Architecture for a word processing application that facilitates operating on mathematical symbols, expressions, and/or equations input to a word processing document, and returning results back to the document. User input to the document in the form of math symbols, expressions or equations is transformed into a format for processing by a math engine. The engine returns one or more operations to the user that can be performed on the input, including calculating mathematical solutions, graphing equations and viewing steps to solving math problems. A user interface allows the user choose from the possible operations and to interactively manipulate input and graphs in the word application. The results can be inserted directly into the document and also be graded automatically.

Abstract: A system is disclosed for generating and displaying intermediate steps in an educational computer algebra system. The system combines templates with an algorithm to generate intermediate steps and explanatory text which may be displayed to the user.