## Virtual Pencil Algebra

Individuals who are pencil impaired (blind, motor impaired, or learning disabled) have a very difficult time writing and manipulating Algebraic equations, since operating a pencil effectively is very difficult if not impossible. If they are blind or visually impaired they have the additional problem of not being able to see the equation and its elements. It is very difficult for them to learn how to do the higher-level mathematics, such as advanced Algebra, Trigonometry, Calculus, etc. So, the goal of this project was to develop an environment on a computer that would allow pencil impaired students to learn and demonstrate that they have the ability to solve higher-level math problems.

A standard Windows application has been produced to present equations visually and audibly. Phase I was devoted to developing solutions to the basic issues that a blind student encounters when dealing with simple Algebraic equations. There were three specific technical challenges we were looking to overcome:

1. The presentation of the Algebraic equation audibly in an understandable fashion, so blind students can more effectively "read" the equation. This also provides reinforcement for learning disabled students.

2. A mechanism to navigate around an Algebraic equation, including equation specific location information.

3. A mechanism to input data and manipulate the equation, making it possible for the student to work through and solve the problem.

We have accomplished all three of these goals. Our research has resulted in a product, VPAlgebra, that incorporates the following capabilities:

Reading Equations - When working through an Algebraic equation, a blind student first needs to have the ability to have the entire equation "read" to them, to get an overview. So, it is important to develop a method to present the entire equation verbally, in an easily understandable way. VPAlgebra will read the equation, describing the various parts with phrases like "the quantity squared", "square root of", and "fraction of". Naturally the entire equation is displayed visually on the screen, with fractions, radicals, quantities, exponents, etc., in the students choice of colors and font sizes.

Navigating Equations - After reading the entire equation, it is important for the student to be able to navigate to any point within the equation. In addition, a method needs to be developed that will provide, on demand, an exact description of the current location. A sighted student can visually see and understand the location; however, blind students need this information textually. Therefore terms such as operand, quantity and fraction are used, and prefix specifiers such as first, second, third, are used to indicate locations of these macro elements. Otherwise, the appropriate term for sub-elements, such as numerator, denominator, sub (subscript) and Exponent (superscript) are used. A focus rectangle, like in a spread sheet, points out visually where the focus or insertion point is in the equation.

There are commands for navigation among the elements at any particular level, to access sub-elements, and to back out to additional macro elements such as quantities and fractions. There are other commands to navigate among these macro elements, regardless of the current location. The users have the option to assign their own preferred keystroke to these commands. This approach provides access to, and location information about, any point in an Algebraic equation for students using the keyboard or the mouse or other alternative input devices.

Manipulating Equations - Although it is very valuable to have the ability to navigate to any point in an equation, a student must also be able to manipulate elements of the equation at that location. This manipulation includes editing, copying and inserting elements.

It is difficult for pencil impaired students to take a complicated equation, and re-write it manipulating portions along the way. Commands to perform each of these operations have been developed, so the equation can be re-written and solved a piece at a time. These steps are all recorded and saved so they can be reviewed later, or printed out to hand in to a sighted teacher.

Features for Educators - to Teachers are provided the ability to build up multi-problem assignments, which can be provided to the able-bodied students in print and for the pencil impaired students electronically in VP Algebra . This allows the teacher to produce an assignment or test just once, for all their students regardless of their disability, saving a lot of time and effort. The electronic version can be emailed or distributed over the network, and password-protected so the original problems cannot be changed by the student.

VP Algebra can be used by itself with no special access technology, such as when a teacher demonstrates the techniques or creates the assignments. It can be used with a variety of alternative input devices, like IntelliKeys or other keyboards, track balls, switches, or on-screen keyboards. Blind users must use it with the Jaws screen reader for now, until we configure other screen readers to work with it.