The authors discuss a truly universal learning system that will allow all children including blind and deaf children to do arithmetic using standard algorithms. This system uses the three main learning modalities, sight, sound, and touch, allowing students to simultaneously use multiple senses when learning. The product was designed with a flexible user-interface so that students can receive and enter information in a variety of ways. This product makes use of scalable vector graphics and uses XForms to create input fields within graphics.
Making arithmetic accessible to blind children in mainstream schools is difficult. Young blind children are still learning Braille skills and often have not learned how to access two dimensional grids at the age that they should be learning arithmetic. Consequently they have difficulty learning math the same way sighted children do and must rely on skilled vision teachers to teach them math often using an abacus. Unfortunately, these are specialized topics and there are not enough skilled math-knowledgeable vision teachers. As a result, far too many blind children just do not learn arithmetic well. This becomes a lifelong handicap because one cannot learn further math without being able to work symbolically which is initially learned through doing arithmetic.
The authors of this paper believe that the best way for blind children to learn math is to use the same learning/doing arithmetic method that sighted children use. Arithmetic algorithms are traditionally learned and done in mainstream schools using a two dimensional layout. Numbers to be added or subtracted are written in rows, and answers are written below these initial rows. Regrouping (carrying, borrowing) is usually indicated by writing numbers above the problem. Algorithms for multiplication and division of multi-digit numbers often require repeated multiplications, as well as addition and subtraction, often with regrouping.
A blind child cannot easily use paper and pencil, but she can use the audio/touch method to read two dimensional arithmetic problems easily. Audio/touch is known , to provide good access by blind people to two-dimensional graphical information. It is broadly useful and has a relatively small learning curve. Extension of audio/touch technology that allows numbers to be entered into a selected position on the two dimensional problem permits the blind child to quickly do exactly the same arithmetic manipulations that a sighted child does with pencil and paper.
The authors have begun to develop graphical access technology for arithmetic based on the ViewPlus IVEO technology , for graphical accessibility. The commercial IVEO software permits users with print disabilities to access nearly any static diagram, map, or table through audio/touch. IVEO uses Scalable Vector Graphics (SVG) , an xml-based format as defined by the World Wide Web Consortium (W3C). Because it is a vector format, and not a raster format, images can be enlarged without loss of resolution. This makes it possible for blind users to enlarge an image and distinguish small objects tactilely when the image is printed on a tactile embosser. It also allows low-vision users to enlarge objects so that they may see them. Because it is an xml format, SVG files can be generated easily programmatically. The IVEO Arithmetic Tutor, for example, generates worksheets from simple problem files and templates. The xml-based format also allows easy annotation of elements, say, for accessibility, and the ability to add custom attributes, if desired.
IVEO SVG files may be printed to a ViewPlus Tiger embosser to obtain a high resolution tactile image. That tactile image is then placed on a touchpad, and the user may feel it and press on text or graphical objects. Text labels or titles of graphical objects speak when pressed. Additionally, if a user scales or pans an image on the screen, they can print the new image and place that on the touchpad. The computer automatically adjusts so that it voices the object that the user is touching on the scaled tactile image.
Prior to this project, IVEO has been essentially a presentation platform. The user could interact with the system by touching or clicking an object or text, but this was only to indicate the object about which they wished to obtain information. The IVEO technology has now been enhanced to allow users to input data. This permits students to input numbers, operations, and text, and will soon include the ability to make selections using buttons and lists. This makes audio/touch arithmetic applications straightforward. The Accessible Arithmetic project incorporates XForms, a W3C recommendation for forms creation, into IVEO.
The IVEO® technology has a huge potential for applications in the field of Education. This hands-on learning system allows students to use any or all of the three main learning modalities, sight, sound, and touch. Using the IVEO touchpad with an embossed tactile image, a student can touch a tactile object and the computer will voice a preset message. For example, when a student places the embossed space shuttle on the touchpad and touches the main engines, the computer voices the words “main engines” and plays a sound clip of engines firing. An arithmetic problem speaks the problem as well as the individual numbers of that problem when touched appropriately. Thus, the student can see the printed image, feel the tactile image, and hear related sounds.
Fig. 1. A young student doing arithmetic using the Arithmetic Learning System alpha prototype.
Multi-modal learning has been shown to be successful for many students, including mainstream and learning disables students   . In addition, Ginns  found that these effects hold across age groups and instructional materials. Tactile pages can easily be overprinted with color ink, using the ViewPlus Emprint SpotDot, allowing the student to see the information, touch the information, and hear the information simultaneously. This concurrent learning through different senses is in keeping with research showing that multi-modal learning is most effective when given together .
This learning system has the potential for use in multiple learning areas. It is currently possible for students to read labeled diagrams using the IVEO touch system, and now that students can enter information using XForms, various types of tests could be taken using this system. Students will even be able to take geography tests, where they are required to fill in country names on a map.
The IVEO hands-on learning system is a truly universal learning system. It can be used and enjoyed by any student, from a gifted student to a deaf-blind student. A teacher can easily make standard learning materials that are accessible to all of her students.
The IVEO Arithmetic Tutor is a series of randomly generated interactive worksheets that let students practice arithmetic algorithms. The standard United States algorithms are used for addition and subtraction. Multiplication and division will be completed and tested at a later date, also using standard algorithms. The worksheets include both practice problems, where students are given an addition or subtraction exercise, and story problems, requiring students to understand what the operation does in order to write a number sentence and solve the problem.
Fig. 2. An addition example, with regrouping boxes, of the Arithmetic Tutorial for the IVEO Hands-on Learning System
Fig. 3. A subtraction example, with no regrouping boxes, of the Arithmetic Tutorial for the IVEO Hands-on Learning System
An authoring distribution software tool is also being created for teachers. With this tool, teachers can quickly and easily create a set of arithmetic worksheets and require or permit one or more students to complete them. These worksheets can be generated at a variety of levels, allowing the teacher to customize the program for each student. The worksheets may be practice sheets that provide feedback, in the form of sounds, to students on whether their answers are correct, giving them a chance to redo a problem, or they may be tests that provide no such feedback.
The computer will keep track of student’s work including the number of problems a student has completed, the average time per problem and the numbers correct. The teacher can then easily generate a report on the student’s progress. The teacher can also print out a worksheet with the student’s answers to share with parents or other educators.
A fundamental principle that guides ViewPlus Technologies’ work is the desirability of creating materials that are accessible to all users. Consequently, the arithmetic tutor includes a variety of ways for the student to receive and input information from the computer to meet student’s diverse sensory and learning needs. Text and numbers are displayed onscreen and can be voiced when selected by the student using a standard mouse. Tactile arithmetic pages on a touchpad allow the student to touch a tactile or Braille number from the problem and hear it voiced. Students can enter their answers using the touchpad, the mouse, or the keyboard.
Fig. 4. A young student using only the touchpad to complete arithmetic problems
Thus, students have wide flexibility in how they interact with the worksheets. Students with no disabilities may use the worksheets on screen with numbers entered by keyboard or using the mouse with an on-screen number keypad. Those with severe print disabilities may work problems with the tactile copies and touchpad in a way entirely analogous to what is done visually on-screen. This is in keeping with the authors’ philosophy that students with print disabilities are most likely to learn at the same rate as students without disabilities if both are using the same learning technologies.
Fig. 5. A young student completing arithmetic problems on a standard computer.
These arithmetic learning/testing modules are currently in alpha testing and will be subject to initial student user testing by mid-2008. Extended pilot testing in US classrooms is scheduled to begin in the 2008-2009 school year. Early teacher reactions are positive. Many teachers feel that this system can benefit most children, not just those with sensory disabilities, and they are excited for this system to become available for their classrooms.
Early student reactions are also positive. Students like working on the computer, and they like being able to touch, hear and see the material. Children also like the feeling of being in control of what they are doing, being able to decide how they’re going to use the software. Preliminary usability data will be presented at the conference, and the application will be demonstrated.
This development has been supported in part by a Phase IIB Small Business Innovation Research (SBIR) grant from the National Science Foundation. Parkes D.: Nomad: an Audio-Tactile Tool for the Acquisition, Use and Management of Spatially Distributed Information by Partially Sighted and Blind Persons. In Tatham, A.F. Dodds, A.G. (eds.) Proceedings of the Second International Symposium on Maps and Graphics for Visually Handicapped People, , pp. 24—29 King’s College, University of London (1998)
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