Making arithmetic accessible to blind children is difficult. Young blind children are still learning Braille skills and seldom have 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. Unfortunately, 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 much 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 (Parkes 1988, Parkes 1991) 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 that blind child to do exactly the same arithmetic manipulations that a sighted child does with pencil and paper.

The ViewPlus IVEO graphical access technology is being used presently to make graphical information accessible. The audio/touch method requires a tactile graphic on a touchpad attached to a computer that speaks information about tactile objects when touched. An arithmetic problem for example, should speak the problem as well as individual numbers of that problem when touched appropriately. The IVEO technology has now been enhanced to permit data input, making audio/touch arithmetic applications straightforward.

This new Arithmetic access product is a series of interactive worksheets that let students practice arithmetic algorithms. The standard algorithms are used for addition, subtraction, and multiplication. Division is done using the partial quotient algorithm in the fewest possible number of steps. This algorithm, while not the traditional one, is becoming more usual and can be found in US textbooks such as Everyday Mathematics (The University of Chicago School Mathematics Project 2004). The worksheets include both practice problems and story problems requiring students to understand what the operation does in order to write a number sentence and solve the problem. A fundamental principle that guides ViewPlus Technologies’ work is the desirability of creating materials that are accessible to all users. Consequently, the arithmetic product includes a variety of ways for the student to receive information from the computer. Text and numbers are displayed onscreen and voiced when selected by the student. Additionally, the voiced text and numerical data are shown in a display bar as they are voiced, so that students can focus on a particular part of the screen. Students can easily enlarge the display bar and/or the onscreen text and graphics. Students can also use tactile pages on a touchpad connected to a computer that voices information associated with what the student is feeling. Tactile pages can 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.

The authors believe that students should be able to use technology in ways that feel most natural to them. Therefore, this product is designed to give students the option of using several different input modes. Students can pick the mode that they feel most comfortable with or they can use a combination of modes. Students can input numerical answers from the keyboard or they can use the displayed keypad. This keypad is on the right side of the screen and the tactile pages, and it resembles a telephone keypad with which students are already familiar. Students use this by selecting their answers with the mouse or by touching the answer on the touchpad. There is a user-adjustable delay which allows the student to hear which button has been pressed before inserting the number. This prevents them from inadvertently inputting the wrong number.

Students also have several options for navigating between and within problems. They can use the keyboard navigation arrows, move to the next field using the tab key, or simply select a field using the mouse. Furthermore, on the right side of both the screen and each tactile page is a navigation pad. This pad consists of four direction arrows surrounding a middle square. Students can use the arrows either with the mouse or the touchpad to move within a problem, they can use the center square followed by an arrow to move between problems, and they can press the center square twice to have the entire problem voiced.

To make it easier to keep track of where you are in the grid using only touch there are “Where am I” buttons on the screen and the tactile pad. When pushed, using the mouse or the touchpad, the computer voices the row (e.g. regroup boxes, addend1, addend 2, and sum) and/or the column (ones, tens, hundreds, etc.). This allows the student to concentrate on the problem without having to continually keep track of their position in the grid.

The authors are concerned with flexibility of use from the teacher’s perspective as well as from the student’s perspective. Teachers can assign randomly generated problems or input their own problems. They can pick the difficulty of randomly generated problems based on the number of digits and the size of the digits. Finally, they can choose between test mode, where no feedback is given, and practice mode where immediate feedback and a chance to redo the problem are given.

For each student, the teacher will have access to the number of problems worked, the number correct, the number incorrect, the percent correct, the total time used, and the number of problems per minute. The teacher will also be able to print out the questions and the student’s answers marked for correctness. This printout will look like a regular worksheet.

The ViewPlus Arithmetic access product will have the flexibility required to meet the needs of all students as well as their teachers. There are multiple input, output and navigation modes so that students can use the ones that they are most comfortable with at a given time. Teachers can use the software for testing or practice with randomly generated problems or with problems that they write themselves.

One of the team’s long term goals is to expand this product to include interactive instructional materials beginning with arithmetic but also including such topics as place value and fractions. These will be added in such a way as to maintain the flexibility of the product and will allow students to move at a rate that is based on their individual needs.

This development has been supported in part by a Phase IIB Small Business Innovation Research (SBIR) grant from the National Science Foundation.

[1] Parkes D (1988), “Nomad: an Audio-Tactile Tool for the Acquisition, Use and Management of Spatially Distributed Information by Partially Sighted and Blind Persons”, eds Tatham AF and Dodds AG, Proceedings of the Second International Symposium on Maps and Graphics for Visually Handicapped People, King’s College, University of London, pp. 24-29
[2] Parkes (1991), “Nomad: Enabling Access to Graphics and Text Based Information for Blind, Visually Impaired and Other Disability Groups”, Conference Proceedings, Vol. 5. World congress on Technology 1991, Arlington, Virginia, pp. 690-714
[3] The University of Chicago School Mathematics Project. (2004). Everyday Mathematics (2nd Ed.). Chicago, Illinois: Wright Group/McGraw-Hill.

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