Adding it up

Mathematics has always been taught at Perkins, but the tools and techniques have evolved over the past century

Hands positioning pegs on an old-fashioned arithmetic slate

Teaching math at Perkins has evolved since the 1850s, when students used wooden arithmetic slates to show numeric values and to add, subtract or multiply. Today, students can use a tactile graphics pad for complex equations.

November 4, 2016

Samuel Gridley Howe, the first director of Perkins School for the Blind, believed that children who were blind should be presented with the same educational opportunities as their sighted peers – including the opportunity to learn math.

In addition to learning how to read, write and spell, Howe’s students also studied arithmetic, mathematics, algebra and geometry. In their 1835 Annual Report, the Trustees of Perkins noted that “several of the pupils are advancing in the science of geometry, algebra is familiar to many, and arithmetic almost to all.”

While many people who are blind did, and still do, rely on mental arithmetic, mathematics, like other subject areas, required the development of tactile teaching tools. Nicholas Saunderson (1682-1739), an English mathematician who lost his sight as a child, is credited with inventing the first calculating device for people who were blind – an arithmetic board. It allowed students to perform calculations by positioning pins on an engraved surface that resembled a cribbage board.

During the 18th and 19th centuries, arithmetic slates and counting grids appeared in many variations. The slates often had movable counters with raised numbers or symbols on the ends. Students could position the counters to show values and to add, subtract or multiply.

Students also used traditional wooden abacuses to make mathematical calculations, but that could be challenging because the slightest movement dislodged the beads. Terrence V. Cranmer, who was blind himself, solved that problem in the 1960s with the Cranmer abacus, which had felt backing that stabilized the beads. That innovation permitted the abacus to be moved or stored in mid-calculation.

As braille gained more widespread acceptance, braille slates and braille writers became popular and useful tools for teaching math. While they could be more time-consuming and cumbersome than a simple counting grid, braille writers had the advantage of emulating how sighted individuals perform arithmetic calculations.

When the Perkins Brailler was introduced in 1951, Dr. Edward Waterhouse, the school’s fifth director and a math teacher, noted that some of its “most popular features” were introduced “for the convenience of mathematics pupils.” In fact, many of the same features that made the Brailler so popular for writing – like ease-of-use and the ability to reinsert embossed paper to type more braille – also made it convenient for math.

Another major mathematic milestone was the introduction of the Nemeth Code for Mathematics and Science Notation, which was adopted in 1956 by the Braille Authority of North America. Developed by Abraham Nemeth, the code used the same alphabet as Standard English Braille, but assigned many braille cells different meaning as mathematical symbols. That allowed students to transcribe and perform complex mathematical equations.

Today, Perkins teachers and staff use a variety of tools to teach math in the classroom. While the Cranmer abacus and the Perkins Brailler are still used, teachers have also turned to new technologies to convey basic and advanced mathematical concepts.

For example, students in Perkins’ Secondary Program can use a tactile graphics pad for complex equations and functions like graphing. Students who need to create an X-Y axis and plot a point on a graph can draw on the tactile film, causing a raised line to appear. Other students use accessible iPad apps to practice basic arithmetic.

Whatever the tool, Perkins continues to develop innovative ways to help students who are visually impaired connect the dots – and add them up.

This blog post incorporates research and language from Betsy McGinnity, Jan Seymour-Ford and K.J. Andries. For more information about the history of Perkins School for the Blind, sign up for the Perkins Archives’ newsletter.