van Leendert, A., Doorman, M., Drijvers, P., Pel, J., & van der Steen, J. (2019). An exploratory study of reading mathematical expressions by braille readers . Journal of Visual Impairment & Blindness , 113 (1), 68–80.

Journal Article

van Leendert, A., Doorman, M., Drijvers, P., Pel, J., & van der Steen, J. (2019). An exploratory study of reading mathematical expressions by braille readers. Journal of Visual Impairment & Blindness, 113(1), 68–80.


Braille; High school; International (non-U.S.); Math; Multiple ages; No disability; Postsecondary; Visual impairment (including blindness)




Tactile reading of braille by students with visual impairments including blindness, and visual reading by students without visual impairments, were investigated. The reading strategies used and difficulties encountered by both groups were examined. The braille version was provided in Dutch pre-braille notation on a laptop computer with braille display, and the visual reading version was presented on a laptop screen.


For each of the two settings, a distinct student participant group was enlisted: (Setting 1) the Dutch braille version on finger-tracking, and (Setting 2) the visual display of standard numbering on eye-tracking. (Setting 1) Three youth who were blind, and who had demonstrated mastery of grade 9 math, from the Rotterdam area in the Netherlands participated; they were in grade 9, grade 10, and postsecondary education. Additional information about their development of blindness and learning of braille were also reported. (Setting 2) Five grade 10 students without visual impairments from a suburban secondary school in the Netherlands participated to completion; an additional student had difficulties with the eye-tracking wearable device. All participants, in both settings, were expected to have already developed the math knowledge and skills needed to complete this study's academic tasks.

Dependent Variable

The task was to read and solve a series of four mathematical expressions combining more than one operation: addition, subtraction, and multiplication. This task required a non-linear process, in which test-takers needed to perform calculations according to the math rule of the order of operations. Participants' reading, thinking processes, and solutions were all reported orally. Each of the participant groups also provided data on the patterns by which they read the math expressions: an infrared motion-capturing system and a video camera documented braille readers' hand movement patterns, and a wearable eye-tracking device recorded sighted test-takers' eye gaze while reading. Time taken to read and solve each expression were documented as combined reading, comprehending, and processing time spans; timer data for each blind participant, as well as both groups' means, were reported.


All Setting 1 and Setting 2 participants completed all or nearly all mathematical expression tasks correctly. The braille reading group used an average of 171 seconds for all four math items, and the visual reading group used an average of 32 seconds. One of the braille readers used twice as much time as the other two, attributed to less experience with braille. The other two braille readers, on average, required about 111.5 seconds for all four items, which was about 3.5 times the average amount needed by the print readers for the four items. One of each group made mistakes on one item each; correctness of responses did not differ by group. The braille readers each displayed unique hand movement patterns that differed from one another; each also repeated tactile patterns several times for each of these non-linear math expressions. In contrast, the print readers showed similar eye gaze patterns as one another, and these seemed tailored to the structure of each of the four math expressions. In other words, students reading braille had difficulties aligning their personal strategies to the structure of the non-linear math expressions.