Introduction: Braille readers encounter difficulties when reading mathematical expressions. In this exploratory study, we created a setting to investigate these difficulties. Method: Using a motion-capturing system, we analyzed the tactile strategies of three braille readers while they read mathematical expressions. To compare tactile with visual reading strategies, we also analyzed the oculomotor performance in five print readers. Results: The analysis showed that the two experienced braille readers needed about 3.5 times as much time as print readers to read and solve four items involving mathematical expressions. The braille readers used personal reading strategies for all items with little use of the structure of the expression. In contrast, the reading strategies of print readers showed item-dependent and structure-related characteristics. Discussion: The braille readers had difficulties, within the constraints of tactile reading, to align their reading strategies with the solution procedures required by the mathematical structure of the items. Implications for practitioners: Teachers need to become aware of the kind of problems that braille readers confront when they try to comprehend and solve mathematical problems.

Braille readers use a braille display and text-to-speech synthesizer while reading and comprehending mathematical expressions and equations. Teachers need to have technological, pedagogical and content (TPACK) knowledge and skills for exploiting the potential of these devices in mathematics education. They have to understand how the use of assistive technology influences the teaching and learning of mathematics. Therefore, the aim of the current study is to support teachers to better understand the dynamic relation between the different TPACK domains. That is why a professional development course was developed in which five mathematics teachers of braille readers in special secondary education participated. The development of the teachers’ TPACK knowledge was analyzed, and course characteristics that helped to develop this knowledge were identified. The results show an increased awareness of the importance of assistive devices, but only a small positive effect in TPACK knowledge and skills. Course activities related to the braille display, the mathematical braille notation and mathematical vocabulary helped to develop TPACK knowledge. However, course activities related to the text-to-speech synthesizer and working in heterogeneous groups did not work out so well. A better understanding of what teaching mathematics to braille readers means is expected to improve their learning.

Introduction Across the world, mathematical expressions are represented very differently in braille. The aim of this study was (1) to gain an overall insight in mathematical braille notations and (2) to investigate how mathematical braille notations support braille readers in reading and comprehending mathematical expressions. Method Twenty teachers from sixteen countries (thirteen European Union, EU, and three non-EU) were asked to transform 21 mathematical expressions and equations into the mathematical braille notation currently used by their braille readers. Three mathematical expressions were selected, and the transformed expressions in the different braille notations were qualitatively compared at braille and mathematical structure level. Results The results illustrated that most mathematical braille notations use mathematical structures that either support braille readers in getting an overview of an expression—for example, by announcing the start and end of a fraction—or facilitate communication between braille readers and people who can see. Discussion The method of comparing transformed expressions at structure level can be extended to other types of mathematical expressions and other mathematical braille notations. Agreement on the structure of different mathematical expressions can be a first step towards a universal mathematical braille notation. Implications for Practitioners Mathematics teachers should be aware of and use the strengths of the mathematical braille notation and try to compensate for weaknesses of the notation in the support of braille readers.

Braille readers read and comprehend mathematical expressions while moving their fingertips over braille characters. The aim of this exploratory study was to investigate the effect of an intervention that teaches braille readers who use a braille display to use finger movements with a focus on the expression’s mathematical structure. The finger movements involved movements where the two index fingers are about one or two braille cells apart and movements where the index fingers explore different parts of the expression. We investigated to what extent the intervention supports an interplay between finger movements and the expression’s mathematical structure to make the process of calculating the value of an expression easier and to make braille readers more aware of the expression’s structure. Three braille readers, respectively in Grades 7, 8, and 11, received the intervention consisting of five individual lessons. During the pre-, post-, and retention test, the braille readers’ finger movements were video recorded, as well as the time needed to read and process the mathematical tasks. Four expressions were selected for further analysis. The results show that during the posttest, each braille reader required at least 29% less time to read and process the expressions. The retention test results were even better. Scanpaths indicated that braille readers picked up features of mathematical structures more easily after the intervention. Based on our findings, we recommend that braille readers receive lessons in tactile reading strategies that support the reading and processing of mathematical expressions and equations.