Improving Usability of Math Editors
Neil Soiffer · 2018 · Proceedings of the 15th International Web for All Conference (W4A 2018) · doi:10.1145/3192714.3192835
Summary
This short paper presents an empirical analysis of mathematical symbol usage across US grade 6-12 textbooks to demonstrate that context-aware math editors could dramatically reduce the number of buttons needed for symbol entry, significantly improving usability for screen reader and switch device users. WYSIWYG math editors typically provide palettes containing hundreds of symbols (MathType has ~210, WIRIS ~370), organised into subpalettes for Greek letters, relational operators, and so on. While keyboard shortcuts and special character sequences (e.g., \alpha) work for many users, they require memorisation of non-intuitive names. For screen reader and switch users, finding the right symbol from a large palette is a particularly burdensome process because they access buttons in a semi-linear fashion, similar to navigating items in a nested list. The study was motivated by an observation from Dave Schleppenbach that in an algebra textbook, just 10 symbols accounted for 95% of all operators. The author analysed public domain math textbooks from OpenStax covering pre-algebra, algebra, geometry, algebra II, pre-calculus, and calculus — containing 205,000 instances of math with 603,000 MathML operators and 435,000 identifiers. The textbooks used MathML to represent math expressions rather than images, enabling automated frequency analysis of exactly which characters, operators, and identifiers appear at each educational level.
Key findings
The analysis confirms that a very small number of non-keyboard characters account for the vast majority of math content at each level. For identifiers, the top 10 account for 69-87% of all usage across subjects — and in pre-algebra through algebra II, almost all identifiers are Roman letters already on the keyboard. Non-keyboard identifiers needed at the 0.05% threshold are remarkably few: pre-algebra needs just 2 (pi and delta), algebra needs 2 (delta and pi), algebra II needs 2 (pi and infinity), pre-calculus needs 8, and calculus needs 13. For operators, the six most common across all subjects are =, -, +, comma, and parentheses — all available on standard keyboards. The number of non-keyboard operators needed at the 0.05% threshold ranges from 10 (pre-algebra) to 24 (calculus). Combining identifiers and operators, the total palette entries needed range from just 12 for pre-algebra to 37 for calculus — vastly less than the 210-370 buttons in standard math editor palettes. The methodology also uncovered systematic MathML coding errors in the textbooks: Unicode synonym confusion (minus sign U+002D vs U+2212), multiplication dot variants (U+00B7 vs U+22C5 vs U+2022), and widespread mis-tagging of elements as mtext rather than the semantically correct mi, mn, or mo tags — affecting 24,000 instances. These errors point to bugs in the authoring tools that generated the MathML.
Relevance
This paper provides a simple but powerful insight for improving the accessibility of math authoring tools: if the subject area is known, the symbol palette can be reduced by an order of magnitude without sacrificing coverage. For screen reader users who must linearly navigate palette buttons, reducing from 370 to 12-37 options transforms the experience from tedious to manageable. For switch users with even more constrained input, the improvement is even more significant. The data-driven approach is immediately actionable — math editor developers can create subject-specific palettes based on the frequency tables provided. The study also has implications for math education platforms: knowing which symbols students will need at each level enables better default configurations in learning management systems and online assessment tools. The MathML coding errors discovered highlight an underappreciated problem in math accessibility: even when content is represented in accessible markup, semantic errors in that markup can confuse assistive technologies. The recommendation for math editor developers is clear: offer context-aware palettes that adapt to the user’s educational level, reducing cognitive and navigational burden for all users while particularly benefiting those who rely on assistive technologies.
Tags: mathematics accessibility · STEM accessibility · MathML · equation editors · screen readers · switch access · universal design · keyboard accessibility · visual impairment
Standards referenced: MathML