Readable text can carry the wrong meaning
A PDF text layer can return letters and digits while losing their spatial relationships. Correct character encoding does not show whether an exponent fell to the baseline or a fraction broke into separate parts. The result can describe a different mathematical expression.
Our examination of an Arabic textbook established the need for visual reading. The image gives reviewers evidence of what was printed; structured representation helps inspect components and relationships. Neither form can perform every task of the other.
Why not make every formula a picture?
An image preserves appearance but does not alone provide explicit structure for linking or later processing. Conversely, inserting formula encoding into explanatory prose entangles educational text, rendering and searchable material.
Warda separates the formula as a unit referenced by its explanatory text, accompanied by an Arabic reading. Paragraph boundaries follow educational meaning rather than the number of equation lines. A worked chain can remain coherent while containing several mathematical relations.
Shared representation does not require identical display
One curriculum may use an Arabic variable while another uses a different convention. Processing needs a structured meaning; presentation needs the edition’s notation profile. Treating those conventions as data keeps one textbook’s choices from becoming universal code rules.
This distinction also matters for the tutor. The material used to explain a concept should preserve its intended Arabic expression, while machine representation belongs to the service that needs it. We do not ask the model to freely translate between two formula forms and then treat that translation as authoritative.
Correct display has an independent requirement
Mathematical content therefore requires visual evidence showing the formula, not merely an image filename. Depending on layout, that evidence may include the full passage or a separate formula view. Reference checks are mechanical; confirming that the image contains the right expression still needs visual review.
Content approval and a correct serving path are separate responsibilities. Successful import alone does not prove that the learner will see the notation correctly. The contract extends across authoring, validation and presentation.
Two reading contracts: human and machine
Import validates encoding and references; presentation must ensure visible symbols suit the edition. Successful parsing does not replace inspection of the printed page, and a clear image does not detect a broken formula reference. Each representation is checked for the questions it can actually answer, rather than asking one step for an absolute guarantee.
Important cases include a worked equation chain, a formula beside its explanation and a symbol displayed differently across editions. Preserving Arabic reading with a shared representation requires an explicit reviewed mapping. A display difference does not necessarily imply different meaning, while visual similarity alone does not prove equivalence.
Good representation is not a complete checker
Preserving meaning makes mathematical verification possible, but does not establish a checker for every learner-authored step. Structured formulas are not proof of accurate assessment of every solution method. Meaning, explanation and verification have connected but independent responsibilities.
For Warda, the decision preserves the Arabic textbook and future processing options without reauthoring content for each interface. The depth lies in contracts protecting meaning from page to conversation, beyond a visually attractive formula.
Sources and context
- Warda engineering decision — mathematical content representation
Decision grounded in a printed-book review and package contracts, with later presentation and item-bank amendments.
- W3C — MathML Core
A specification for web mathematics layout, not a translation table for every Arabic curriculum.
Internal records document Warda’s decisions and engineering contracts. External references, where included, explain a pattern or specification; design quality and effects on student learning are different questions.