Editing Textual descriptions in mathematics (section)

===Step 2: Description of mental tasks needed to overcome the bottleneck===
To illustrate the issue let's consider the following description of a set:
{{Textbox|boxtype=neutral|header=|text=The set ''P'' of all subsets of the set {1,…,10}, '''which''' are disjoint to the set {1,…,5}.|icon=yes}}

In order to make sense of this statement one has to understand how all its entities relate to each other. As is often the case, here this can be done by only using grammatical (rather than semantic) information. In particular this involves the question to which noun the relative pronoun "which" refers to. This could be the phrases 

* "set ''P''", 
* "all subsets" or 
* "the set {1,...,10}"

in the main clause. Students typically find it hard to decide<ref name=":0">Riegler, Peter (2019): [[Lost in Language Comprehension:     Decoding putatively extra-disciplinary expertise]]. In: Proceedings of EuroSoTL19: Exploring new fields through the scholarship of teaching and learning, Bilbao, pp. 685-691.</ref> while experts use their grammatical knowledge about languages to decide (as revealed in a [[Step 2 - Decoding Interview|Decoding interview]]):

The relative pronoun "which" needs to refer to a plural noun as indicated by the verb "are". This rules out all stated possibilities except "all subsets". Therefore the relative clause qualifies the subsets to be disjonint to the set {1,...,5}.

It is worth noting that in this particular example experts exlusively use grammatical information. No semantic knowledge of mathematics is needed. In constrast to that students seem to rely on semantic experience when relating parts of a sentence to each other.

These different approaches of novices and experts are well aligned with the findings of Good Enough (GE) Theory in Psycholinguistics.<ref>Ferreira, F., Bailey, K. G. D., and Ferraro, V. (2002). Good-enough representations in language comprehension. ''Curr. Dir. Psychol. Sci.'' 11, 11–15. doi: 10.1111/1467-8721.00158</ref> This theory is in contrast to traditional theories of language comprehension which assume that sentence processing is algorithmic and based on grammar.  GE posits that human beings do not necessarily make use of syntactic structure, in particular when it comes to more complex sentences. They tend to use a semantic heuristic rather than syntactic algorithms such as parsing in order to obtain the meaning of more difficult sentences. This approach, however, is futile for learners as they cannot yet have access to semantic heuristics.