No edit summary Tag: 2017 source edit |
mNo edit summary |
||
| (23 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
{{Textbox|boxtype=important|header=Change lemma|text=--> Parsing textual descriptions in mathematics|icon=yes}} | |||
'''Parsing''' textual description is a grammar based strategy for analyzing statements in order to understand them. Although mathematics makes extensive use of formal language, it also represent statements as '''textual descriptions'''. While experts do, students tend to not parse textual descriptions even if the can do so in other contexts. | |||
==Decoding work done== | ==Decoding work done== | ||
===Identification of bottleneck=== | ===Identification of bottleneck=== | ||
Given statements in natural language | Given statements in natural language students find it difficult to formalize such statements. This is especially the case for statements in predicate logic and set theory which involve more than one quantifier or if sets are nested, such as in | ||
{{Textbox|boxtype=neutral|header=|text=There is more than one bottleneck in mathematics which is difficult for all students in class.|icon=yes}} | |||
{{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}} | |||
The set ''P'' of all subsets of the set {1,…,10}, '''which''' are disjoint to the set {1,…,5}. | |||
Give specific example | Give specific example here | ||
===Description of mental tasks needed to overcome the bottleneck=== | ===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. In particular this involves the question to what object the relative pronoun "which" refers to. This could be "set ''P''", "all subsets" or "the set {1,...,10}" in the main clause. Students tyipcally find it hard to decide<ref>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, 685-691</ref> while experts use their grammatical knowledge about languages to decide: | |||
... | |||
The different approaches of novices and experts are well aligned with the findings of Good Enough Theory in Psycholinguistics. | |||
===Modelling the tasks=== | ===Modelling the tasks=== | ||
| Line 27: | Line 40: | ||
===Sharing=== | ===Sharing=== | ||
Decoding work on this issue has been published in [[Lost in Language Comprehension: Decoding putatively extra-disciplinary expertise]]. | |||
==Researchers involved== | ==Researchers involved== | ||
Peter Riegler | Peter Riegler | ||
==Available Resources== | |||
==See also== | ==See also== | ||
==References== | |||
<references /> | |||
[[Category:Decoding work]] | |||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
[[Category:Set theory]] | |||
[[Category:Predicate logic]] | |||
[[Category:Bottleneck]] | |||
Latest revision as of 18:01, 5 April 2025
Parsing textual description is a grammar based strategy for analyzing statements in order to understand them. Although mathematics makes extensive use of formal language, it also represent statements as textual descriptions. While experts do, students tend to not parse textual descriptions even if the can do so in other contexts.
Decoding work done
Identification of bottleneck
Given statements in natural language students find it difficult to formalize such statements. This is especially the case for statements in predicate logic and set theory which involve more than one quantifier or if sets are nested, such as in
The set P of all subsets of the set {1,…,10}, which are disjoint to the set {1,…,5}.
Give specific example here
Description of mental tasks needed to overcome the bottleneck
To illustrate the issue let's consider the following description of a set:
In order to make sense of this statement one has to understand how all its entities relate to each other. In particular this involves the question to what object the relative pronoun "which" refers to. This could be "set P", "all subsets" or "the set {1,...,10}" in the main clause. Students tyipcally find it hard to decide[1] while experts use their grammatical knowledge about languages to decide:
...
The different approaches of novices and experts are well aligned with the findings of Good Enough Theory in Psycholinguistics.
Modelling the tasks
....
Practice and Feedback
...
Anticipate and lessen resistance
...
Assessment of student mastery
...
Sharing
Decoding work on this issue has been published in Lost in Language Comprehension: Decoding putatively extra-disciplinary expertise.
Researchers involved
Peter Riegler
Available Resources
See also
References
- ↑ 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, 685-691
