m (saving work) |
m (saving work) |
||
| Line 15: | Line 15: | ||
{{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}} | {{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 nount 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[ | 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 nount 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 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: | ||
The relative pronoun "which" needs to refer to a plural noun as indicated by the verb "are". This rules out all possibilities except "all subsets". Therefore the relative clause qualifies the subsets to be disjonint to the set {1,...,5}. | The relative pronoun "which" needs to refer to a plural noun as indicated by the verb "are". This rules out all possibilities except "all subsets". Therefore the relative clause qualifies the subsets to be disjonint to the set {1,...,5}. | ||
| Line 29: | Line 30: | ||
===Step 3: Modelling the tasks === | ===Step 3: Modelling the tasks === | ||
An activity suggested in | An activity suggested in <ref name=":0" /> asks students to answer the following question in a [[wikipedia:Peer_instruction|Peer Instruction]] setting: | ||
{{Textbox|boxtype=neutral|header=|text=Consider the following description of a set: The set ''P'' of all subsets of the set {1,…,10}, '''which''' are disjoint to the set {1,…5}. Which phrase does the relative pronoun “'''which'''” refer to? | {{Textbox|boxtype=neutral|header=|text=Consider the following description of a set: The set ''P'' of all subsets of the set {1,…,10}, '''which''' are disjoint to the set {1,…5}. Which phrase does the relative pronoun “'''which'''” refer to? | ||
Revision as of 16:36, 22 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
Step 1: Identification of bottleneck
Given mathematical 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
Step 2: 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 nount 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 relative pronoun "which" needs to refer to a plural noun as indicated by the verb "are". This rules out all possibilities except "all subsets". Therefore the relative clause qualifies the subsets to be disjonint to the set {1,...,5}.
The setP of all subsets of the set {1,…,10}, which are disjoint to the set {1,…,5}.
The different approaches of novices and experts are well aligned with the findings of Good Enough Theory in Psycholinguistics which posits that human beings tend to use
Interview at DiZ
Step 3: Modelling the tasks
An activity suggested in [1] asks students to answer the following question in a Peer Instruction setting:
(A) “The set P”
(B) “subsets”
(C) “the set {1,…,10}”
(D) to something else not mentioned in (A)-(C)
(E) This is no unambiguous answer to this question.
Step 4: Practice and Feedback
...
Step 5: Anticipate and lessen resistance
...
Step 6: Assessment of student mastery
...
Step 7: Sharing
Decoding work on this issue has been published in Lost in Language Comprehension: Decoding putatively extra-disciplinary expertise.
Researchers involved
Peter Riegler
See also
- Sentence processing on Wikipedia
References
- ↑ Jump up to: 1.0 1.1 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.
