Combined use of the extended theory of connections and the onto-semiotic approach to analyze mathematical connections by relating the graphs of f and f

The literature reports that students have difficulties connecting different meanings, multiple representations of the derivative, and performing reversibility processes between representations of f and f’ . The research goal is to analyze the mathematical connections that university students establi...

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Bibliographic Details
Published in:Educational studies in mathematics 2023-09, Vol.114 (1), p.63-88
Main Authors: Rodríguez-Nieto, Camilo Andrés, Rodríguez-Vásquez, Flor Monserrat, Moll, Vicenç Font
Format: Article
Language:English
Subjects:
College Freshmen
Colleges & universities
Concept Formation
Education
Encapsulation
Foreign Countries
Graphic methods
Graphs
Mathematical analysis
Mathematics
Mathematics Activities
Mathematics Education
Problem Solving
Representations
Semiotics
Students
Study and teaching
Symbols (Mathematics)
Undergraduate study
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Summary:The literature reports that students have difficulties connecting different meanings, multiple representations of the derivative, and performing reversibility processes between representations of f and f’ . The research goal is to analyze the mathematical connections that university students establish when solving tasks that involve the graphs of f and f’ when the two functions do not have associated symbolic expressions. Seven students from the first year of undergraduate studies in mathematics from a university in southern Mexico participated. For data collection, two tasks involving the graphical context of the derivative were applied. An analysis of the mathematical activity was carried out by the participants with the analysis model proposed by the onto-semiotic approach, and thematic analysis with types of mathematical connections from the extended theory of connections was carried out to infer the connections made in that mathematical activity, which allowed us to consider the reversibility connection between the graphs of f and f’ as the encapsulation of a portion of the mathematical activity. Four students establish the reversibility relationship between the graph of f and the graph of f’ . It has been concluded that some students can establish the reversibility connection between the graphs of f and f’ , but the complexity of the mathematical activity that encapsulates the connection explains (by showing everything that the student must do) why some students are not able to establish it.
ISSN:0013-1954
1573-0816
DOI:10.1007/s10649-023-10246-9