Designing Tasks for Introducing Functions and Graphs within Dynamic Interactive Environments
In this paper, we elaborate on theoretical and methodological considerations for designing a sequence of tasks for introducing middle and high school students to functions and their graphs. In particular, we present didactical activities with an artifact realized within a dynamic interactive environ...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-03-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/5/572 |
| _version_ | 1797412583110606848 |
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| author | Samuele Antonini Giulia Lisarelli |
| author_facet | Samuele Antonini Giulia Lisarelli |
| author_sort | Samuele Antonini |
| collection | DOAJ |
| description | In this paper, we elaborate on theoretical and methodological considerations for designing a sequence of tasks for introducing middle and high school students to functions and their graphs. In particular, we present didactical activities with an artifact realized within a dynamic interactive environment and having the semiotic potential for embedding mathematical meanings of covariation of independent and dependent variables. After laying down the theoretical grounds, we formulate the design principles that emerged as the result of bringing the theory into a dialogue with the didactical aims. Finally, we present a teaching sequence, designed and implemented on the basis of the design principles and we show how students’ efforts in describing and manipulating the different graphs of functions can promote their production of specific signs that can progressively evolve towards mathematical meanings. |
| first_indexed | 2024-03-09T05:05:15Z |
| format | Article |
| id | doaj.art-92af0eada99049dfaf5bcdb279819277 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:05:15Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-92af0eada99049dfaf5bcdb2798192772023-12-03T12:56:05ZengMDPI AGMathematics2227-73902021-03-019557210.3390/math9050572Designing Tasks for Introducing Functions and Graphs within Dynamic Interactive EnvironmentsSamuele Antonini0Giulia Lisarelli1Department of Mathematics “F. Casorati”, University of Pavia, 23100 Pavia, ItalyDepartment of Mathematics, University of Pisa, 56127 Pisa, ItalyIn this paper, we elaborate on theoretical and methodological considerations for designing a sequence of tasks for introducing middle and high school students to functions and their graphs. In particular, we present didactical activities with an artifact realized within a dynamic interactive environment and having the semiotic potential for embedding mathematical meanings of covariation of independent and dependent variables. After laying down the theoretical grounds, we formulate the design principles that emerged as the result of bringing the theory into a dialogue with the didactical aims. Finally, we present a teaching sequence, designed and implemented on the basis of the design principles and we show how students’ efforts in describing and manipulating the different graphs of functions can promote their production of specific signs that can progressively evolve towards mathematical meanings.https://www.mdpi.com/2227-7390/9/5/572functioncovariationdesign-based researchdynamic graphdynamic interactive environments |
| spellingShingle | Samuele Antonini Giulia Lisarelli Designing Tasks for Introducing Functions and Graphs within Dynamic Interactive Environments Mathematics function covariation design-based research dynamic graph dynamic interactive environments |
| title | Designing Tasks for Introducing Functions and Graphs within Dynamic Interactive Environments |
| title_full | Designing Tasks for Introducing Functions and Graphs within Dynamic Interactive Environments |
| title_fullStr | Designing Tasks for Introducing Functions and Graphs within Dynamic Interactive Environments |
| title_full_unstemmed | Designing Tasks for Introducing Functions and Graphs within Dynamic Interactive Environments |
| title_short | Designing Tasks for Introducing Functions and Graphs within Dynamic Interactive Environments |
| title_sort | designing tasks for introducing functions and graphs within dynamic interactive environments |
| topic | function covariation design-based research dynamic graph dynamic interactive environments |
| url | https://www.mdpi.com/2227-7390/9/5/572 |
| work_keys_str_mv | AT samueleantonini designingtasksforintroducingfunctionsandgraphswithindynamicinteractiveenvironments AT giulialisarelli designingtasksforintroducingfunctionsandgraphswithindynamicinteractiveenvironments |