The hypothetical learning trajectories: an example in a linear algebra course
This article proposes and evaluates a hypothetical learning trajectory (HLT) for the concepts of span and spanning set. This HLT was designed following the approach of Simon (1995), the design heuristics of emergent models and the mechanism of reflection on activity-effect relationship. We carried o...
| Main Authors: | , , |
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| Format: | Article |
| Language: | Spanish |
| Published: |
Universitat Autònoma de Barcelona
2021-03-01
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| Series: | Enseñanza de las Ciencias |
| Subjects: | |
| Online Access: | https://ensciencias.uab.es/article/view/2857 |
| _version_ | 1797763828188971008 |
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| author | Andrea Cárcamo Josep Maria Fortuny Claudio Fuentealba |
| author_facet | Andrea Cárcamo Josep Maria Fortuny Claudio Fuentealba |
| author_sort | Andrea Cárcamo |
| collection | DOAJ |
| description | This article proposes and evaluates a hypothetical learning trajectory (HLT) for the concepts of span and spanning set. This HLT was designed following the approach of Simon (1995), the design heuristics of emergent models and the mechanism of reflection on activity-effect relationship. We carried out an experiment with university students to determine if this HLT contributed to the expected learning of these concepts. We contrast this HLT with the actual learning trajectory (ALT) of two students showing approximation to key phases of the designed HLT. The results show that the notion of set is useful for the construction of the concept of span. In addition, we found it is necessary to incorporate new questions in HLT that facilitate the reflection on the activity-effect relationship to better account for the learning progression. |
| first_indexed | 2024-03-12T19:46:56Z |
| format | Article |
| id | doaj.art-241d076e42604c2c800f7504f0403d1b |
| institution | Directory Open Access Journal |
| issn | 0212-4521 2174-6486 |
| language | Spanish |
| last_indexed | 2024-03-12T19:46:56Z |
| publishDate | 2021-03-01 |
| publisher | Universitat Autònoma de Barcelona |
| record_format | Article |
| series | Enseñanza de las Ciencias |
| spelling | doaj.art-241d076e42604c2c800f7504f0403d1b2023-08-02T03:27:34ZspaUniversitat Autònoma de BarcelonaEnseñanza de las Ciencias0212-45212174-64862021-03-01391456410.5565/rev/ensciencias.2857722The hypothetical learning trajectories: an example in a linear algebra courseAndrea Cárcamo0Josep Maria Fortuny1Claudio Fuentealba2Universidad Austral de ChileUniversitat Autònoma de BarcelonaUniversidad Austral de ChileThis article proposes and evaluates a hypothetical learning trajectory (HLT) for the concepts of span and spanning set. This HLT was designed following the approach of Simon (1995), the design heuristics of emergent models and the mechanism of reflection on activity-effect relationship. We carried out an experiment with university students to determine if this HLT contributed to the expected learning of these concepts. We contrast this HLT with the actual learning trajectory (ALT) of two students showing approximation to key phases of the designed HLT. The results show that the notion of set is useful for the construction of the concept of span. In addition, we found it is necessary to incorporate new questions in HLT that facilitate the reflection on the activity-effect relationship to better account for the learning progression.https://ensciencias.uab.es/article/view/2857trayectoria hipotética de aprendizajemodelos emergentesactividad-efectoálgebra lineal |
| spellingShingle | Andrea Cárcamo Josep Maria Fortuny Claudio Fuentealba The hypothetical learning trajectories: an example in a linear algebra course Enseñanza de las Ciencias trayectoria hipotética de aprendizaje modelos emergentes actividad-efecto álgebra lineal |
| title | The hypothetical learning trajectories: an example in a linear algebra course |
| title_full | The hypothetical learning trajectories: an example in a linear algebra course |
| title_fullStr | The hypothetical learning trajectories: an example in a linear algebra course |
| title_full_unstemmed | The hypothetical learning trajectories: an example in a linear algebra course |
| title_short | The hypothetical learning trajectories: an example in a linear algebra course |
| title_sort | hypothetical learning trajectories an example in a linear algebra course |
| topic | trayectoria hipotética de aprendizaje modelos emergentes actividad-efecto álgebra lineal |
| url | https://ensciencias.uab.es/article/view/2857 |
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