This chapter presents the results of a research project whose purpose was to analyze an activity called Reforestation, under the six design principles of a Model Eliciting Activity (MEA): Reality, Model Construction, Self-Assessment, Construct Documentation, and Generalizability. When an activity adheres to these principles, it not only supports the development of mathematical (disciplinary) knowledge in a way that is integrated into the context but also promotes the acquisition of modeling skills such as communication, self-assessment, and model generalization. The participants were four pre-service teachers engaged in building and refining models to address the Reforestation activity. The theoretical framework was the models and modeling perspective. Epistemic Network Analysis (ENA) was employed to identify, quantify, and compare the structural connections in teacher–researcher interactions, providing evidence complementary to the qualitative results. The analysis focused on the phase of model review through the group discussion. Results show that the Reforestation MEA satisfied elements of five design principles, with Principle 6 (Effective Prototype) remaining pending. Differences in how teachers interpreted the real-world context, constructed their models, and documented and self-evaluated them led to a variety of solutions, confirming the activity’s nature as an MEA. These findings highlight both the potential of ENA for detecting adherence to MEA principles and the reciprocal influence between researcher facilitation and teacher learning in professional development contexts.

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Analysis of an Activity Based on the Six Design Principles of a Model-Eliciting Activity

  • Verónica Vargas-Alejo,
  • Guadalupe Carmona,
  • Luis Montero-Moguel,
  • Brendan Eagan

摘要

This chapter presents the results of a research project whose purpose was to analyze an activity called Reforestation, under the six design principles of a Model Eliciting Activity (MEA): Reality, Model Construction, Self-Assessment, Construct Documentation, and Generalizability. When an activity adheres to these principles, it not only supports the development of mathematical (disciplinary) knowledge in a way that is integrated into the context but also promotes the acquisition of modeling skills such as communication, self-assessment, and model generalization. The participants were four pre-service teachers engaged in building and refining models to address the Reforestation activity. The theoretical framework was the models and modeling perspective. Epistemic Network Analysis (ENA) was employed to identify, quantify, and compare the structural connections in teacher–researcher interactions, providing evidence complementary to the qualitative results. The analysis focused on the phase of model review through the group discussion. Results show that the Reforestation MEA satisfied elements of five design principles, with Principle 6 (Effective Prototype) remaining pending. Differences in how teachers interpreted the real-world context, constructed their models, and documented and self-evaluated them led to a variety of solutions, confirming the activity’s nature as an MEA. These findings highlight both the potential of ENA for detecting adherence to MEA principles and the reciprocal influence between researcher facilitation and teacher learning in professional development contexts.