Bridging Problem-Solving and Problem-Posing: Third Graders Learning to Formulate Mathematical Problems in Geometry and Measurement

• Fernandes, Hugo ^[1] ; Jacinto, Hélia ^[1] ; Oliveira, Hélia ^[1]
  1. [1] Universidade de Lisboa

     Universidade de Lisboa

     Socorro, Portugal

     
• Localización: Avances de investigación en educación matemática: AIEM, ISSN-e 2254-4313, Nº. 28, 2025 (Ejemplar dedicado a: La importancia de la formulación de problemas en el desarrollo de conocimiento matemático), págs. 31-53
• Idioma: inglés
• DOI: 10.35763/aiem28.7553
• Títulos paralelos:
  • Conectando resolución y formulación de problemas: Estudiantes de tercer grado aprendiendo a plantear problemas en Geometría y Medición
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Este estudio explora la relación entre resolución de problemas (RP) y formulación de problemas (FP) en educación matemática, con énfasis en la capacidad de estudiantes de tercer grado para crear problemas en Geometría y Medición. Se adoptó un marco teórico que considera la complejidad matemática y lingüística para analizar la evolución de los problemas formulados. También se compararon problemas resueltos y formulados para comprender mejor la conexión entre RP y FP. El estudio, realizado en ocho clases con tareas alineadas al currículo, combinó actividades de RP y FP. Se analizaron cualitativamente los trabajos escritos del alumnado. Los resultados muestran avances significativos en FP: mejor uso del lenguaje matemático, mayor claridad expresiva, adecuación a las consignas y resolubilidad de los problemas. El estudio resalta el valor del diseño de tareas y la articulación RP-FP para potenciar competencias matemáticas, ofreciendo una vía para integrar la FP como objetivo de aprendizaje en primaria.

  • English

    This study examines the relationship between problem solving (PS) and problem posing (PP) in mathematics education, focusing on 3rd-graders’ ability to create problems in Geometry and Measurement. A theoretical framework was adopted to assess the evolution of the problems posed, which considers mathematical and linguistic complexity. The study also compared posed and solved problems, for a deeper understanding of the connections between PS and PP skills. Conducted over eight lessons, it combined curriculum-aligned PS and PP tasks. Students’ written work was analyzed qualitatively. Findings show substantial improvements in PP skills, including better mathematical language, grammar and expression, alignment to task prompt, and problem solvability. Initially, students replicated structures from solved problems but gradually showed more creativity and autonomy. The study highlights how task design and the interplay between PS and PP enhance mathematical competencies and offer a viable approach to integrating PP as a learning objective in primary mathematics education.

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