Basic geometric-trigonometric equalities and problem-solving: Linear and angular elements
Parole chiave:
Matematica, Didattica, Uguaglianze trigonometriche, Uguaglianze geometriche, Elementi angolari, Elementi lineari, Problem-solvingAbstract
In questo lavoro si presentano alcune uguaglianze che riteniamo utili per la risoluzione di problemi di carattere geometrico a livello di scuola secondaria superiore di secondo grado. Le uguaglianze presentate coinvolgono elementi lineari ed elementi angolari contemporaneamente. L’obiettivo del lavoro è quello di monitorare, in scala molto ridotta, il grado di competenze acquisite dagli studenti dell’undicesimo e del dodicesimo anno di scolarità (L11 & L12) nella regione italiana denominata Puglia. Questo obbiettivo è stato raggiunto tramite diversi esercizi nei quali è stato chiesto a 27 studenti di:
- riconoscere la struttura di uguaglianze proposte;
- risolvere espressioni con uguaglianze.
In conclusione, i risultati sono stati presentati e discussi.
Riferimenti bibliografici
Andreescu T., Feng Z., (2004). 103 Trigonometry Problems: From the Training of the USA IMO Team, Birkhauser, Boston.
Anonymous, (1904). Relations entre les éléments d’un triangle. Vuibert et Nony, Éditeurs, Paris.
Altshiller-Court N., (2007). College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle, Dover Publications.
Bottema O., Djordjevic R.Z., Janic R.R., Mitrinovic D.S., Vasic P.M., (1969). Geometric Inequalities, Wolters-Noordho Publishing Groningen.
Duckworth A., (2016). Grit. The power of passion and perseverance, Scribner.
Engel A., (1998). Problem Solving Strategies, Springer Verlang.
Hang K.H., Wang H., (2017). Solving Problems in Geometry: Insights and Strategies, World Scientific Pub Co Inc.
Hobson E.W., (2005). A Treatise on Plane and Advanced Trigonometry, Dover Publications, Inc. Mineola, New York.
Larson L.C., (1983). Problem-Solving Through Problems, Springer-Verlag.
Ligouras P., (2017a). Basic Geometric Equalities and Problem-Solving: Linear Elements, Experiences of Teaching with Mathematics, Sciences and Technology — ISSN 2421-7247, vol. 3, n. 1, 475-487.
Ligouras P., (2017b). Basic Geometric Equalities and Problem-Solving: Angular Elements, Experiences of Teaching with Mathematics, Sciences and Technology — ISSN 2421-7247, vol. 3, n. 2, 515-526.
Ligouras P., (2010). 1691 Algebraic Inequalities: Problem Solving – Old and New Problems for the Mathematical Olympiads, AGA editrice.
Ligouras P., (2008). Geometrical Olympiad 2008, AGA editrice, ISBN: 88-95089-11-9 (Italian).
Prasolov V.V., Tikhomirov V.M., (2001). Geometry, American Mathematical Society.
Shariguin I., (1989). Problemas de Geometría Planimetría. Editorial Mir.
Todhunter I., Problems and Solutions in Plane Trigonometry (LaTeX Edition): For the use of Colleges and Schools, Ancient Science Publishers, 2016.
Vygotsky L.S., (2012). Thought and Language, 2nd Edition, The MIT Press.
Zeitz P., (2006). The Art and Craft of Problem Solving, Wiley International Student edition.
Anonymous, (1904). Relations entre les éléments d’un triangle. Vuibert et Nony, Éditeurs, Paris.
Altshiller-Court N., (2007). College Geometry: An Introduction to the Modern Geometry of the Triangle and the Circle, Dover Publications.
Bottema O., Djordjevic R.Z., Janic R.R., Mitrinovic D.S., Vasic P.M., (1969). Geometric Inequalities, Wolters-Noordho Publishing Groningen.
Duckworth A., (2016). Grit. The power of passion and perseverance, Scribner.
Engel A., (1998). Problem Solving Strategies, Springer Verlang.
Hang K.H., Wang H., (2017). Solving Problems in Geometry: Insights and Strategies, World Scientific Pub Co Inc.
Hobson E.W., (2005). A Treatise on Plane and Advanced Trigonometry, Dover Publications, Inc. Mineola, New York.
Larson L.C., (1983). Problem-Solving Through Problems, Springer-Verlag.
Ligouras P., (2017a). Basic Geometric Equalities and Problem-Solving: Linear Elements, Experiences of Teaching with Mathematics, Sciences and Technology — ISSN 2421-7247, vol. 3, n. 1, 475-487.
Ligouras P., (2017b). Basic Geometric Equalities and Problem-Solving: Angular Elements, Experiences of Teaching with Mathematics, Sciences and Technology — ISSN 2421-7247, vol. 3, n. 2, 515-526.
Ligouras P., (2010). 1691 Algebraic Inequalities: Problem Solving – Old and New Problems for the Mathematical Olympiads, AGA editrice.
Ligouras P., (2008). Geometrical Olympiad 2008, AGA editrice, ISBN: 88-95089-11-9 (Italian).
Prasolov V.V., Tikhomirov V.M., (2001). Geometry, American Mathematical Society.
Shariguin I., (1989). Problemas de Geometría Planimetría. Editorial Mir.
Todhunter I., Problems and Solutions in Plane Trigonometry (LaTeX Edition): For the use of Colleges and Schools, Ancient Science Publishers, 2016.
Vygotsky L.S., (2012). Thought and Language, 2nd Edition, The MIT Press.
Zeitz P., (2006). The Art and Craft of Problem Solving, Wiley International Student edition.
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Pubblicato
2018-12-07
Come citare
Ligouras, P. (2018). Basic geometric-trigonometric equalities and problem-solving: Linear and angular elements. EDiMaST: Esperienze Didattiche Con Matematica, Scienze E Tecnologia, 3(3), 549–565. Recuperato da https://www.edimast.it/index.php/edimast/article/view/58
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Sezione
Articoli - Esperienze e Ricerca
