Abstract
This paper presents a study involving three well-known optimization problems within the Operations Research community. These problems provide an interesting context for creating tasks for the mathematics classroom, from the 1st to the 12th grades, given the connections with real contexts that they establish. Studies, about approaches and experiences with students at the basic and high school levels, are presented and the processes standards are discussed. The three proposed problems (path optimization, packing optimization and linear programming), which can be solved at different grades, are discussed focusing on the resolution strategies and on the dynamics of the mathematics classroom, thus promoting reasoning, communication, representation, connections and problem solving processes. The results of this study show that these problems provide a rich context to involve students in their learning process and to promote mathematics discussions. They share different strategies to solve the problems, emerging and relate different representations (active, iconic and symbolic), depending on the problem and the grade. Also, they explore connections between mathematics and real life.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Biehl, C. (1997). Discrete mathematics: A fresh start for secondary students. In J. Rosenstein, D. Franzblau, & F. Roberts (Eds.), Discrete mathematics in the schools (Vol. 36, pp. 317–322). Reston, VA: NCTM.
Bouma, C. (1991). Design your own city: A discrete mathematics project for high school students. In M. Kenney & C. Hirsch (Eds.), Discrete mathematics across the curriculum, K-12 (pp. 235–245). Reston, VA: NCTM.
Casey, N., & Fellows, M. (1997). Implementing the standards: Let’s focus on the first four. In J. Rosenstein, D. Franzblau, & F. Roberts (Eds.), Discrete mathematics in the schools (Vol. 36, pp. 51–65). Reston, VA: NCTM.
Colaço, S. (2007). Optimização em grafos num contexto de redes sociais, tecnológicas e no ensino da Matemática. Estudo do problema de balanceamento de uma comunidade na World Wide Web. Tese de doutoramento (Unpublished), Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal.
Colaço, S., Rebelo, C., & Pato, M. V. (2005). Problemas de optimização em redes sociais e tecnológicas. Algumas actividades para a aula de Matemática. In Actas do ProfMat2005. Évora: Associação de Professores de Matemática.
DeBellis, V., Rosenstein, J., Hart, E., & Kenney, M. (2011). Navigating through discrete mathematics in prekindergarten—Grade 5 (2nd printing). Reston, VA: National Council of Teachers of Mathematics.
Feiteira, R., & Pires, M. (2011). O ensino da teoria de grafos. Educação e Matemática, 112, 19–23.
Henriques, M., & Santos, P. (2003). Matemática Discreta no 1º CEB: Influência nas Concepções e atitudes dos alunos acerca da Matemática (Unpublished monografy). Escola Superior de Educação de Santarém, Santarém.
Karp, A., & Wasserman, N. (2015). Mathematics in middle and secondary school: A problem solving approach. Charlotte, NC: Information Age Publishing Inc.
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standard school mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: NCTM.
Rosenstein, J. (1997). A comprehensive view of discrete Mathematics: Of the New Jersey mathematics curriculum framework. In J. Rosenstein, D. Franzblau, & F. Roberts (Eds.), Discrete mathematics in the schools. DIMACS—Series in discrete mathematics and theoretical computer science (Vol. 36, pp. 121–132). Providence, RI: American and Mathematical Society and National Council of Teachers of Mathematics.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Colaço, S., Branco, N., Pato, M.V. (2018). Optimization Problems at School: Some Examples from the 1st to the 12th Grades. In: Beliën, J., Teixeira, A., W.Ittmann, H., de Miranda, J., Laumanns, M., Vaz Pato, M. (eds) Advances in Operations Research Education. Lecture Notes in Logistics. Springer, Cham. https://doi.org/10.1007/978-3-319-74104-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-74104-8_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-74103-1
Online ISBN: 978-3-319-74104-8
eBook Packages: EducationEducation (R0)