journal article
Open Access
Dec 08, 2022
Design, Construction and Validation of a Rubric to Evaluate Mathematical Modelling in School Education
Abstract
This study describes the design, construction and validation of a rubric for assessing mathematical modelling processes throughout schooling (3–18 years), especially those oriented by modelling cycles. The final version of the “Rubric for Evaluating Mathematical Modelling Processes” (REMMP) consists of seven elements with their respective performance criteria or items, corresponding to the different phases of a modelling cycle. We concluded that REMMP can be used by both researchers and teachers at different educational levels from kindergarten to high school. The rubric is designed to assess group work developed by students; however, it can eventually be used individually.
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References
49
[1]
Kaiser "Towards a didactical theory for mathematical modeling" ZDM Math. Educ. (2006) 10.1007/bf02655882
[2]
National Governors Association Center for Best Practices and Council of Chief State School Officers (2010). Common Core State Standards Mathematics, National Governors Association Center for Best Practices and Council of Chief State School Officers.
[3]
National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standars for School Matematics, NCTM.
[4]
National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics, NCTM.
[5]
National Council of Teachers of Mathematics (2014). Principles to Actions: Ensuring Mathematical Success for All, NCTM.
[6]
Albarracín, L., and Gorgorió, N. (2020). Mathematical Modeling Projects Oriented towards Social Impact as Generators of Learning Opportunities: A Case Study. Mathematics, 8.
10.3390/math8112034
[7]
Alsina "Desarrollando habilidades de modelización matemática temprana en Educación Infantil: Un análisis comparativo en 3 y 5 años" Quadr. Rev. Investig. Educ. Matemática (2021)
[8]
Garfunkel, S., and Montgomery, M. (2019). What is mathematical modeling?. Guidelines for Assessment and Instruction in Mathematical Modeling Education, COMAP.
10.1137/1.9781611975741
[9]
Blum "Mathematical Modelling: Can It Be Taught and Learnt?" J. Math. Model. Appl. (2009)
[10]
Kaiser, G., Blum, W., Borromeo Ferri, R., and Stillman, G. (2011). Mathematical Modeling of Daily Life in Adult Education: Focusing on the Notion of knowledge. Trends in Teaching and Learning of Mathematical Modeling, Springer.
10.1007/978-94-007-0910-2
[11]
Haines, C., Galbraith, P., Blum, W., and Khan, S. (2007). Mathematical Modelling: A teacher’s training study. Mathematical Modelling (ICTMA12): Education, Engineering and Economics, Horwood Publishing.
10.1533/9780857099419
[12]
Toalongo "Creando los primeros modelos matemáticos: Análisis de un ciclo de modelización a partir de un problema real en Educación Infantil" CADMO (2021) 10.3280/cad2021-001006
[13]
Trelles "Una actividad de modelización matemática en primaria con datos auténticos de la COVID-19" Enseñanza Cienc. (2022)
[14]
Trelles "La presencia de la modelización matemática en tareas de estadística y probabilidad de libros de texto ecuatorianos" Innova Res. J. (2022) 10.33890/innova.v7.n2.2022.2076
[15]
Wess, R., and Greefrath, G. (2022, May 21). Professional Competencies for Teaching Mathematical Modelling—Supporting the Modelling-Especific Task Competency of Prospective Teachers in the Teaching Laboratory. Available online: https://hal.archives-ouvertes.fr/hal-02409039/document.
10.1007/978-3-030-78071-5_2
[16]
Alsina "Nuevos Conocimientos para una Educación Matemática del S. XXI: Panorama internacional de la modelización en el currículo" Unión Rev. Iberoam. Educ. Matemática (2017)
[17]
Fredj "Modes of modelling assessment-a literature review" Educ. Stud. Math. (2013) 10.1007/s10649-013-9491-5
[18]
Andrade "Using rubrics to promote thinking and learning" Educ. Leadersh. (2000)
[19]
Alsina, C., García-Raffi, L.M., Gómez, J., and Romero, S. (2007). Modelling in science education and learning. SUMA, 51–53.
[20]
Villa "La modelación como proceso en el aula de matemáticas. Un marco de referencia y un ejemplo" Tecno Lógicas (2007) 10.22430/22565337.505
[21]
Borba, M.C., and Villareal, M.E. (2005). Humans-with-Media and the Reorganization of Mathematical Thinking: Information and Communication Technologies, Modeling, Experimentation and Visualization, Springer.
10.1007/b105001
[22]
"El uso de la modelación en la enseñanza de las matemáticas" Innovación Educ. (2009)
[23]
Kaiser "A global survey of international perspectives on modelling in mathematics education" Zent. Didakt. Math. (2006) 10.1007/bf02652813
[24]
Blomhøj, M., and Carreira, S. (2009). Mathematical applications and modelling in the teaching and learning of mathematics. Different Perspectives on Mathematical Modelling in Educational Research-Categorising the TSG21 Papers, Proceedings of the Topic Study Group 21 at the 11th International Congress on Mathematical Education, Monterrey, Mexico, 6–13 July 2008, ICME. Available online: http://milne.ruc.dk/imfufatekster/pdf/461.pdf.
[25]
Abassian "Five different perspectives on mathematical modeling in mathematics education" Investig. Math. Learn. (2019) 10.1080/19477503.2019.1595360
[26]
Kaiser, G., Blum, W., Borromeo Ferri, R., and Stillman, G. (2011). Factors Affecting Teachers’ Adoption of Innovative Practices with Technology and Mathematical Modeling. Trends in Teaching and Learning of Mathematical Modeling, (ICTMA 14), Springer.
10.1007/978-94-007-0910-2
[27]
Kaiser, G., Blum, W., Borromeo Ferri, R., and Stillman, G. (2011). Secondary Teacher’s Beliefs on Modeling in Geometry and Stochastics. Trends in Teaching and Learning of Mathematical Modeling, Springer.
10.1007/978-94-007-0910-2
[28]
Kaiser, G., Blum, W., Borromeo Ferri, R., and Stillman, G. (2011). Using Technologies: New Possibilities of Teaching and learning Modeling—Overview. Trends in teaching and Learning of Mathematical Modeling, (ICTMA 14), Springer.
10.1007/978-94-007-0910-2
[29]
Graumann, G., Jahnke, T., Kaiser, G., and Meyer, J. (1995). Realitätsbezüge im Mathematikunterricht: Ein Überblick über die aktuelle und historische Diskussion. Materialien für Einen Realitätsbezogenen Mathematikunterricht, Verlag Franzbecker.
[30]
Haines, C., Galbraith, P., Blum, W., and Khan, S. (2007). How do students and teachers deal with modelling problems?. Mathematical Modelling: Education, Engineering and Economics, Woodhead Publishing.
[31]
Czocher "Mathematical modelling cycles as a task design heurisctic" Math. Enthus. (2017) 10.54870/1551-3440.1391
[32]
Garfunkel, S., and Montgomery, M. (2019). Guidelines for Assessment and Instruction in Mathematical Modeling Education, COMAP.
10.1137/1.9781611975741
[33]
Colwell "“When I hear literacy”: Using pre-service teachers’ perceptions of mathematical literacy to inform program changes in teacher education" Teach. Teach. Educ. (2016) 10.1016/j.tate.2015.11.001
[34]
Aydin "The PISA Tasks: Unveiling Prospective Elementary Mathematics Teachers’ Difficulties with Contextual, Conceptual, and Procedural Knowlege" Scand. J. Educ. Res. (2017) 10.1080/00313831.2017.1324906
[35]
"The role of contextual, conceptual and procedural knowledge in activating mathematical competencies (PISA)" Educ. Stud. Math. (2009) 10.1007/s10649-008-9167-8
[36]
Olande "Graphical artefacts: Taxonomy of students’ response to test items" Educ. Stud. Math. (2014) 10.1007/s10649-013-9493-3
[37]
Blum "Applied mathematical problem solving, modelling, applications, and links to other subjetcs: State, trends and issues in mathematics instruction" Educ. Stud. Math. (1991) 10.1007/bf00302716
[38]
"Mathematical modelling in European education" J. Math. Educ. Teach. Coll. (1991)
[39]
Blum, W., Galbraith, P.L., and Henn, H.N. (2007). Mathematical and applications: Ability and competence frameworks. Modelling and Applications in Mathematics Education, Springer. The 14th ICMI Study.
10.1007/978-0-387-29822-1
[40]
Leong "Assessment of mathematical modeling" J. Math. Educ. Teach. Coll. (2012)
[41]
"A rubric development study for the assessment of modeling skills" Math. Educ. (2018)
[42]
Turner "Mathematical Modeling in the Elementary Grades: Developing and Testing an Assessment" Int. J. Sci. Math. Educ. (2022) 10.1007/s10763-021-10195-w
[43]
Turner "Validating a student assessment of mathematical modeling at elementary school level" Sch. Sci. Math. (2021) 10.1111/ssm.12494
[44]
Mas "Les rúbriques per a una avaluació plantejada com a aprenentatge" Perspect. Esc. (2016)
[45]
Osterlind, S.J. (1989). Constructing Test Items, Kluwer.
10.1007/978-94-009-1071-3
[46]
Linn, R.L. (1989). The specification and development of test of achievement and ability. Educational Measurement, Macmillan.
[47]
A QUANTITATIVE APPROACH TO CONTENT VALIDITY1
C. H. LAWSHE
Personnel Psychology
1975
10.1111/j.1744-6570.1975.tb01393.x
[48]
"Modificación al modelo de Lawshe para el dictámen cuantitativo de la validez de contenido de un instrumento objetivo" Av. Med. (2008)
[49]
"On the use of realistic Fermi problems for introducing mathematical modelling in school" Math. Enthus. (2009) 10.54870/1551-3440.1157
Cited By
5
Okul Dışı Öğrenme Etkinliği Değerlendirme Rubriği Geliştirme Çalışması
Dokuz Eylül Üniversitesi Buca Eğiti...
Mustafa Zeki Aydoğdu, Funda Gündoğdu Alaylı · 2026
Metrics
5
Citations
49
References
Details
- Published
- Dec 08, 2022
- Vol/Issue
- 10(24)
- Pages
- 4662
- License
- View
Authors
Funding
Corporación Ecuatoriana para el Desarrollo de la Investigación y Academia—CEDIA
Award: CEPRA XVI-06
University of Girona
Award: CEPRA XVI-06
Cite This Article
Ximena Toalongo, César Trelles, Ángel Alsina (2022). Design, Construction and Validation of a Rubric to Evaluate Mathematical Modelling in School Education. Mathematics, 10(24), 4662. https://doi.org/10.3390/math10244662
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