Teaching Mathematical Modeling in Teacher Education: Efforts and Results

The purpose of this study is to investigate secondary teacher candidates’ experience of mathematical modeling task design. In the study, 54 teacher candidates in a university-based teacher education program created modeling tasks and scoring rubrics. Next, the participants pilot-tested the tasks with students and had the opportunity to revise the original tasks and rubrics based on student responses. The data included participants’ statements, in which they described and reflected on the design and revision process of modeling tasks. The study describes six didactic revision strategies in revising modeling tasks and identifies five emerging pedagogical ideas from revising tasks and rubrics. The study also discusses the way modeling task design activities have the potential to support teacher candidates’ learning through a bottom-up modeling curriculum in teacher education.

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Measuring pre-service teachers’ noticing competencies within a mathematical modeling context – an analysis of an instrument

Educational Studies in Mathematics ◽

10.1007/s10649-021-10102-8 ◽

2021 ◽

Author(s):

Alina Alwast ◽

Katrin Vorhölter

Keyword(s):

Mathematical Modeling ◽

Teacher Education ◽

Factor Analysis ◽

Confirmatory Factor Analysis ◽

Construct Validity ◽

Qualitative Analysis ◽

Content Validity ◽

Confirmatory Factor ◽

Validity Indicators ◽

Expert Ratings

AbstractTeaching mathematical modeling is a demanding task. Thus, fostering teachers’ competencies in this regard is an essential component of teacher education. Recent conceptualizations of teachers’ competencies include situation-specific skills based on the concept of noticing, which is of particular interest for the spontaneous reactions needed when teaching mathematical modeling. The study described in this paper aims to analyze the development of a video-based instrument for measuring teachers’ noticing competencies within a mathematical modeling context and obtain evidence for the validity of the instrument. Three kinds of validity are examined in three different studies: content validity, elemental validity and construct validity. Indicators for content validity could be found through different expert ratings and implementation with the target group, where participants were able to perceive all relevant aspects. The qualitative analysis of participants’ reasoning, which is consistent with the coded level, indicates elemental validity. Moreover, the results of the confirmatory factor analysis suggest construct validity with one overall factor of noticing competence within a mathematical modeling context. Taken together, these studies imply a satisfactory validity of the video-based instrument.

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Mathematical Modeling in Teacher Education

Mathematical Modelling in Education and Culture ◽

10.1533/9780857099556.5.197 ◽

2003 ◽

pp. 197-208 ◽

Cited By ~ 6

Author(s):

Mikael Holmquist ◽

Thomas Lingefjärd

Keyword(s):

Mathematical Modeling ◽

Teacher Education

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Formação de professores em Modelagem Matemática: uma hermenêutica dos relatórios do GT 10 – Modelagem Matemática da SBEM Teacher education in Mathematical Modeling: a hermeneutics of the reports of WG 10 - Mathematical Modeling of SBEM

Educação Matemática Pesquisa Revista do Programa de Estudos Pós-Graduados em Educação Matemática ◽

10.23925/1983-3156.2017v19i2p167-186 ◽

2017 ◽

Vol 19 (2) ◽

Author(s):

Wellington Piveta Oliveira ◽

Tiago Emanuel Klüber

Keyword(s):

Mathematical Modeling ◽

Qualitative Research ◽

Teacher Education ◽

Mathematics Education ◽

Mathematical Modelling ◽

International Research ◽

Working Group ◽

Initial Teacher Education ◽

Main Theme ◽

Phenomenological Hermeneutics

ResumoEsse texto tem sua gênese em um estudo mais amplo, no qual focamos a formação inicial de professores de Matemática em Modelagem. O movimento de pesquisa efetuado nos remeteu à leitura e compreensão da formação de professores em Modelagem no âmbito da pesquisa, a partir dos relatórios do Grupo de trabalho, GT-10, Modelagem Matemática da SBEM, nas últimas quatro edições do Seminário Internacional de Pesquisa em Educação Matemática, SIPEM (2006-2015). Dessa perspectiva, interrogamos: “O que revelam os relatórios do GT-10 de Modelagem Matemática (2006, 2009, 2012, 2015), vinculados a SBEM, sobre a formação de professores em Modelagem Matemática na Educação Matemática brasileira?”. Essa pesquisa de abordagem qualitativa, fenomenológico-hermenêutica, revela que a formação de professores em Modelagem na Educação Matemática tem sido discutida na comunidade só recentemente e que, embora seja jovem, os relatórios apontam que o foco das pesquisas ainda não se reporta diretamente a ela como temática principal.AbstractThis text has the genesis in a larger study, in which we focus on the initial teacher education in Mathematics Modeling. The research movement sent us to the reading and understanding of teacher education in Modeling as part of the research, from the Working Group reports, GT-10, SBEM Mathematics Modeling in the last four editions of the International Research Seminar Mathematics Education, SIPEM (2006-2015). From this perspective, we question: "What reveal the reports of the GT-10 Mathematical Modelling (2006, 2009, 2012, 2015), linked to SBEM on teacher education in Mathematical Modeling in Brazilian Mathematics Education?". This qualitative research, phenomenological-hermeneutics reveals that teacher education in Mathematics Modeling in Mathematics Education has been discussed in the community only recently and, although young, the reports show that the focus of the research has not directly report to it main theme.

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Pembelajaran Etnomatematika Sunda untuk Meningkatkan Kemampuan Pemodelan Matematik dan Kecerdasan Kreatif Mahasiswa PGSD

EduBasic Journal: Jurnal Pendidikan Dasar ◽

10.17509/ebj.v1i1.26223 ◽

2019 ◽

Vol 1 (1) ◽

pp. 1-10

Author(s):

Supriadi Supriadi

Keyword(s):

Mathematical Modeling ◽

Teacher Education ◽

Creative Thinking ◽

Design Research ◽

School Teacher ◽

Mathematics Learning ◽

Educational Background ◽

Primary School Teacher ◽

Research Subjects ◽

Creative Intelligence

Aspects of local culture in learning mathematics in primary school teacher education are still not optimally presented in learning. One way to realize this learning is by learning Sundanese ethnomathematics. The mathematical modeling is very supportive ability in the learning process. The process of mathematical modeling can develop creative intelligence. This article uses the Didactical Design Research method to further optimize the quality of teaching materials. The number of research subjects was 180 of first semester student. The teaching material was tested for success by an experimental method through a test instrument that measured mathematical modeling abilities and creative intelligence. Research results in mathematical modeling ability among students who get mathematics learning using Sundanese ethnomathematics learning is significantly better than students who use conventional learning. There is no interaction between learning models used with educational background groups on mathematical modeling abilities. There is no interaction for creative intelligence. Sundanese ethnomathematics learning with didactic design material can be used as a model of mathematics learning to develop the abilities and dispositions of mathematical creative thinking abilities and dispositions in the elementary school teacher education environment.

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Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task

Mathematics Teacher Educator ◽

10.5951/mathteaceduc.7.2.0007 ◽

2019 ◽

Vol 7 (2) ◽

pp. 7-26 ◽

Cited By ~ 3

Author(s):

Julia M. Aguirre ◽

Cynthia O. Anhalt ◽

Ricardo Cortez ◽

Erin E. Turner ◽

Ksenija Simic-Muller

Keyword(s):

Mathematical Modeling ◽

Teacher Education ◽

Social Justice ◽

Mathematics Teacher ◽

Teacher Educators ◽

Mathematics Teacher Education ◽

Teacher Understanding ◽

Teacher Survey ◽

Field Notes ◽

Survey Responses

Two major challenges in mathematics teacher education are developing teacher understanding of (a) culturally responsive, social justice–oriented mathematics pedagogies and (b) mathematical modeling as a content and practice standard of mathematics. Although these challenges may seem disparate, the innovation described in this article is designed to address both challenges in synergistic ways. The innovation focuses on a mathematical modeling task related to the ongoing water crisis in Flint, Michigan. Through qualitative analysis of instructor field notes, teachergenerated mathematical models, and teacher survey responses, we found that teachers who participated in the Flint Water Task (FWT) engaged in mathematical modeling and critical discussions about social and environmental justice. The evidence suggests that integrating these 2 foci–by using mathematical modeling to investigate and analyze important social justice issues–can be a high-leverage practice for mathematics teacher educators committed to equity-based mathematics education. Implications for integrating social justice and mathematical modeling in preservice and in-service mathematics teacher education are discussed.

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Learning How to Teach Mathematical Modeling in School and Teacher Education

10.1007/978-3-319-68072-9 ◽

2018 ◽

Cited By ~ 15

Author(s):

Rita Borromeo Ferri

Keyword(s):

Mathematical Modeling ◽

Teacher Education

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Pre-service mathematics teachers’ professional modeling competencies: a comparative study between Germany, Mainland China, and Hong Kong

Educational Studies in Mathematics ◽

10.1007/s10649-021-10064-x ◽

2021 ◽

Author(s):

Xinrong Yang ◽

Björn Schwarz ◽

Issic K. C. Leung

Keyword(s):

Mathematical Modeling ◽

Teacher Education ◽

Hong Kong ◽

Content Knowledge ◽

Mathematics Teachers ◽

Mainland China ◽

Cultural Traditions ◽

Pedagogical Content ◽

Teaching Culture ◽

History Of

AbstractAlthough mathematical modeling plays an important role in many curricula worldwide, significant discrepancies persist in the importance of mathematical modeling in ordinary mathematics classrooms and teacher education. This paper compares pre-service mathematics teachers’ professional mathematical modeling competencies in three different regions—Germany, Mainland China, and Hong Kong—where educational and cultural traditions differ, including the role of mathematical modeling. In total, 232 pre-service mathematics teachers from the three regions completed a modeling task covering mathematics content knowledge (MCK) of modeling and mathematical pedagogical content knowledge (MPCK) of modeling. The results show that pre-service teachers from Germany demonstrated the strongest MCK and MPCK of mathematical modeling; by contrast, pre-service mathematics teachers from Mainland China and Hong Kong demonstrated relatively weaker MCK and MPCK of mathematical modeling. MCK and MPCK of mathematical modeling were also found to be unevenly developed at different competence levels for the three regions. These differences may be attributed to the history of mathematical modeling in mathematics curricula, teacher education, and teaching culture in these three regions.

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