A framework for identifying student blockages during transitions in the modelling process

Galbraith, Peter; Stillman, Gloria

doi:10.1007/bf02655886

Cited by 255 publications

(207 citation statements)

References 6 publications

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“…Most teachers thought that context-based tasks should provide only the information needed to find the solution and should explicitly provide the required mathematical procedures. In line with other researchers (Chapman 2009;Galbraith and Stillman 2006;Maass 2010;Verschaffel et al 2010), we argue that having such beliefs about context-based tasks and perceiving context-based tasks as straightforward word problems will not be supportive for providing students OTL to solve context-based tasks. Teachers who have such beliefs might only focus on the mathematical properties or structures of a context-based task without attaching great value to the problems' context (Chapman 2009).…”

Section: Conclusion and Discussionsupporting

confidence: 77%

“…Teachers who have such beliefs might only focus on the mathematical properties or structures of a context-based task without attaching great value to the problems' context (Chapman 2009). Furthermore, they might abandon daily life knowledge and experiences during the solving process (Galbraith and Stillman 2006) and might not contribute to the students' sense-making of a problem (Verschaffel et al 2010).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…In line with this, Kramarski et al (2002, p. 228) suggested that teachers should encourage students to formulate and answer self-addressed questions such as "What are the similarities or differences between this problem and the problems I have ever solved?" What all these approaches have in common is that OTL in the transformation stage needs to orient students toward identifying relevant mathematical procedures for solving the problem (Galbraith and Stillman 2006).…”

Section: Otl Connected To the Transformation Stagementioning

confidence: 99%

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Teachers’ teaching practices and beliefs regarding context-based tasks and their relation with students’ difficulties in solving these tasks

2015

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In this study, we investigated teachers' teaching practices and their underlying beliefs regarding context-based tasks to find a possible explanation for students' difficulties with these tasks. The research started by surveying 27 Junior High School teachers from seven schools in Indonesia through a written questionnaire. Then, to further examine teachers' teaching practices related to context-based tasks, four teachers were observed and video recorded in two mathematics lessons in which they were asked to deal with context-based tasks. The questionnaire data revealed that the teachers had a tendency toward a view on teaching and learning mathematics which includes encouraging students to be actively involved in solving problems in various contexts. Although this finding suggests that the teachers may offer opportunities to learn context-based tasks to students, the questionnaire data also revealed that the teachers saw context-based tasks as plain word problems. Furthermore, the observations disclosed that their teaching was mainly teacher-centered and directive, which is not considered to be supportive for learning to solve context-based tasks. Combining the findings of this study with the results from our earlier study on Indonesian students' errors when solving context-based tasks, we found a relationship between how Indonesian teachers teach context-based tasks and the errors Indonesian students make in solving these tasks. These findings support the conclusion that insufficient opportunity-to-learn to solve context-based tasks offered by teachers is a possible explanation for students' difficulties in solving these tasks.Math Ed Res J (2015) 27:637-662 DOI 10.1007/s13394-015-0157-

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Section: Conclusion and Discussionsupporting

confidence: 77%

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Otl Connected To the Transformation Stagementioning

confidence: 99%

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Teachers’ teaching practices and beliefs regarding context-based tasks and their relation with students’ difficulties in solving these tasks

2015

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“…The researchers seeing mathematical modeling as a content in its own right focuses on describing and teaching the modeling cycle, the phases in modeling cycle, modeling abilities and competencies. Research studies following this tradition uses the description of modeling as the conceptual frame for describing students' and teachers' behaviors during modeling process, modeling competencies, and assessment of modeling competencies (e.g., Borromeo Ferri, 2006;Crouch & Haines, 2004;Frejd, 2013;Galbraith & Stillman, 2006;Houston, 2007;Lingefjärd, 2006;Maaß, 2006). The focus from this perspective is the teaching of mathematical modeling with its many technical details.…”

Section: Mathematical Modeling As a Bridge For Stem Educationmentioning

confidence: 99%

Mathematical Modeling: A Bridge to STEM Education

Kertil¹,

Gürel²

2016

IJEMST

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The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may contribute to theoretical conceptualization of STEM education by specifically addressing the professional competencies that teachers need. The discussion followed on how mathematical modeling activities and project-based learning contexts contribute to integrated STEM education by providing two research-based experiences, one of which is the model rocketry project carried out by pre-service physics teachers and the other one of which is a mathematical modeling activity solved by pre-service mathematics teachers.

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“…They used mathematical knowledge to adjust and redevelop their models. This reinforced the importance of mathematical modelling as a cyclic process involving the development of assumptions, formulation of a solution and continued refinement (Galbraith, 2006). Here, we present a methodology for investigating the UVI using mathematical concepts familiar to middle school aged children.…”

Section: Resultsmentioning

confidence: 99%

Solar Radiation and the UV index: An application of Numerical Integration, Trigonometric functions, Online Education and the Modelling Process

Downs

Parisi

Galligan

et al. 2015

IJRES

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A short series of practical classroom mathematics activities employing the use of a large and publicly accessible scientific data set are presented for use by students in years 9 and 10. The activities introduce and build understanding of integral calculus and trigonometric functions through the presentation of practical problem solving that focuses on Public Health and developing a personal understanding of solar ultraviolet radiation and the UV Index. The classroom activities are presented using an approach that encourages self-discovery of mathematical concepts by application of mathematical modelling. These activities also develop critical thinking skills through application of data mining, data processing and presentation. They also emphasize the importance of drawing valid conclusions, concepts important to scientific research, statistics and epidemiology.

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A framework for identifying student blockages during transitions in the modelling process

Cited by 255 publications

References 6 publications

Teachers’ teaching practices and beliefs regarding context-based tasks and their relation with students’ difficulties in solving these tasks

Teachers’ teaching practices and beliefs regarding context-based tasks and their relation with students’ difficulties in solving these tasks

Mathematical Modeling: A Bridge to STEM Education

Solar Radiation and the UV index: An application of Numerical Integration, Trigonometric functions, Online Education and the Modelling Process

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