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• W2593456887 abstract "Since there are many theoretical perspectives on modeling (Sriraman, Kaiser, & Blomhoj, 2006) - and no consensus as to a definition of mathematical modeling (Cai et al., 2014) -assessments of mathematical modeling tend to be ad hoc or based on experience rather than theoretically grounded (Frejd, 2013). Therefore, research presented here sought to take advantage of modeling task principles in order to generate tasks that would evoke students' mathematical modeling processes. Typically in research reports, smallest amount of space is accorded to instrument development despite fact that all data, results, interpretations, and conclusions are derived from instrument and therefore dependent upon its genesis. This paper attempts to make transparent considerations and decisions that are present in a researcher's logs but that typically are cut from dissemination of results. I then use these ideas to reflect on domain-specific theory of modeling cycles and methods used to tasks.Theoretical PerspectivesSituating Task Design ProjectKieran, Doorman, and Ohtani (2015) reviewed of sets of principles for task in mathematics education studies. The review was organized around two dimensions. The first dimension was scope of theory informing research objectives (grand, intermediate, or domain-specific) and second was whether could be characterized as as implementation or as intention. Design as implementation studies focus attention on the process by which a designed sequence is integrated into classroom environment and subsequently is progressively refined (Kieran et al., 2015, p. 28). This is consistent with how research projects are understood(Cobb, Confrey, DiSessa, Lehrer, & Schauble, 2003). In contrast, as intention studies address initial formulation of design and use well developed theoretical frames in order to provide clarity and coherence to intention (Kieran et al., 2015, p. 28). Grand theoretical frames explain learning in general (e.g., cognitive constructivist or social constructivist theories). Intermediate-level frames can be applied across many mathematical areas and domains (e.g., theory of didactical situations). Finally, domain-specific frames specify reasoning processes (e.g., conjecturing or modeling) or content (e.g., place value, geometry).Using Kieren et al.'s dimensions, I can situate this task project as as intention using a domain-specific theory. The objective of research program was to study mathematical thinking from within a mathematical modeling paradigm. The participants were to be undergraduate engineering students in a course on differential equations. One sub goal of this project was to create an observational rubric that could be used to systematically observe students' modeling activity as it unfolded. Thus, domain-specific theories related to mathematical modeling processes were adopted. The creation of rubric was to be guided by microanalysis of students' work on modeling tasks within a one-on-one interview setting. This required a bootstrapping approach that studies are able to handle (DiSessa, Cobb, & Disessa,2004, p. 85). The tasks and rubric were developed through an iterative process grounded in students' mathematical modeling. The development of rubric through qualitative analysis of students' work on tasks is presented elsewhere (Czocher, 2016).The tasks designed needed to satisfy a particular intention, namely, evoking students' modeling processes so that those processes could be documented systematically. The goal in designing tasks was not to create a direct measure of students' competencies nor to teach modeling. Instead, it was an attempt to study and explain in greater detail components of mathematical modeling identified by literature as central to mathematical modeling process or as difficult for students. …" @default.
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• W2593456887 date "2017-01-01" @default.
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• W2593456887 title "Mathematical Modeling Cycles as a Task Design Heuristic" @default.
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