Designing Tasks For Math Modeling In College Algebra: A Critical Review

Abstract

ABSTRACT

Secondary Teacher Candidates’ Mathematical Modeling Task Design and Revision

“…This study sheds light on one possible use of the design of mathematical modeling tasks as a learning activity in teacher education. Existing frameworks [5][6][7][8] on mathematical modeling mainly highlight the use and process of student learning through modeling activities in the classroom. However, the framework did not say much about how the teacher may facilitate modeling activities and support students.…”

“…In Maaβ [6] and Staats and Robertson [7], the modeling process framework connects two domains, such as reality and mathematics, and identifies the steps involved in mathematical modeling as simplifying, mathematizing, working within the mathematics, interpreting, and validating. Hernández et al [5] add more components to the modeling process, such as "identifying the problem" and "iterating", which has the effect of underscoring mathematical modeling as a human activity.…”

“…Park et al [17] used spreadsheets in a modeling task to teach derivatives and integrals. At the post-secondary level, Staats and Robertson [7] introduce a calendar game in teaching college algebra, and Harwood [18] illustrates modeling tasks with multiple themes. These studies document an approach to teaching modeling that features a prescribed cycle of modeling steps generally categorized into a situation, mathematizing, building mathematical models, solving the problems, and validating and interpreting the solutions.…”

Extending Universal Design for Learning through Concurrent Enrollment: Algebra Teachers’ Perspectives

“…Mathematical modeling is a professional approach in applied mathematics in which an initial solution is improved systematically through multiple cycles of problem-solving [17]. In the U.K. and in Europe, mathematical modeling has been used as a teaching approach in secondary and early undergraduate mathematics classes since at least the 1980s, but has only begun to enter early undergraduate mathematics teaching in the U.S. over the last fifteen years [18]. Using the modelling perspective, students create mathematical methods for solving realistic problems instead of recreating a predetermined method that the teacher demonstrates.…”

“…Several teachers, however, commented on how difficult it was to learn to grade writing, and that they do not enjoy this aspect of the class. Rating student explanations that are different from each other, and that are presented in writing, is a long-standing challenge for teachers using mathematical modeling pedagogy, but several useful guides for grading written mathematical reports exist (see [18,32]). Three teachers also noted that the writing component of the course could be a barrier for English Language Learners: I think the write-up part is hard for some of my ELL students.…”