Modeling Applied to Problem Solving

Abstract

Abstract. We describe a modeling approach to help students learn expert problem solving. Models are used to present and hierarchically organize the syllabus content and apply it to problem solving, but students do not develop and validate their own Models through guided discovery. Instead, students classify problems under the appropriate instructor-generated Model by selecting a system to consider and describing the interactions that are relevant to that system. We believe that this explicit System, Interactions and Model (S.I.M.) problem modeling strategy represents a key simplification and clarification of the widely disseminated modeling approach originated by Hestenes and collaborators. Our narrower focus allows modeling physics to be integrated into (as opposed to replacing) a typical introductory college mechanics course, while preserving the emphasis on understanding systems and interactions that is the essence of modeling. We have employed the approach in a three-week review course for MIT freshmen who received a D in the fall mechanics course with very encouraging results.

A Simulated peer-assessment approach to improve students’ performance in numerical problem-solving questions in high school biology

“…Researchers in the field of physics education have investigated numerical problem solving for at least three decades (Hsu, Brewe, Foster & Harper, 2004). This has focused on the definition of problems in physics (Heller and Reif, 1984), the investigation of how students solve problems (Larkin, McDermott, Simon & Simon, 1980), and the development of effective pedagogy to effect deep learning (Heller and Hollabaugh, 1992;Pawl, Barrantes, & Pritchard, 2009). It has been argued that the use of mathematics in physics is more complex than the application of rules and calculations that students are taught in a mathematics class (Bing & Redish, 2009).…”

Toward an Integrated Online Learning Environment

“…Our pedagogical emphasis is Modeling Applied to Problem Solving (MAPS) pedagogy [2], but the curricular materials are editable and re-arrangeable to accommodate any pedagogy. MAPS was able to raise students' problem-solving skills from D-level to B-level in a three-week intensive ReView Mechanics course at MIT.…”

“… It involves Modeling Applied to Problem Solving (MAPS) [2] -a promising pedagogy to imparting strategic knowledge.  The integrated environment is available to others wishing to extend it to other subjects.…”

Development of a mechanics reasoning inventory

“…Since 2009 the authors have been responsible for a three-week January "ReView" course at MIT offered to students who have just completed the regular mechanics course (8.01) with a grade of D which is explicitly designed to provide intensive training in the type of reasoning that the inventory is designed to test. It has proved successful in elevating the problem solving ability of the students [11]. The inventory was administered as a pre-and post-ReView assessment in 2010 and 2011 to a total of 77 students.…”