ERIC Number: EJ1026048
Record Type: Journal
Publication Date: 2013-Aug
Reference Count: 8
The Footprint Problem: A Pathway to Modeling
Imm, Kara L.; Lorber, Meredith D.
Mathematics Teaching in the Middle School, v19 n1 p46-54 Aug 2013
This article describes "modeling" as the act of creating an "idealized version of a real-life situation" that has been "translated into mathematical terms." By exploring an open-ended investigation involving proportional reasoning, sixth grade students were able to walk through both problem solving and modelling. The authors used as an example the "Footprint problem" where the students were not asked to find the height of a particular person whose footprints were left behind, but to develop a "how to" tool kit that could be generalized for any footprint. This problem-solving task of "modeling" was an iterative activity that began with a situation and lead to the formulation of a mathematical question or problem. This different kind of thinking was required because "real-world situations are not organized and labeled for analysis," thus, students were required to formulate, sort, prioritize, and make sense of the problem at hand. When teachers think of "modeling" as a way to create mathematics, not simply as a place to apply the mathematics currently possessed, then students' notions are shifted from mathematics-as-procedure toward mathematics-as-interpretation.
Descriptors: Mathematical Models, Thinking Skills, Problem Solving, Middle School Students, Grade 6, Urban Schools, Class Activities, Social Environment, Feedback (Response), Mathematics Instruction
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: email@example.com; Web site: http://www.nctm.org/publications/
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Grade 6; Middle Schools
Authoring Institution: N/A