Developing Mathematical Intuition by Building Estimation Skills

Open-ended problems are challenging for many students because they often have little sense of what a “correct” answer would be and struggle with evaluating the quality of an answer derived from a calculator or computer model. It is difficult for them to see patterns or associate one type of problem with another and they have few intuitive skills to use to judge the completeness of their answers. These can be significant obstacles for students who don’t define themselves as mathematicians, but whose careers require what we will call “mathematical intuition” to support the use of technology in solving problems and to anticipate a correct solution. The goal of this paper is to describe a project-based learning experience that has the potential to help students build their mathematical intuition by requiring them to formally estimate within the solution process. By requiring estimations, the project becomes open-ended; students understand that their answers are not exact, or ‘right’, but are still valid. Framing the project as one that corresponds well to students’ sense of what one ‘does’ in their discipline provides a greater degree of student autonomy in completing the project because they understand what a completed project should look like. Finally, allowing students to work in teams encourages the dialogs that often help establish the ‘reasonableness’ of the results. This project was assigned to two groups of lower division students in media arts and engineering, taught, respectively, by the two authors.