Heating and Cooling in a Bakery

Undergraduate Students Gala Comacho, Colby Kaess
Date of Involvement 2007
Faculty Advisor Jim Curry and Anne Dougherty

Background

A tour of the local Great Harvest Bread Company inspired this research project. A bakery consists of several heating and cooling processes that can be replicated using the appropriate heat equations. During the fall semester of 2006, there were four total bakery processes modeled: the cooling of flour after milling, the heating of honey in a barrel to maintain proper viscosity, the simultaneous heating and cooling processes of the dough as it proofs and rises along with the fermentation that occurs, and the baking of the dough into bread. Experiments were devised to find empirical data to validate these representations.

Mr. Scott Creevy, the owner of the Boulder Great Harvest Bread Company, offers support for this project with his knowledge of baking and experimental samples, as well as allowing students to explore and conduct experiments in his bakery.

Process

A second-order partial differential equation was chosen to model these three-dimensional heating processes. Both analytical and numerical solutions were designed to reflect the phenomena and outcomes of the heat equation. These were found in the form of Fourier series by applying the Fourier separation of variables method and the superposition concept.

Two semester projects which focused on modeling the heating and cooling occurrences in a bakery will be discussed together in a single paper. Student efforts will focus on three specific goals: developing an experimental module for use in future Fourier Series and Boundary Value Problems courses, isolating and correcting any errors in the models and analytical solutions for the various phenomena, and consolidating research into a paper suitable for publication in a mathematical journal.

Metacognition and the APPM 4350 Bakery Project

A document is currently being developed to serve as a guide for future students enrolled in the program to do this experiment and create their very own Heating and Cooling in a Bakery project. The authors refer to this document as a metacognitive guide that can be used for other mathematical modeling projects, but is specifically designed for the APMM 4350 bakery project.

Metacognition, the idea of self-monitoring while solving a problem, has been linked to success in mathematics and science in prior mathematics education research. Metacognition involves being aware of your own learning, paying attention to every step you take towards solving a problem, and assessing the importance and goal of each step in the progression. Utilizing this process requires that one stop working for a few minutes, take a step back, and consider in which direction the work is headed taking care to evaluate progress within the context of upcoming project goals.

The metacognitive guide gives students a set of questions that will help build the path to developing a mathematical model. However, this guide will not act as a cookbook-like set of steps to complete. The questions given will provide guidance to be able to explain what investigators are thinking, why they are thinking it, and how they can back it up with solid evidence. This project is strictly to help college students develop into a metacognitive state of mind while doing research.

About Colby Kaess

Colby is currently pursuing undergraduate degrees in Aerospace Engineering and Applied Mathematics. His professional interests include human space exploration and rocket propulsion systems. He is a member of the International Mars Society as well as the American Institute of Aeronautics and Astronautics (AIAA).

About Gala Comacho

Gala is currently an Applied Mathematics undergraduate at The University of Colorado at Boulder, as well as seeking a degree as a Secondary Mathematics Educator. She is originally from Mexico City where she spent most of her life, and aspires to work all over the world in international schools as a high school math teacher. Eventually she hopes to become a college professor. She currently works as a Learning Assistant for Calculus 1, and at the Fiske Planetarium as a docent.

References

Hammer, D. (1994), Epistemological beliefs in introductory physics; Cognition and Instruction, (12) 2.

Schoenfeld, A. (1987). What's All the Fuss About Metacognition?, In A. Schoenfeld (Ed.) Cognitive Science and Mathematics Education, Hillsdale, N.J. : Lawrence Erlbaum Associates, 189-215.

Jimenez-Aleixandre, M., Rodrigues, A., Duschl, R. (2000). "Doing the Lesson" or "Doing Science".

Lederman, N.G. (1998), The state of science education: Subject matter without context; Electronic Journal of Science, (3) 2.