Math With Meaning The argument for strong, relevant, and timely technical prerequisites. Thomas Frankie and Brian Schertz University of Illinois at Urbana-Champaign Engineer of the Future 2.0 Summit March 31 – April 1, 2009 Olin College Needham, MA

Justification for Technical Prerequisites Math is a prevalent component of engineering curricula. These courses demonstrate the ability of the student to learn and apply difficult technical concepts to solve problems. Math is the toolbox at the engineer’s disposal.

Math is a prevalent component of engineering curricula.

These courses demonstrate the ability of the student to learn and apply difficult technical concepts to solve problems.

Math is the toolbox at the engineer’s disposal.

Challenges Faced Attrition due to traditional “weed-out” courses Varying preparedness level of students that are retained Inability to perform at higher levels due to rusty, unorganized, or incomplete toolboxes Balance of these courses with important non-technical electives

Attrition due to traditional “weed-out” courses

Varying preparedness level of students that are retained

Inability to perform at higher levels due to rusty, unorganized, or incomplete toolboxes

Balance of these courses with important non-technical electives

Further Fundamental Challenge Engineering Professors: Often lack a knowledge of the topics covered in courses in the math department Do not know if and how certain material was taught in prerequisite courses Mathematics Professors: Often do not have an understanding of how the topics they teach will be applied in future engineering courses Have limited contact with and investment in the engineering undergraduate students throughout their education

Engineering Professors:

Often lack a knowledge of the topics covered in courses in the math department

Do not know if and how certain material was taught in prerequisite courses

Mathematics Professors:

Often do not have an understanding of how the topics they teach will be applied in future engineering courses

Have limited contact with and investment in the engineering undergraduate students throughout their education

How can courses better help the student? Mathematics applied to engineering problems Timely instruction of material Not all at the beginning of the undergraduate years Taught just in time to be effectively applied Taught by faculty with an interest/investment in the students Cooperation between Engineering and Math Departments Beneficial to each department to have motivated students

Mathematics applied to engineering problems

Timely instruction of material

Not all at the beginning of the undergraduate years

Taught just in time to be effectively applied

Taught by faculty with an interest/investment in the students

Cooperation between Engineering and Math Departments

Beneficial to each department to have motivated students

Traditional System vs. Proposed System Advanced mathematics taught within Math Department No math courses taught. Junior-Senior Years Toolbox growing, new pieces, continued use Rusty, unused toolbox Smaller, simpler, and more efficient toolbox New, cluttered, overly complex toolbox Applied Engineering Mathematics and Introductory Engineering Courses Standard Calculus Sequence in Math Department Freshmen-Sophomore Years Proposed System Traditional System

Desired Effect/Intended Results Students that are: Still in the field of engineering Better equipped and prepared Thinking more critically Students with: More motivation Complete toolboxes

Students that are:

Still in the field of engineering

Better equipped and prepared

Thinking more critically

Students with:

More motivation

Complete toolboxes

Examples of Existing Studies/Models MIT Study (Karen Willcox, Gergana Bounova) “ Mathematics in Engineering: Identifying, Enhancing and Linking the Implicit Mathematics Curriculum” Wright State University Model NSF Grant “A National Model for Engineering Mathematics Education” http://www.engineering.wright.edu/cecs/engmath/

MIT Study (Karen Willcox, Gergana Bounova)

“ Mathematics in Engineering: Identifying, Enhancing and Linking the Implicit Mathematics Curriculum”

Wright State University Model

NSF Grant “A National Model for Engineering Mathematics Education”

http://www.engineering.wright.edu/cecs/engmath/