Course Goals: Math 101, Introduction to Problem Solving

I. Process

The heart of the course is mathematical thinking; process not product.

Students should be able demonstrate:

• The ability to explore mathematical problems they have never seen before. This may include looking at special cases, drawing pictures, developing patterns, or reframing the problem.
• The ability to form and test conjectures.
• The ability to use a variety of standard techniques to solve problems including: working backwards, finding patterns, using parity, thinking logically through a case analysis, and applying mathematics they know to new situations.
• The ability to review their solutions for correctness, subjecting solutions to basic reality checks (does the answer make sense?), or comparing the solution to easy-to-check special cases. 
• The ability to communicate their solutions through well-written explanations.

II. Context 

We want students to leave the course with the knowledge that mathematics is not an isolated academic subject with no connections or purposes outside the classroom.

Students should be able demonstrate:

• An awareness of the applications and importance of mathematics in society. For example the “Careers That Count” booklet exposes students to a broad range of fields which display  mathematics as a creative, people-oriented discipline used to solve human problems. 
• An awareness of some of the political issues surrounding mathematics such as the current reform controversy, gender issues (raised by “Overcoming Math Anxiety” for example), or the race issues brought out by Bob Moses’ Algebra Project.
• An awareness of the Wisconsin Model Standards in mathematics to see the connections between what we do in the course and the standards Wisconsin is setting for school students. This is valuable for our students as future citizens and (in some cases) future teachers.
• The ability to  see work through for themselves at least some relevant applications of mathematics. Examples might be in science (Carbon-14 dating for example), finance (compound interest which is also a model for population growth), genetics (probability theory), and decision theory (expected values).
• An awareness of mathematics’ connections outside the sciences. Examples might include the role of mathematics in Enlightenment philosophy (Descartes, Leibnez, Pascal) or the concept of mathematical beauty.

III. Skills 

Although not the main part of the course we use it as a gatekeeper to ensure students have minimal skills in some areas that are, properly, school mathematics.

Students should be able demonstrate:

• The ability to mentally estimate solutions to pure and applied arithmetic problems.
• Proficiency in simple problems involving percents.

Approved April 7, 2002

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Copyright © 2001 Ken Jewell & Edgewood College All rights reserved.
Revised: June 07, 2004  

For more information please contact:  jewell@edgewood.edu