Mathematics is a deductive science that requires rigorous proof of discovered facts about numbers and shapes. It employs the axiomatic method of inquiry in its method and modes of presentation of its discoveries and creations. Along with other academic departments at Principia College, the Mathematics Department has identified various learning outcomes each mathematics student, minor, and especially major needs to demonstrate in his or her work and habits of learning. The nine learning outcomes for mathematics are based on the following objective for mathematics minors and majors.
Learning Outcomes Objective: To coordinate with Principia’s mission to serve the Cause of Christian Science, the Mathematics Department at Principia College continues to encourage majors and non-majors in mathematics to strive to become careful, compassionate, creative, tolerant, logical, analytical, and critical thinkers and problem solvers. Since Christian Science is also a deductive science, students of mathematics should be guided through their courses of study to demonstrate to a significant degree the usage, understanding, and assimilation of the following learning outcomes. These outcomes are intended to promote the proper practice of deductive reasoning necessary for both mathematics and Christian Science.
Learning Outcomes for Mathematics:
1. Problem Solving
Our students should accurately assess problems and think about them creatively, conceptually, critically, insightfully, analytically, and metaphysically. They should choose appropriate processes and heuristics and apply them skillfully and confidently to gain the solution.
2. Reasoning and Proof
Our students should understand as well as create proofs using both direct and indirect deductive methods. They should also be able to use induction to analyze patterns and formulate conjectures about them.
3. Abstraction and Generalization
Our students should identify the character and underlying properties of mathematical objects.
4. Modeling and Representation
Our students should analyze contextual constructs and create appropriate mathematical models which reflect the fundamental features of the constructs.
5. Effective Communication
Our students should convey and receive information and ideas accurately, consistently, and efficiently in oral, visual, and written form, formally and informally across a diversity of audiences. Good communication necessitates honesty and effectual listening.
6. Intellectual Integrity
Our students should embody intellectual integrity in discovering and presenting solutions to problems and answering questions.
Our students should recognize and create connections between mathematics and other disciplines and within mathematics itself.
8. History and Development of Mathematics
Our students should demonstrate knowledge of the historical and cultural context of mathematics as it has evolved over the centuries.
9. Facility with Computer Tools and Algorithmic Thinking
Our students should use computerized tools such as programming languages, calculators, and software such as Mathematica to explore mathematical concepts visually, verbally, symbolically, and numerically, thereby getting insight into the underlying mathematics.