Riverside Community College District
Integrated Course Outline of Record

Mathematics 32

Define the concept and identify the components of an argument.

1. Critical Thinking - Generalize appropriately from specific contexts

Translate English sentences into symbolic ones, and vice versa.

1. Critical Thinking - Consider and evaluate rival hypotheses
2. Critical Thinking - Generalize appropriately from specific contexts
3. Critical Thinking - Integrate knowledge across a range of contexts

Define the concepts of validity and soundness and distinguish between them.

1. Critical Thinking - Generalize appropriately from specific contexts

Present arguments in argument form and determine whether they are valid and sound.

1. Critical Thinking - Construct sound arguments and evaluate arguments of others
2. Critical Thinking - Generalize appropriately from specific contexts

Construct symbolizations of arguments and determine their validity using truth value analysis.

1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
2. Critical Thinking - Construct sound arguments and evaluate arguments of others
3. Critical Thinking - Generalize appropriately from specific contexts
4. Critical Thinking - Integrate knowledge across a range of contexts
5. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results

Derive valid conclusions from the premises using equivalences and rules of inference 

1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
2. Critical Thinking - Construct sound arguments and evaluate arguments of others
3. Critical Thinking - Generalize appropriately from specific contexts
4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

• Present class lectures/discussions/demonstrations in order to familiarize students with the elements of formal reasoning.
• Create small group activities in order to provide an opportunity for students to practice skills of formal reasoning with group interaction and support.
• Develop and assign class exercises that build formal reasoning skills.
• Design class handouts to demonstrate logical principles for both visual and verbal learning styles.
• Show videos/films/computer programs that demonstrate or perform logical operations.
• Conduct individual conferences in order to identify strengths, weaknesses, and learning styles.
• Develop and assign web-enhanced/online/distance learning tasks such as further reading and the investigation of logic websites to deepen understanding of formal reasoning.

• Oral reports/presentations aimed to demonstrate knowledge of logical principles.
• Quizzes and examinations designed to evaluate ability to define key concepts, translate statements into symbolic form, and to present, evaluate and formulate arguments.
• Written assignments designed to assess progress in ability to define key concepts, translate statements into symbolic form, and present, evaluate and formulate arguments.
• Group and individual projects designed to demonstrate ability to solve problems in formal reasoning cooperatively with others and to appreciate different approaches to solving such problems.
• Final examination

• Layman, C. S. . The Power of Logic. 3rd ed. McGraw Hill, 2005.
• Bergman, Moor, and Nelson. The Logic Book. 4th ed. McGraw Hill, 2004.
• Copi, Irvin M, Carl Cohen. Introduction to Logic. 12th ed. MacMillan, 2004.
• Johnson, Robert M. . A Logic Book: Fundamentals of Reasoning. Thompson-Wadsworth, 2007.