When we think of the material covered by a course, it’s common to think about the topics we cover: linear functions, transformations of functions, etc. But doing math is a holistic practice that cultivates a variety of useful skills and approaches to thinking, and the skills that students build around their mathematical knowledge serve their long term academic and career needs as much as the mathematical topics students learn in the course. Among the these skills are the following, with explanations of what they allow students to do. Below, we list the mathematical topics we cover.
| Mathematical Fluency | 1. Use appropriate mathematical concepts and techniques with fluency, including defining key terms, calculating solutions, and identifying relationships between different kinds of functions. |
| Rule of 4 | 2. Translate concepts of functions between four points of view (i.e., the “Rule of Four”): geometric (graphs), numeric (tables), symbolic (formulas), and verbal (words), with a particular emphasis on translating between words and other representations. |
| Problem-solving | 3. Develop approaches to solving mathematical problems, including breaking down and organizing provided information, choosing appropriate methods to solve a problem, and reassessing and shifting strategies when challenges are encountered. |
| Modeling | 4. Model a real-life situation using an appropriate function. 5. Make predictions and conclusions using a model about a situation. |
| Communication | 6. Clearly communicate mathematical ideas using precise language, including verbally, in writing, and with appropriate diagrams. |
| Teamwork | 7. Work productively on your teams and with your whole class to learn and solve problems, including asking questions and sharing ideas respectfully, listening to understand, supporting classmates, and valuing the perspectives and experiences of others. |
| Reflection | 8. Analyze solutions and answers to determine whether they are reasonable. 9. Reflect on your learning process and progress, including identifying what you know, what you need more help in, how you can continue improving, and when and how to get help. |
| Attitudes about Math | 10. See yourself as capable of doing and persevering in mathematics; and see mathematics as worthwhile. |
Mathematical Content
The mathematical content that we cover in Math 105 include the essential topics of pre-calculus mathematics. In broad terms, we cover functions and rates of change, common types of functions and how we use and change them. A more formal topic list is:
- Linear Functions and Change
- Functions
- Quadratic Functions
- Exponential Functions
- Logarithmic Functions
- Transformations of Functions and Their Graphs
- Trigonometry and Periodic Functions
- Triangle Trigonometry and Polar Coordinates
- Trigonometric Identities, Models, and Complex Numbers
- Compositions, Inverses, and Combinations of Functions
- Polynomial and Rational Functions
