Course Syllabus

TMATH 124 E/F: Calculus with Analytic Geometry I  •  Instructor: Erik R. Tou  •  Link to Drop-in Hours

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Course Description

From the Catalog: First quarter in calculus of functions of a single variable. Emphasizes differential calculus. Emphasizes applications and problem solving using the tools of calculus. Cannot be taken for credit if credit earned in TMATH 122. Prerequisite: a minimum grade of 2.0 in either TMATH 116 or TMATH 120, minimum score of 68 on the MPT-A, minimum score of 75 on the MATHEC test, minimum score of 2 on the AP MATH test (AB or BC), minimum score of 276 on the ACC-AAF test, or a minimum score of 500 on the Tacoma Directed Self Placement Math Test; Recommended co-requisite: TMATH 159.

From the Instructor: At its most basic level, calculus is a blend of algebra and geometry, and these two fields are bound together with analysis—coordinates, functions, limits, and derivatives. In this course, we will ex-amine modern differential calculus for single-variable functions, and explore its many applications in the sciences. More generally, the techniques developed in this course will aid you in critical thinking and problem-solving, in addition to providing an appreciation for the more abstract structures that mathematics seeks to understand.

Student Learning Outcomes

By the end of the course, students should be able to:

• #1. apply pre-calculus concepts in the calculus setting to solve problems,
• #2. compute limits,
• #3. determine if a function is continuous,
• #4. find the derivative using its definition,
• #5. differentiate algebraic, exponential, trigonometric, and logarithmic functions, as well as combinations
  of these functions and their inverses,
• #6. apply differentiation techniques to find tangent lines, rates of change, and local extrema,
• #7. set up and solve related rates and optimization problems,
• #8. apply differentiation to find information about a function’s graph,
• #9. demonstrate the relationship between derivatives and integrals by applying the Fundamental Theorem of Calculus.

Course Format

This is a partially hybridized course, which means I will use a combination of in-person and online activities to guide your learning process. My teaching philosophy is based on growth-focused grading, which will conform to the following learning sequence:

1. Absorb the material – for each concept, watch the video lecture(s), read the textbook, engage with interactive demos, etc., following the resources provided in the concept study guide.
2. Practice the material – complete the WebAssign homework for the week.
3. Discuss and inquire – attend class, participate in exercises and group discussions, ask follow-up questions on assignments.
4. Show what you've learned – complete each unit quiz and project, make quiz revisions and post reflections as needed, retest quiz topics as needed.

Components 1 and 2 will occur before our weekly class meeting, and can be completed on your own schedule. We will meet once each week, for 2 hours, to cover Component 3. Class meetings will be seminar-style, with exercises, group discussion, and reflection activities to build confidence in the current course topics. Component 4 will occur online after each class meeting, with quiz revisions and reflections to follow.

Growth-Focused Grading 

I am doing something different in this course. It's called growth-focused grading, and it's the approach I’ll take for all our quizzes during the quarter. To better explain the what and the why of this approach, here's a comparison with traditional grading: 

Traditional Grading. Readings are assigned for each class day, and give a basis for the class lecture. Homework is usually weekly or biweekly. After a few weeks, a high-stakes exam is given and graded (hopefully quickly!). The class then moves on to the next set of topics. This repeats a couple of times, culminating in a final exam at the end of the term. 

Growth-Focused Grading. Material is assigned in chunks: the textbook is used more as a reference guide, with videos and other resources used as a partial substitute for readings. A quiz is given each week, with questions chosen from a list of concepts. Students read quiz feedback, and have a chance to revise their work before grading, at which point each concept is graded on a pass/fail basis. Concepts can be retested more than once. 

Why do this? Basically, the goal is to make mathematical learning match more closely with real-world learning. We all know that learning something new takes multiple attempts, errors, corrections, and gradual growth. Math should be no different. Moreover, each student brings their unique strengths and weaknesses to the classroom, and should be able to devote less time to proving their strengths and more time to shoring up their weaknesses. In short, growth-focused grading values perseverance and understanding. 

Assignments & Grading 

Your grade in this course will be determined by your performance on reading responses, homework, unit quizzes, mini-projects, and a final exam. These assignments are constructed to guide your progress through the 6 units of course content. 

Homework [20%]: There will be weekly homework assignments in this course, and you'll receive 50% credit for attempting each problem on an assignment. The goal of homework is practice, so assignments will be due before class—this will allow us to discuss difficult problems and concepts together, and focus on under-standing and improvement. 

Concept Quizzes [35%]: After completing all the homework for a given unit, you can take the unit quiz during one of our weekly Thursday testing times. After taking a quiz for the first time, I will provide written feedback, after which point you'll have a week to revise your work and write a short reflection. Then, I'll assign a grade of Proficient (1 pt.) or Needs Improvement (0 pts.). You can retest any topic once more, as needed. 

Mini-Projects [25%]: In addition to testing your understanding of the fundamental skills in each unit, for three of the units I'll ask you to provide a multi-step analysis of a single problem involving a real-life application of Calculus. These will be more in-depth than a typical homework or quiz problem. (Note: unlike quizzes, mini-projects are graded in the traditional way, though I may assign retroactive credit to relevant quiz topics that you've mastered on these assignments.)

Final Exam [20%]: There will be one final exam given at the end of the quarter, on Tuesday, December 14 from 1:30-3:30pm. This exam will combine problems from Units B, C, D, E, F, and some of the mini-projects. Some problems will count retroactively as quiz questions (so if you demonstrate proficiency on a concept you missed on the quiz, I'll go back and revise your score upward). 

Relation to SIAS Goals

The course also supports the following student learning outcomes in the School of Interdisciplinary Arts and Sciences:

• (Env. Sci.) Cultivate skills critical to interpreting scientific concepts for public understanding,
  including familiarity with the scientific method, information literacy, statistical data analysis, hypothesis formulation, and conceptual modeling, research project design and working collaboratively.
• (Env. Sci.) Participate in engaged inquiry as a means of connection classroom learning to real-world environmental problem solving and establishing the skills needed for lifelong learning.
• (Env. Sci) Develop advanced scientific skills necessary to achieve an understanding of and solutions to environmental problems including physical and biological measurement techniques, statistical data analysis, hypothesis formulation and conceptual modeling, research project design and working collaboratively.
• (PPE) Students will strengthen their analytic skills
• (PPE) Students will develop their ability to write with style and precision.
• (PPE) Students will become more competent with quantitative analysis.
• (PPE) Student will develop their ethical and logical reasoning.
• (Info. Tech. & Sys.) Students will be able to apply knowledge of computing and mathematics,
  appropriate to the discipline.
• (Biomed) The ability to apply statistics and other mathematical approaches to examine biological
  systems.

Resources

For information on our textbook and WebAssign, read this announcement. Also check out my drop-in hours for the quarter.

For information on campus and student resources, including Disability Resources for Students, Bias Incident Reporting, and The Pantry, read our course's Campus Resources page.

A complete list of resources is also available at the UW Tacoma e-Syllabus: Campus Information, Resources, Policies and Expectations page.