## Information and Guidelines

- Mathematics Teaching Majors are required to prepare, deliver and pass a 10- to 12-minute calculus presentation.
- The purpose of the calculus presentation is for students to demonstrate aspects of their mathematical content knowledge and communication skills.
- Two faculty members from the Department of Mathematical Sciences will attend the calculus presentation and use a four-level rubric to assess the student's mathematical content knowledge and communication skills.
- The report, with scores and comments, will be emailed to the student no later than one week after all presentations are completed. Scores from the evaluation rubric will be entered into Tk20.

Eligibility & Instructions

- Students may give a presentation after completing MATH 166 (Calculus II or its equivalent).
- A typical presentation will be 10 minutes in length, followed by approximately five minutes for questions and/or discussion.
- The mode of delivery is open. Options include using the chalkboard/whiteboard or a document camera.
- The calculus presentation should include the following components:

- introduction that provides an overview of the topic
- body where you discuss the topic with appropriate detail and illustrative examples
- conclusion that summarizes the content that was shared

Choose a Topic

At the beginning of the term in which they intend to give the calculus presentation, students should choose a topic for their presentation.

Topics may be selected from the following list of topics that are commonly addressed in MATH 165 or 166:

- Continuity
- Definition of the definite Riemann integral
- Definition of the derivative
- Derivation of the power rule for derivatives
- Derivatives of the trigonometric functions
- Derivatives of logarithmic and exponential functions
- Intermediate Value Theorem
- Limits
- Linear and quadratic approximations
- Mean Value Theorem
- Newton’s method
- Related rates
- Alternating series
- Arc length
- Convergence/divergence of sequences and series
- Convergence tests for positive-termed series
- Fundamental Theorem of Calculus
- Improper integrals
- Maclaurin series
- Numerical methods for estimating definite integrals
- Power series
- Taylor series / Taylor’s Theorem
- Volumes and surface areas of surfaces of revolution

Tips & Suggestions

- In a short talk, you cannot do everything that you would do in a real class. Ten minutes is not a long time!
- Rehearse the delivery so you are not reading from your prepared notes (except when complex formulas or numerical data arise).
- Whether or not there is enough time to present the proof of a theorem, you should be able to talk intelligently about the proof if asked.
- Strive for clear diction, and speak meaningfully. Face the audience.
- Be very alert to proper use of terminology and notation, especially be careful with the use of the equal sign, but avoid undue usage of technical terms.
- Think carefully about the mode of presentation (chalkboard/whiteboard or document camera). On the one hand, if there is a substantial amount of information to show, then there may not enough time to write everything out. On the other hand, writing out at least some of the content (e.g. examples) during the talk is important to demonstrate written communication.
- Practice writing on the chalkboard/whiteboard or document camera. Keep information up long enough for the faculty to read the text.
- If using the chalkboard/whiteboard, begin on the upper left portion of the board, and produce columns of writing that progress to the right end of the board. In general, do not erase until you require more board space.
- Color may be used, but make sure that it is dark enough to be seen.
- Be enthusiastic and cheerful.
- Consider having a fellow teaching major observe you presenting a practice run of your talk. They may notice flaws that have escaped your attention.
- The most common reasons not to pass a calculus presentation are:

- not deeply understanding the mathematical topic
- making improper or incorrect use of terminology or notation

## Schedule Your Presentation

Deadlines for submission of the registration form are September 6 for fall term presentations and February 7 for spring term presentations. The completed registration form should be returned to the Department of Mathematical Sciences Office in Robert Bell Building (RB), room 465.