Mathematics Teaching Majors are required to prepare, deliver and pass a 10-12 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 4-level rubric to assess the student's mathematical content knowledge and communication skills. Their 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 rGrade.

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 5 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

**Step One: 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

**Step Two: Schedule your Presentation**

Deadlines for submission of the registration form are September 7 for fall term presentations and February 8 for spring term presentations. The completed forms should be returned to the Department of Mathematical Sciences Office (RB 465).

**Step Three: Prepare your Presentation**

What follows are tips and suggestions that have been compiled by faculty members:

● Do not bite off too much. In a short talk, you cannot do everything that you would do in a real class. 10 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 not 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 of the material from a student’s perspective. Each time you consider an example or an explanation, ask yourself, How will a student (who is not as up on this as I am) really interpret this?

● 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

**EVALUATION OF THE CALCULUS PRESENTATION **The faculty committee will use a 4-level rubric to evaluate the calculus presentations. Each faculty committee member will use the rubric to rate components of the presentation and will give an overall rating. The ratings from each of the three faculty committee members will be compiled and presented to students as a single report.