Does it make more sense to teach the Second Fundamental Theorem of Calculus before the First Fundamental Theorem of Calculus? An AP® Calculus curriculum module explores the interesting question. A set of five worksheets first looks at...

It'd be a shame to get a question wrong just by not accounting for the domain. An article on AP® Calculus looks at the importance of considering the domain of solutions to differential equations by looking at examples from past AP®...

Take a closer look at increasing and decreasing behavior by zooming in on graphs. An AP® Calculus reference document examines how increasing/decreasing behavior should be considered in terms of intervals rather than points. The resource...

Differentiable or not, that is the question. An informational website gives two theorems on the differentiability of piecewise functions at their endpoints. It goes on to apply the theorems to present two solution methods to a past AP®...

Ready to field questions about slope fields? An article on AP® Calculus teaching methods describes how to teach about slope fields to solve differential equations. It gives some sample problems to consider with the class and how to...

Local linearity isn't the first thing that comes to mind to start off an AP® Calculus course. A scholarly article discusses one possible beginning to the AP® Calculus course: investigating and introducing derivatives through activities...

It's important to spice up your lessons. An online article discusses teaching strategies for AP® Calculus. In-class activities include matching games, placemats, multiple choice questions, scripted discussion, involuntary discussion,...

All's fair in math and war. Scholars examine the Battle of Trafalgar using calculus. They set up and solve a system of differential equations to determine the number of ships remaining in each fleet over time.

What's the most common type of problem assessed on the AP® Calculus exam? Why motion, of course. A curriculum module for AP® Calculus provides suggestions on instruction for position, velocity, and acceleration problems. It encourages...

Knowledge of definite integrals is fundamental to the understanding of calculus. Instructors of an AP® Calculus course consult a comprehensive guide to the Fundamental Theorem of Calculus. The document provides teaching suggestions and...

Sometimes close enough is appropriate. A curriculum document for AP® Calculus examines the importance of providing approximation questions throughout the course. It looks at approximating derivative values, approximating definite...

Here's a solid resource for solids of revolution. Volumes of solids of revolution with a line of rotation other than the x- or y-axis give learners a difficult time. An AP® Calculus curriculum module provides instructors with four...

No need to go to extreme lengths to find resources on extrema. The central focus of an AP® curriculum module is on critical points and extrema, and how to cover these concepts throughout the course. A set of three worksheets helps assess...

Functions defined by integrals need to be carefully integrated into the course. An AP® Calculus curriculum module discusses functions defined by integrals. It explains several reasons why pupils have difficulty with the concept and...

Don't table the resource—use it now. An AP® Calculus curriculum module encourages the use of tabular data throughout the course. It provides some example topics, such as rate of change, net change, and average value of a function, where...

Need some help teaching differential equations? Here's a perfect resource for you. An analysis of differential equations gives instructors a better understanding of the concept. The resource gives suggestions on how to incorporate...

Motivation is key to learning. The author points out that it is important to engage intuition for aspects of statistics that pupils find counter-intuitive. Three strategies—using multiple representations, using intuitive analogies, and...

Unlike mathematics, statistics comes with a context. The author reminds teachers that data analysis involves using the context to make sense of the numbers. The article stresses good communication skills by highlighting the scoring...

But this is math—we don't need to know how to write! The article makes a point that class members in AP® Statistics should be comfortable writing as the exams require it. Individuals quickly realize that quality writing is crucial to a...

Not explaining reasoning falls short of perfect. The article covers problem number four on the 2005 AP® Calculus BC exam. Using a similar problem, the author discusses the Euler Method procedure to answer the question. With the...

It's not always easy to persuade others. However, it may even be harder to teach others how to be persuasive. Educators get personal insight from Brent Staples, an influential commentator, as well as gain ideas and activities on teaching...

Sample some statistics with Satterthwaite. Instructors of AP® Statistics read up on the Satterthwaite formula for degrees of freedom in the two-sample t-test. They see where it comes from and learn about the mathematics underpinning the...

Calculators sure come in handy. An AP® Statistics instructional resource provides suggestions for using calculator simulations. It gives activities for adding variances, normal probability plots, and t distributions.

Plan to use the activities on planning studies and experiments. A curriculum module for AP® Statistics gives instructors some useful information on how to conduct studies, sample surveys, and experiments. It also has some ideas for...