The jumble of rules for taking derivatives never truly clicked for me. The addition rule, product rule, quotient rule — how do they fit together? What are we even trying to do?

Here’s my take on derivatives:

• We have
… Read article

How do you wish the derivative was explained to you? Here's my take.

Psst! The derivative is the heart of calculus, buried inside this definition:

But what does it mean?

Let's say I gave you a magic newspaper that listed… Read article

Sine waves confused me. Yes, I can mumble "SOH CAH TOA" and draw lines within triangles. But what does it mean?

I was stuck thinking sine had to be extracted from other shapes. A quick analogy:

You: Geometry is … Read article

Calculus examples are boring. "Hey kids! Ever wonder about the distance, velocity, and acceleration of a moving particle? No? Well you're locked in here for 50 minutes!"

I love physics, but it's not the best lead-in. It makes us wait… Read article

Euler's identity seems baffling:

It emerges from a more general formula:

Yowza -- we're relating an imaginary exponent… Read article to sine and cosine! And somehow plugging in pi gives -1? Could this ever be intuitive?

Not according to 1800s mathematician Benjamin

So many math courses jump into limits, infinitesimals and Very Small Numbers (TM) without any context. But why do we care?

Math helps us model the world. We can break a complex idea (a wiggly curve) into simpler parts (rectangles):… Read article

Integrals are often described as finding the “area under the curve”. This description is misleading, like saying multiplication is for finding “the area of a rectangle”. Finding area is a useful application… Read article, but not the purpose. Integrals help us

Accepting that numbers can do strange, new things is one of the toughest parts of math:

• There’s numbers between the numbers we count with? (Yes — decimals)
• There’s a number for nothing at all? (Sure — zero
… Read article

Pi is mysterious. Sure, you “know” it’s about 3.14159 because you read it in some book. But what if you had no textbooks, no computers, and no calculus… Read article (egads!) — just your brain and a piece of paper. Could you