Before Calculus

Topics from earlier math courses

Arabic: the unknown thing

Unknown Thing – A link to a TED talk explaining why we use x for the “unknown.”

Show Me the Math! – A note on Is God a Mathematician? by Mario Livio, an excellent book on how math works. A discussion of whether mathematics was invented or discovered.

Absolutely – Notes on teaching absolute value with a quiz and Absolute Value with the answers to the quiz and a further discussion.

The Opposite of Negative – On the use of the minus sign: get it right from the start.

Stamp Out Slope-intercept Form! – Starting in Algebra 1 write equations of lines using point-slope form It’s easier; it’s faster.  

A Note on Notation – A personal preference to make things clearer.

For Any – For Every – For All – Three phrases that mean the same thing. Use them all every time!

On Inverse functions (The first three of five posts on inverses. The others which involve calculus are in Unit 3)

                Inverses – The basic idea leads to two concerns.

                Writing Inverses – Concern 1: What if you can’t solve for y?

                The Range of the Inverse – Concern 2: What if the inverse is not a function?

Inequalities – Solving inequalities the easy way

My Favorite Function – A graphing calculator exploration.

Amortization – An important real-life use of Geometric Series – no calculus involved.

Teaching and Learning Theorems – The things students should know about theorems.

A Lesson on Sequences – All real numbers are sequences. No calculus here.         

A Problem with 4 Solutions and 2 Morals – Simplifying radicals. A post for trig and calculus.

Mathematical Structure

Theorems = Notes on learning theorems.

Theorems and Axioms – Notes on theorems and axioms.

Definitions – Notes on learning definitions.

Definitions 2 – How to write a definition and therefore what to look for in your textbook’s definition.

Proof – To prove or not to prove.

Then there is this – Existence Theorems – Explains existence theorems.