When I was taught math, the focus was mostly on the “how”:
- How to multiply numbers.
- How to work with fractions.
- How to use calculus.
But even more useful is to know the when:
- When to multiply numbers.
- When to work with fractions.
- When to use calculus.
Knowing how to do something is useful, but it’s just knowledge of one tool.
For example, take a hammer. It’s nice to know how to bang in a nail without sending yourself to the hospital, but not all situations require a hammer. To select the best tool for the job, we need to know “when” each tool should (or shouldn’t) be used.
Especially nowadays, where computers can solve so many mathematical problems for us, knowing “when” allows us to navigate choice, and select between multiple tools. Once we select the right tool, then it’s easy to find the resources to teach us the “how” part.
I ran a bunch of Google searches for “when should I use x?”, and collected them into a list:
Joining multiple items together.
Removing items from a set.
Repeating a set of items.
Breaking a set of items into parts.
Working with partial units.
Abbreviating large numbers.
Describing how multiple variables relate to each other.
Visualizing math with drawings.
Working with sets of equations.
A language for reasoning.
Finding all possible outcomes.
Discovering relationships between numbers.
Finding aproximate solutions to equations.
Gathering, reviewing, analyzing, and drawing conclusions from data.
Extracting algorithms from data.