My series on the nature of multiplication can be accessed best through What Is Multiplication – The Series.
My series on Operators, Functions and Properties is summarized in Operators, Functions and Properties: The Series.
My series on vector algebra and matrix algebra is summarized in Groupings, Shopping Lists, and Vectors: The Series.
A series on different conceptions of “middle” and weighted averages can be accessed through In the Middle – The Series.
My series on Math in the Comics is summarized in Math in the Comics – The Series.
The series on different kinds of quantities is summarized in Quantity – The Series.
The series on when the whole is more than the sum of the parts is summarized in The Whole and the Parts – The Series.
The series on mathematical notation and schools is incomplete. It is summarized in Mathematical Notation and Schools: The Series.
The series on black boxes is incomplete. So far, it has two installments:
Representations – Black Boxes – a way of picturing situations where we are thinking about what it is that drives a certain behavior
Representations – Black Boxes – Equivalence -when different designs drive identical behavior
There is a broader series on Representations, also on-going. Here are the installments:
Representations – Processes and Snapshots – traditional representations – for good reasons – are static. How much is lost?
Representations – Foreground and Background – any representation will relegate certain details to the background and emphasize others by putting them in the foreground. This isn’t bad, and even if it was, it is simply unavoidable. Are the relevant bits in the foreground?
Representations – Formulas and Some Alternatives – we’re used to a particular way of writing formulas. Fine. But no need to be stuck with them.
Representations – Number and Some Alternatives – we’re used to a particular way of writing numbers. Fine. But no need to be stuck with them. Real-life examples of alternatives.
Representations – Black Boxes – when parts of the world have an inside and an outside.
Here is a series, complete for now, which deals with key mathematical ideas (made explicit and articulated in computer science) that are quite simple, important, but somehow never found their way into the normal math curriculum:
Key Math Ideas Not Taught In School – introduction, in response to a TED talk by Arthur Benjamin
Key Math Ideas Not Taught In School – Invariants – when you do something that takes multiple steps, the natural inclination is to look at what is changing. Equally important is to look at what it is that stays the same. We specifically look at counting in this post.
Key Math Ideas Not Taught In School – Invariants II – in this post we look at sorting, from the perspective of what stays the same while we are doing the sorting.
Key Math Ideas Not Taught In School – Transactions – when something takes multiple steps, you need to keep track of things. Transactions provide a way to think about how you keep track of things along the way. A look at escrow and marriage ceremonies.
Key Math Ideas Not Taught In School – Transactions II – more on keeping track. The example explored here is that of taking your pills, neither forgetting to take them at all nor risking taking them twice.