Top Posts

Recent Posts
 Mathematical Notations and Schools – 15
 Mathematical Notation and Schools – 14
 Mathematical Notation and Schools – 13
 Mathematical Notation and Schools – 12
 Mathematical Notation and Schools – 11
 Mathematical Notation and Schools – 10
 Mathematical Notation and Schools – 9
 Mathematical Notation and Schools – 8
 Mathematical Notations and Schools – 7
 Mathematical Notations and Schools – 6
 Mathematical Notation and Schools – 5
 Mathematical Notation and Schools – 4
 Mathematical Notation and Schools – 3
 Mathematical Notation and Schools – 2
 Mathematical Notation and Schools: The Series
Blogroll
 attribution
 black box
 deferred computation
 denominations
 discoverable
 education
 embedding
 equivalence
 extending patterns
 gauntlet
 graded hurdles
 invariants
 lookup
 math class
 math in the comics
 matrix multiplication
 models
 naming
 notation
 puzzle
 recurrence relationship
 representational proof
 representations
 reverse engineering
 selection
 series on math learning
 sieve
 sorting
 standing on nothing
 state
 unlearning
 whole vs. parts
Archives
 July 2011
 June 2011
 May 2011
 April 2011
 February 2011
 January 2011
 December 2010
 November 2010
 October 2010
 September 2010
 August 2010
 July 2010
 May 2010
 April 2010
 March 2010
 February 2010
 January 2010
 December 2009
 September 2009
 August 2009
 July 2009
 June 2009
 May 2009
 April 2009
 March 2009
 February 2009
 January 2009
 December 2008
Monthly Archives: August 2009
Representations – Black Boxes
The idea of a “black box” is common in engineering, but the idea has much wider application. It’s a simple idea, really. Just imagine something that has an inside that is inaccessible from the outside. Easy, right? For example, a … Continue reading
Posted in Uncategorized
Tagged black box, extending patterns, models, representations, reverse engineering, whole vs. parts
2 Comments
Representations – Number and Some Alternatives
There are lots of ways to represent number – such as the number “ten”. As grownups, we’re so used to a particular way of representing “ten” that we don’t often stop to think about what we’re doing – we just … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, invariants, representations, unlearning
Leave a comment
Representations – Foreground and Background
It is pretty clear that a representation of something is not the same as the something itself. “A map is not the territory” Korzybski wrote famously, and most of us would react “well, of course!” You would expect to encounter … Continue reading
Representations – Processes and Snapshots
When we talk about representation in mathematics, it is surprising how often we limit ourselves to looking at formulas. Pictures, diagrams, graphs and tables are also part of how you can represent mathematical ideas and mathematical thinking. Most representations of … Continue reading
Posted in Uncategorized
Tagged extending patterns, math class, models, naming, representations
2 Comments
Key Math Ideas Not Taught In School – Transactions II
This post is a continuation of the prior one, but won’t yet deliver on showing a direct connection between transactions and the kind of thinking we typically call mathematical thinking. In the previous post, I introduced the idea of a … Continue reading
Posted in Uncategorized
Tagged extending patterns, invariants, models, representations
Leave a comment
Key Math Ideas Not Taught In School – Transactions
Things take time. As the saying goes, time is God’s way to keep everything from happening all at once. There is a sequence to solving a problem, and even the most rotebased solutions tend to involve multiple steps. You may … Continue reading