Top Posts
 Notes on Representation  Tally Marks
 Groupings, Shopping Lists, Vectors: part 18
 Tally Marks and Roman Numerals
 Math in the Comics  part 8
 Mathematical Notation and Schools  2
 "Ontogeny recapitulates phylogeny" in math education
 Operators, Functions, and Properties  part 29
 A Multiplication Nomograph
 Math in the Comics  part 7

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
Tag Archives: state
Operators, Functions, and Properties – part 41
In this series, we’ve pictured operators as black boxes with inputs and outputs. In the previous post we looked at rather ordinary addition from a less ordinary perspective: we imagined the number line arranged as a cylindrical spiral, like a … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, representations, state
1 Comment
Operators, Functions, and Properties – part 5
In earlier parts of this series, we have talked about devices that change their state when you press some button. Such devices are both very normal and very common. A very simple example of this is a counter, where the … Continue reading
Operators, Functions, and Properties – part 4
In the two previous posts in this series, we looked at decidedly different models that each could explain the same simple external behavior. To recap, we have been looking at internal models for a device that looks like this: and … Continue reading
Posted in Uncategorized
Tagged black box, extending patterns, models, representations, reverse engineering, state
1 Comment
Operators, Functions, and Properties – part 2
In the previous post I introduced the idea of a device like the one pictured below: where the single digit on the little screen was observed to cycle through a repeating pattern every time the red button is pushed, as … Continue reading
Posted in Uncategorized
Tagged extending patterns, models, representations, reverse engineering, state
3 Comments
Operators, Functions, and Properties – part 1
I intend to write some things on operators in mathematics, beginning in this post. Functions and properties will be brought in as appropriate. The idea of operators is absolutely basic and central to computers and computing; they are also important … Continue reading
Posted in Uncategorized
Tagged deferred computation, extending patterns, models, naming, representations, state, unlearning
7 Comments