Top Posts
 Groupings, Shopping Lists, and Vectors: The Series
 What is Multiplication  the Series
 Groupings, Shopping Lists, Vectors: part 12
 Groupings, Shopping Lists, Vectors: part 24
 Groupings, Shopping Lists, Vectors: part 11
 Groupings, Shopping Lists, Vectors: part 9
 Notes on Representation  Tally Marks Ho!
 Groupings, Shopping Lists, Vectors: part 10

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: July 2010
Operators, Functions, and Properties – part 12
In this series, we’ve been looking at operators as something that takes an input and turns it into an output, and we’ve been looking at chains of such operators, which we’ve called trains. In the last post, we posed the … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, representations
3 Comments
Operators, Functions, and Properties – part 11
In the prior post of this series, we looked at pairs of operators in which one of the pair cancels out the effect of the other. We call one of these the inverse operator of the other one. For example, … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, representations, reverse engineering, whole vs. parts
2 Comments
Operators, Functions, and Properties – part 10
In the prior post in this series, we looked at chains of operators for which the net effect was to do nothing. We started by comparing the picture on the left with the picture on the right, below, and noticing … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, extending patterns, invariants, models, representations, reverse engineering
2 Comments
Operators, Functions, and Properties – part 9
In the last few sessions in this series we’ve looked at operators that do things like “add 2″ or “multiply by 3″ or “divide by 10″. Each of these operators takes a number as its input and produces a number … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, equivalence, extending patterns, models, representations, reverse engineering
3 Comments
Operators, Functions, and Properties: The Series
This series of posts introduces the notion of an operator as something that changes the state of some machine or device. Often, an operator is invoked at the press of a button. A special case of an operator is one … Continue reading
Operators, Functions, and Properties – part 8
In the prior post, I played with putting together little boxes that perform actions on numbers coming in – simple actions like adding two – and reported on an experiment with seventh graders to find equivalent boxes. I’m going to … Continue reading
Posted in Uncategorized
3 Comments