Top Posts
 Notes on Representation  Tally Marks
 Notes on Deferred Computation  the Pythagorean Spiral
 Quantity  Different Kinds of Numbers: Intervals
 Math in the Comics: The Series
 Mathematical Notation and Schools  10
 Key Math Ideas Not Taught In School  Invariants
 "Ontogeny recapitulates phylogeny" in math education
 Napier's Logs

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: unlearning
Operators, Functions, and Properties – part 30
In many of the posts in this series we’ve shown operators that work on a single number coming in and that produce a single number coming out. This is a hugely important subcategory of operators, but singlein singleout operators aren’t … Continue reading
Posted in Uncategorized
Tagged extending patterns, models, unlearning, whole vs. parts
Leave a comment
Representations – Black Boxes – Equivalence 2
We ended the previous post in this series by looking at this figure: To recap, a black box is something where we have access to the behavior but not the internal organization. We can propose a model for a black … Continue reading
Posted in Uncategorized
Tagged black box, denominations, equivalence, extending patterns, models, representations, reverse engineering, unlearning
Leave a comment
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
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
Key Math Ideas Not Taught In School – Invariants
“Counting” involves a number of different mathematical ideas If you watch really young children count, you may notice that they aren’t all doing the same thing. For some children, counting “onetwothree” is done in very much the same way as … Continue reading
Posted in Uncategorized
Tagged education, invariants, math class, models, reverse engineering, unlearning
4 Comments