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
Tag Archives: denominations
Operators, Functions, and Properties – part 14
In earlier parts of this series, we’ve looked at operators that take a number coming in, and produce a number coming out. We’ve looked at stringing these operators together in a chain, and we’ve looked at combinations of operators that … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, denominations, extending patterns, models, naming, reverse engineering
2 Comments
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
First, Do No Harm
Wouldn’t that be a great stricture for Math Education to adopt, just like medical professionals do? Whatever else you do, make sure you do no harm. You’d think that this would represent a really low standard of math education: that … Continue reading
Groupings, Shopping Lists, Vectors: part 24
In this series of posts on the topic of vectors, I’ve been primarily interested in playing with situations in which the notion of a vector naturally arises. Looking at shopping lists was one of those. A shopping list is … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, matrix multiplication, models, naming, whole vs. parts
1 Comment
Groupings, Shopping Lists, Vectors: part 23
In this post I’m going to look at something usually referred to as linear combinations. In the prior post, we had an occasion to look at coordinate systems where the axes are not at right angles. We saw that you … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, matrix multiplication, models, naming, representations, whole vs. parts
2 Comments
Groupings, Shopping Lists, Vectors: part 22
In the last few posts in this series I’ve examined some consequences of British values, where we have pounds and shillings (and also pence) – but then have this other value, the guinea, which equals one pound and one shilling. … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, matrix multiplication, models, naming, representations, whole vs. parts
2 Comments
Groupings, Shopping Lists, Vectors: part 21
In the previous post in this series, part 20, I showed a matrix multiplication to convert a value stated in guineas and shillings into one stated in pounds and shillings. We were interested in the same value, expressed in different … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, matrix multiplication, representations, whole vs. parts
2 Comments
Groupings, Shopping Lists, Vectors: part 20
In England, the main currency is called the pound. Smaller units are called shillings and pence. A pound is 20 shillings, a shilling is 5 pence, hence a pound is 100 pence. This system has been in place since 1971; … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, matrix multiplication, models, naming, representations, whole vs. parts
3 Comments
Groupings, Shopping Lists, Vectors: part 19
In this post, I will try to connect a set of equations with matrices and vectors in a way that isn’t simply a notational shift. In part 18 of this series, I brought up the vast preponderance of square matrices … Continue reading
Posted in Uncategorized
Tagged denominations, matrix multiplication, models, naming, representations, whole vs. parts
1 Comment