Top Posts
 Notes on Representation  Large Numbers
 Math in the Comics  part 1
 General Purpose and Special Purpose Tools
 Notes on Representation  Tally Marks
 Running the Math Gauntlet
 Notes on Divisibility  Common Divisors
 Math in the Comics  part 5
 Quantity  Different Kinds of Numbers: Intervals
 Key Math Ideas Not Taught In School
 Mathematical Notation and Schools  2

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: December 2009
Groupings, Shopping Lists, Vectors: part 9
In earlier parts of this series we’ve looked at shopping lists as both an example and a model for something that in math class is called a vector. We’ve looked at the sum of two vectors by imagining you join … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, math class, models, naming, representations, whole vs. parts
1 Comment
Groupings, Shopping Lists, Vectors: part 8
In part 7 of this series, one of the examples for the use of inner product of two vectors was that of a final score based on a series of tests with different weights. We have a vector of weights … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, models, naming, representations, whole vs. parts
2 Comments
Groupings, Shopping Lists, Vectors: part 7
In part 6 of this series, I introduced an operation called inner product between two vectors, as a way to find the total price of an order using a price list. In this post, I want to give a bunch … Continue reading
Posted in Uncategorized
Tagged denominations, lookup, math class, models, naming, representations, whole vs. parts
2 Comments
Groupings, Shopping Lists, Vectors: part 6
In this series on vectors we showed vector addition in this post, and then took a small excursion to show a surprising connection between some vector additions and the distributive property. In this post, I will combine vectors with lookup … Continue reading
Posted in Uncategorized
Tagged denominations, lookup, naming, representations, whole vs. parts
4 Comments
Groupings, Shopping Lists, Vectors: part 5
In the previous post, I introduced vector addition in terms of combining two piles of stuff, while keeping track of what kind of stuff is in our piles, and how many of each of the stuff we’ve got. In this … Continue reading
Posted in Uncategorized
Tagged education, math class, models, representations, whole vs. parts
2 Comments
Groupings, Shopping Lists, Vectors: part 4
Part 1, part 2, and part 3 of this series looked at a particular model for vector algebra, based on some simple notions such as that of a shopping list. In this post, I want to play with vector addition … Continue reading
Posted in Uncategorized
Tagged denominations, models, naming, representations, whole vs. parts
3 Comments
Groupings, Shopping lists, Vectors: part 3
The previous installments in this series can be found here and here. What I am after is a natural way to develop the usefulness of the idea of a vector, and in the previous post I suggested that a shopping … Continue reading
Posted in Uncategorized
Tagged denominations, math class, models, naming, representations, whole vs. parts
2 Comments
Groupings, Shopping Lists, Vectors: part 2
For an introduction to this series of posts, see here. Imagine Joe going up to the drivethrough, to order for himself and his room mates. Their orders are all combined on a piece of paper. He reads it at the … Continue reading
Posted in Uncategorized
Tagged denominations, models, naming, representations, whole vs. parts
3 Comments
Groupings, Shopping Lists, Vectors: part 1
There is a surprisingly versatile part of mathematics that deals with groupings and collections of things. The main ideas involved are really quite easy and practical. If you can make sense of a shopping list written by a spouse or … Continue reading
Posted in Uncategorized
Tagged denominations, math class, models, naming, representations, whole vs. parts
6 Comments