Top Posts
 Math in the Comics  part 1
 Groupings, Shopping Lists, Vectors: part 18
 Groupings, Shopping Lists, Vectors: part 20
 About
 Mathematical Notation and Schools: The Series
 A Multiplication Nomograph
 Mathematical Notation and Schools  2
 Notes on Notation  Variables
 Mathematical Notation and Schools  4
 Mathematical Notation and Schools  5

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: representations
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 39
In this series, we’ve been looking at operators in various settings, and looked for ways to use them to shine a different colored light on some aspects school math. In the last four posts, we’ve explored the notions of equivalence … Continue reading
Posted in Uncategorized
Tagged black box, denominations, equivalence, extending patterns, invariants, lookup, models, naming, recurrence relationship, representations
1 Comment
Operators, Functions, and Properties – part 37
In this series we’ve looked at boxes that take certain inputs and then produce an output. We’ve called such boxes operators, and we’ve thought of them in many different ways. In some cases, the boxes perform arithmetic; in other cases, … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, invariants, models, representations, reverse engineering, whole vs. parts
Leave a comment
Operators, Functions, and Properties – part 36
In the previous post in this series, we broached the subject of equivalence classes. We did so in the context of looking at an addition table and noticing how each value in the table occurred multiple times. We drew a … Continue reading
Operators, Functions, and Properties – part 35
In the previous post of this series, we looked more closely at the mathematical notion of equivalence, through the lens of operators. Specifically, we looked at a split (pair) 213 and then looked at an operator that turns 213 into … Continue reading
Operators, Functions, and Properties – part 34
In the previous post in this series, we looked at some operators that take in two numbers and produce some kind of pair of numbers, an ordered pair, in a way that can be reversed. Here’s another way to produce … Continue reading
Posted in Uncategorized
Tagged black box, denominations, equivalence, invariants, models, representations, reverse engineering
1 Comment
Operators, Functions, and Properties – part 32
In this series, we’ve been looking at a model for presenting and analyzing operators with an intention for it to have applications for students learning math in school. In recent posts, we’ve looked for interesting aspects of school math that … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, invariants, models, naming, representations, reverse engineering
1 Comment
Operators, Functions, and Properties – part 29
In this series, we’ve been looking at simple machines where pushing a button invokes an operator that changes the state of the machine. Stopwatches, coffee makers, calculators are all examples of such machines – some simpler than others. Many of … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, recurrence relationship, representations
Leave a comment
Operators, Functions, and Properties – part 28
The prior post in this series showed that we can get complex and rich behavior from combining simple operators and feeding their output back to their input (through what is called “state”, and the whole arrangement is known as a … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, recurrence relationship, representations, reverse engineering
1 Comment
Operators, Functions, and Properties – part 26
In the previous post in this series, we linked two state machines together, weakly, by arranging to press their Start buttons at the same time and to press their Next buttons at the same time. As a result, we got … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, recurrence relationship, representations, reverse engineering
2 Comments