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: extending patterns
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
Operators, Functions, and Properties – part 25
In this series, we’ve looked at operators in various ways. Recently, we’ve looked at state machines that invoke the same operator repeatedly, and generate a sequence of numbers in doing so. Conversely, sequences of numbers can often be modeled as … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, invariants, recurrence relationship, representations
1 Comment
Operators, Functions, and Properties – part 24
In the previous post in this series, we started to model recurrence relationships with state machines: The idea is that we have a device with two buttons and a screen; after we press the Start button, we can press the … Continue reading
Operators, Functions, and Properties – part 23
In this series, we’ve been looking at operators as something that modifies the state of some machine or device, usually triggered by the pushing of a button. We’ve looked quite a bit at operators that operate on numbers, for example … Continue reading
Operators, Functions, and Properties – part 22
In this series, we’ve lately been modeling a fourfunction calculator as a state machine. A state machine moves from state to state based on operators that are invoked through button presses. Operators take their input, do something with it, and … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, representations, reverse engineering
2 Comments
Operators, Functions, and Properties – part 21
In this series we’ve been looking at operators, which we have visualized as boxes with a value (or multiple values) going in, and a single value coming out. We pictured these boxes as little machines, which sit there waiting for … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, representations, reverse engineering
2 Comments
Operators, Functions, and Properties – part 20
In this series, we started out by looking at operators as little boxes that have a value going in and a value coming out, and that can be chained together in interesting ways, ways that allow us to illustrate key … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, equivalence, extending patterns, models, representations, reverse engineering
2 Comments
Operators, Functions, and Properties – part 19
In this series, we have been playing with the notion of a state machine: a machine that changes states depending on what buttons are pressed, and this has led us to look at the mathematics of operators in an interesting … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, extending patterns, models, representations, reverse engineering
1 Comment
Operators, Functions, and Properties – part 18
In the latest post in this series, we looked at modeling a simple fourfunction calculator as a state machine where key presses invoke operators that operate on the current state of the machine, producing a new state. Missing from this … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, denominations, extending patterns, models, representations, reverse engineering
3 Comments
Operators, Functions, and Properties – part 17
In this series we’ve been looking at machines with buttons, where a button press will invoke an action which we’ve called an operator. The operator operates on the state of the machine. It should be interesting to analyze the workings … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, extending patterns, models, representations, reverse engineering
2 Comments