Top Posts
 Notes on Representation  Tally Marks
 Tally Marks and Roman Numerals
 Notes on Operations  Unary Minus
 Math in the Comics  part 1
 Notes on Deferred Computation  the Pythagorean Spiral
 Math in the Comics: The Series
 Math in the Comics  part 10
 Quantity  The Series
 Walter Warwick Sawyer, 19112008
 Mathematical Notation and Schools  8

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: deferred computation
Mathematical Notation and Schools – 14
Functions: Variant Notations In this series, we’ve done a review of mathematical notation, with an eye on how each notation helps or hinders student learning. In the prior posts, we started to explore function notation, which in middle school and … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, denominations, education, equivalence, math class, models, naming, notation, representations
Leave a comment
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
Operators, Functions, and Properties – part 16
In this series, we’ve been playing with operators in an attempt to make some models for an introduction to algebra that may fit modern kids’ ways of thinking better than some traditional models. A key entry point for us has … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, denominations, extending patterns, models, naming, representations, reverse engineering
1 Comment
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