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
- look-up
- 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: state
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 5
In earlier parts of this series, we have talked about devices that change their state when you press some button. Such devices are both very normal and very common. A very simple example of this is a counter, where the … Continue reading
Operators, Functions, and Properties – part 4
In the two previous posts in this series, we looked at decidedly different models that each could explain the same simple external behavior. To recap, we have been looking at internal models for a device that looks like this: and … Continue reading
Posted in Uncategorized
Tagged black box, extending patterns, models, representations, reverse engineering, state
1 Comment
Operators, Functions, and Properties – part 2
In the previous post I introduced the idea of a device like the one pictured below: where the single digit on the little screen was observed to cycle through a repeating pattern every time the red button is pushed, as … Continue reading
Posted in Uncategorized
Tagged extending patterns, models, representations, reverse engineering, state
3 Comments
Operators, Functions, and Properties – part 1
I intend to write some things on operators in mathematics, beginning in this post. Functions and properties will be brought in as appropriate. The idea of operators is absolutely basic and central to computers and computing; they are also important … Continue reading
Posted in Uncategorized
Tagged deferred computation, extending patterns, models, naming, representations, state, unlearning
7 Comments