Top Posts
- Quantity - Different Kinds of Numbers: Classes
- Series
- BestOf
- Relationships - Percentages
- Walter Warwick Sawyer, 1911-2008
- Quantity - Different Kinds of Numbers: Keys
- Notes on Representation - Large Numbers
- General Purpose and Special Purpose Tools
- What is Multiplication - part IV
- What is Multiplication - part XI
-
Click here to be notified of new posts in this blog -
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
Monthly Archives: March 2009
Relationships – Percentages
If I ask you to count, starting at 103, for five counts, you do so by keeping track of two quantities. You keep track of them in your head, by speaking out loud and listening to what you just said, … Continue reading
Posted in Uncategorized
Tagged denominations, education, extending patterns, models, naming, representations, reverse engineering, unlearning
4 Comments
The Whole and the Parts – Where Units Really are Arbitrary
After several posts where the entire point was to highlight situations where the whole is more than the sum of the parts, I thought it would be interesting to bring in a contrast. In this post, we will look at … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, models, naming, reverse engineering, unlearning, whole vs. parts
4 Comments
The Whole and the Parts – Memory and Hysteresis
Imagine I’ve got a sheet of four (square) postage stamps, like this: If I need a single postage stamp, I need to do some tearing, and that tearing takes a bit of time and effort. To tear along a single … Continue reading
Posted in Uncategorized
Tagged math class, models, representations, reverse engineering, unlearning, whole vs. parts
1 Comment
The Whole and the Parts – Feedback Loops with Delay
In my previous post on feedback loops I promised to look at their limitations. I’ll start that in this post, but think I should say a little more about what they are good for first. In the example of a … Continue reading
Posted in Uncategorized
Tagged extending patterns, models, naming, representations, reverse engineering, unlearning, whole vs. parts
Leave a comment
The Whole and the Parts – Packaging
My earlier posts in The Whole and the Parts series may have seemed “less mathematical” to you than other posts in this blog. They didn’t involve a whole lot of arithmetic, little notation and few if any formulas. Whatever mathematics … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, math class, models, representations, reverse engineering, unlearning, whole vs. parts
3 Comments
Pi Day – How Big Is Pi?
In your time zone Pi Day may already be over. But here, it still is March 14, the traditional day to celebrate Pi. Most kids can rattle off that Pi has the value 3.14 (approximately) and that is used in … Continue reading
Posted in Uncategorized
Tagged extending patterns, math class, models, reverse engineering
Leave a comment
The Whole and the Parts – Feedback Loops
Imagine you live on one of the planets around one of the stars in one of these galaxies: Imagine further that you live in a society that has figured out the physics of Newton’s laws, and that this society has … Continue reading
Posted in Uncategorized
Tagged extending patterns, models, representations, unlearning, whole vs. parts
1 Comment
Math in the Comics – part 9
In today’s Dilbert comic, another opportunity to highlight something about how math is held in society. Dilbert, rather desperately, is trying to convince his audience of something. And, somehow, he does! He invokes the Authority of Mathematical Gobbledygook, represented in … Continue reading
Posted in Uncategorized
Tagged math in the comics, models, representational proof, representations, unlearning
1 Comment
Notes on Representation – Copying
In this blog, I’ve surveyed a number of different representation systems for quantities, including the decimal number system, the number line, tally marks, and prime bags, and I’ve tried to see and say something interesting and fresh about each. When … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, models, naming, representations, reverse engineering, unlearning
Leave a comment
