Top Posts
-
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: January 2009
Powerful Sunglasses
This is a puzzle. Imagine I own a pair of sunglasses that reliably blocks ultraviolet rays so that, out of any ten rays that shine on it, only one of them gets through. So, if 40 rays shine on them, … Continue reading
Notes on Divisibility – Eratosthenes and Euclid
You will want to read the Notes on Divisibility post first. In the figure below, I’ve shown the first 22 mile markers, and the red marks on each. Skip counting by twos leads to the red “2” marks, skip counting … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, look-up, models, naming, recurrence relationship, sieve
3 Comments
Notes On Divisibility
Imagine the numbers 1, 2, 3, … laid out in a regular linear sequence, like mile markers on a long road. The markers don’t need to be a mile apart, you can put them closer if you like, but you … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, look-up, naming, unlearning
Leave a comment
Half a pizza and half a balloon
This is a puzzle If you’ve ever actually tried to divide a pizza into 15 equal pieces – and I mean the kind of dividing that uses a knife or a cutter or piano wire – you’ll find that knowing … Continue reading
Posted in Uncategorized
Tagged extending patterns, math class, models, puzzle, unlearning
4 Comments
Making Change – A Sam Lloyd puzzle
This is a puzzle, taken from the famous puzzle producer Sam Lloyd, complete with original illustration. This puzzle is old: A lady bought a boquet at the florists for thirty-four cents and had a one dollar bill, a three cent … Continue reading
Notes on Notation – Equality
The humble little equal sign, , is called on to do a large number of different tasks. As teachers, we often assume that kids will keep these tasks straight. To an amazing extent, kids actually do. And I suggest this … Continue reading
Math in the Comics – part 1
I saw a poignant comic strip in the newspaper today, and thought it was illustrative to mention here: Paige has no clue what to do with and or how to solve that set of equations. Her brother then asks her … Continue reading
Posted in Uncategorized
Tagged education, math class, math in the comics, models, unlearning
6 Comments
Notes on Notation – Variables
Variables have often been seen as the big bugaboo of the middle school math curriculum and beyond. They have become inextricably identified with that 7-letter curse word “algebra”. I submit most teachers have encountered some variation on student Jesse who … Continue reading
The Lewis Carroll problem
This is a puzzle. Lewis Carroll, the author of Alice in Wonderland, was also a mathematician. In his diary for 1890, he wrote the following statement: is always the sum of two squares where x and y are a pair … Continue reading
Notes on Notation – Division
In the course of normal school, students encounter various notations for division, and boy, are there many. We’ve got 15 / 5, and then there is also 15 ÷ 5 as well as . You may even have come across … Continue reading
