Top Posts
- Math in the Comics - part 1
- Math in the Comics: The Series
- Groupings, Shopping Lists, Vectors: part 18
- Middle School Math - What is Hard?
- Notes on Representation - Large Numbers
- Tally Marks and Roman Numerals
- Math in the Comics - part 5
- Math in the Comics - part 10
- Operators, Functions, and Properties - part 40
- Math in the Comics - part 7
-
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
Tag Archives: invariants
Key Math Ideas Not Taught In School – Transactions II
This post is a continuation of the prior one, but won’t yet deliver on showing a direct connection between transactions and the kind of thinking we typically call mathematical thinking. In the previous post, I introduced the idea of a … Continue reading
Posted in Uncategorized
Tagged extending patterns, invariants, models, representations
Leave a comment
Key Math Ideas Not Taught In School – Invariants II
I want to add a bunch more examples to my prior post about invariants. I intend these examples to be relatively straightforward, and flesh out the key idea behind invariants. To this end, I’m using examples of more elaborate computation … Continue reading
Posted in Uncategorized
Tagged extending patterns, invariants, models, representations
Leave a comment
Key Math Ideas Not Taught In School – Invariants
“Counting” involves a number of different mathematical ideas If you watch really young children count, you may notice that they aren’t all doing the same thing. For some children, counting “one-two-three” is done in very much the same way as … Continue reading
Posted in Uncategorized
Tagged education, invariants, math class, models, reverse engineering, unlearning
4 Comments
Key Math Ideas Not Taught In School
There is a shape, a progression, to the typical school curriculum from Kindergarten through High School, at least in the United States, and this progression hasn’t changed much in the last 50 years or so. We’ve gotten used to this … Continue reading
Posted in Uncategorized
Tagged education, extending patterns, invariants, math class, models, representations, reverse engineering, unlearning
2 Comments
Quantity – Different Kinds of Numbers: Scalars
We’re used to representing quantities by numbers. In this series we’ve been looking at different kinds of quantities, and how certain actions on the numbers are meaningful for some kinds of quantities and meaningless for other kinds of quantities. It … Continue reading
Quantity – Different Kinds of Numbers: Intervals
It is useful to look closely at this graph taken from a Wikipedia article on misleading graphs: The reason given for the graph being misleading is familiar to most of us: the labels on the vertical axis don’t start at … Continue reading
Posted in Uncategorized
Tagged extending patterns, invariants, models, representations, unlearning
2 Comments
