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
Tag Archives: look-up
Operators, Functions, and Properties – part 40
In this series, we’ve spent considerable space playing with operators, which we’ve pictured as black boxes with inputs and outputs, often as part of a machine with state. In more recent posts, e.g. this one , we’ve looked at operators … Continue reading
Posted in Uncategorized
Tagged black box, denominations, equivalence, invariants, look-up, reverse engineering
3 Comments
Operators, Functions, and Properties – part 39
In this series, we’ve been looking at operators in various settings, and looked for ways to use them to shine a different colored light on some aspects school math. In the last four posts, we’ve explored the notions of equivalence … Continue reading
Posted in Uncategorized
Tagged black box, denominations, equivalence, extending patterns, invariants, look-up, models, naming, recurrence relationship, representations
1 Comment
Operators, Functions, and Properties – part 36
In the previous post in this series, we broached the subject of equivalence classes. We did so in the context of looking at an addition table and noticing how each value in the table occurred multiple times. We drew a … Continue reading
Operators, Functions, and Properties – part 15
In this series, we’ve been playing with the mathematical notion of an operator, seeing if we could make it useful for making a bridge between arithmetic and algebra. In the previous post, we started to investigate the notion of a … Continue reading
Posted in Uncategorized
Tagged black box, denominations, extending patterns, look-up, models, reverse engineering
3 Comments
Groupings, Shopping Lists, Vectors: part 7
In part 6 of this series, I introduced an operation called inner product between two vectors, as a way to find the total price of an order using a price list. In this post, I want to give a bunch … Continue reading
Posted in Uncategorized
Tagged denominations, look-up, math class, models, naming, representations, whole vs. parts
2 Comments
Groupings, Shopping Lists, Vectors: part 6
In this series on vectors we showed vector addition in this post, and then took a small excursion to show a surprising connection between some vector additions and the distributive property. In this post, I will combine vectors with look-up … Continue reading
Posted in Uncategorized
Tagged denominations, look-up, naming, representations, whole vs. parts
4 Comments
Notes on Lookup – Another Sieve for the Collatz Problem
This post is a follow-up on an earlier post in which I introduced the Collatz Problem and designed a sieve that systematically builds solutions and is very efficient in the work it does. In this post, I’ll give a version … Continue reading
Posted in Uncategorized
Tagged extending patterns, look-up, models, recurrence relationship, representations, sieve
Leave a comment
Notes on Lookup – Histograms as Sieves
I think I overlooked one interesting example of something like a sieve being used in the typical K-12 math curriculum, and this post is intended to remedy that. It is possible and instructive to look at a histogram as a … Continue reading
Posted in Uncategorized
Tagged denominations, look-up, math class, models, representations, sieve, sorting
Leave a comment
Notes on Lookup – Computation versus Lookup in School
In the previous post, I played with sieves some more. Sieves are a device for getting something calculated. At least since Eratosthenes, 2200 years ago, this simple and illustrative tool has been part of mathematics. Yet you don’t see sieves … Continue reading
Posted in Uncategorized
Tagged education, extending patterns, look-up, math class, representations, reverse engineering
1 Comment
Notes on Lookup – Eratosthenes and Other Sieves
The best known sieve in mathematics is the sieve of Eratosthenes, used for finding a collection of prime numbers. In an earlier post I described a version of that sieve that finds all divisors (and not just whether a number … Continue reading
Posted in Uncategorized
Tagged extending patterns, look-up, models, recurrence relationship, reverse engineering, sieve
3 Comments
