Tag Archives: look-up

Operators, Functions, and Properties – part 40

Posted on 2011/01/17 by Bert Speelpenning

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

Posted on 2011/01/07 by Bert Speelpenning

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

Posted on 2010/12/21 by Bert Speelpenning

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 →

Posted in Uncategorized | Tagged black box, equivalence, look-up, models, representations | 8 Comments

Operators, Functions, and Properties – part 15

Posted on 2010/08/02 by Bert Speelpenning

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

Posted on 2009/12/23 by Bert Speelpenning

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

Posted on 2009/12/20 by Bert Speelpenning

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

Posted on 2009/02/27 by Bert Speelpenning

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

Posted on 2009/02/25 by Bert Speelpenning

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

Posted on 2009/02/22 by Bert Speelpenning

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

Posted on 2009/02/21 by Bert Speelpenning

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