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 attribution black box deferred computation denominations discoverable education embedding equivalence extending patterns gauntlet graded hurdles invariants lookup 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
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Monthly Archives: February 2009
Notes on Representation – Tally Marks
I’m assuming you are quite familiar with tally marks: As a system of representation of quantity, tally marks play a very interesting role. You can view it as a number system, yet as a number system it does not compete … Continue reading
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Tagged denominations, extending patterns, models, naming, representations, reverse engineering
10 Comments
A CollatzInspired Puzzle
This is a puzzle. In prior posts, I used the Collatz Problem, restated here: Each counting number n past 1 is assigned a successor number, as follows: The number “1″ is considered home, and when you’re home, you stop. If … Continue reading
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Tagged models, puzzle, recurrence relationship, representations, reverse engineering
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Notes on Lookup – Another Sieve for the Collatz Problem
This post is a followup 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
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Tagged extending patterns, lookup, models, recurrence relationship, representations, sieve
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Notes on Lookup – Histograms as Sieves
I think I overlooked one interesting example of something like a sieve being used in the typical K12 math curriculum, and this post is intended to remedy that. It is possible and instructive to look at a histogram as a … Continue reading
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Tagged denominations, lookup, math class, models, representations, sieve, sorting
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Math in the Comics – part 6
Today, there is a followup on yesterday’s Non Sequitur comic – in which Danae’s new math system is revealed: henceforth, she will start with the answer and work back to get an equation that fits the problem. This way, she … Continue reading
Math in the Comics – part 5
In today’s comics, there is this Non Sequitur one: Comics, to me, are interesting regardless of whether a particular one is funny, since they reveal a lot about the community and the society in which they appear. Usually, comics make … Continue reading
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Tagged education, gauntlet, graded hurdles, math class, math in the comics, representations
8 Comments
Notes on Lookup – A Sieve for the Collatz Problem
This post is meant as a followup on this one on lookup and sieves, not on my more recent one pondering the diminished status of lookup in K12 math. I’ve been playing with different ways to use a sieve to … Continue reading
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Tagged extending patterns, models, naming, recurrence relationship, representations, reverse engineering, sieve
2 Comments
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
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Tagged education, extending patterns, lookup, math class, representations, reverse engineering
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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
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Tagged extending patterns, lookup, models, recurrence relationship, reverse engineering, sieve
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Mathematical Puzzle – Hinges
This is a puzzle. Imagine I have three rods of length 1 each, and they are connected together with perfect hinges. Together, they form a somewhat flexible shape ABCD (with AB=1, BC=1 and CD=1), even if I fix the two … Continue reading