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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: April 2009
What is Multiplication – part X
Yesterday, in the supermarket, a customer dumped a whole basket full of power bars on the counter. The checkout counter person started to scan them in, one by one. After seeing about seven of them scanned, with a lot more … Continue reading
Posted in Uncategorized
Tagged denominations, math class, models, puzzle, representations, reverse engineering, unlearning
2 Comments
Math in the Comics – part 10
From last week’s Foxtrot comic, another take at the cultural background conversation of math. Who is bad at math? At one level, a puzzle. The top part, the part that starts with “1611135” is not a subtraction problem. It is … Continue reading
Posted in Uncategorized
Tagged gauntlet, graded hurdles, math class, math in the comics, puzzle, selection
2 Comments
What is Multiplication – part VIII
In this series of posts, we looked at various embodiments of multiplicative structure. Each involves ideas about multiplication. How are these ideas learned? From reading this blog, you will have gathered that I mean the question “how is an idea … Continue reading
Posted in Uncategorized
Tagged extending patterns, invariants, models, naming, representations, unlearning
2 Comments
What is Multiplication – part VII
In the prior post we looked at the array model for multiplication. At least, this is the way we usually talk about it: as if it is already clear what multiplication is, and we just want a way to show … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, invariants, models, naming, representations, unlearning
1 Comment
What is Multiplication – part VI
In our series of posts looking at multiplicative structures I wouldnt want to leave out what is often called the area model, though I think array model is a better fit. As I suggested in a prior post, the notion … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, invariants, models, naming, representations, unlearning
3 Comments
What is Multiplication – part V
Numbers provide a way to mark events. This can usually be done in more than one way. We can “slice” reality in more than one way. The picture above shows a common way to look at a single stock on … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, gauntlet, math class, models, naming, representations, unlearning
1 Comment