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Tag Archives: deferred computation
Operators, Functions, and Properties – part 10
In the prior post in this series, we looked at chains of operators for which the net effect was to do nothing. We started by comparing the picture on the left with the picture on the right, below, and noticing … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, extending patterns, invariants, models, representations, reverse engineering
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Operators, Functions, and Properties – part 9
In the last few sessions in this series we’ve looked at operators that do things like “add 2” or “multiply by 3” or “divide by 10”. Each of these operators takes a number as its input and produces a number … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, equivalence, extending patterns, models, representations, reverse engineering
3 Comments
Operators, Functions, and Properties: The Series
This series of posts introduces the notion of an operator as something that changes the state of some machine or device. Often, an operator is invoked at the press of a button. A special case of an operator is one … Continue reading
Operators, Functions, and Properties – part 1
I intend to write some things on operators in mathematics, beginning in this post. Functions and properties will be brought in as appropriate. The idea of operators is absolutely basic and central to computers and computing; they are also important … Continue reading
Posted in Uncategorized
Tagged deferred computation, extending patterns, models, naming, representations, state, unlearning
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Notes on Fractions – Deferred Computation
What would happen if we thought of a fraction as a division that hadn’t been done yet and that we weren’t necessarily interested in doing yet? I’ve suggested in earlier posts (e.g. here and here) that kids often don’t see … Continue reading
Posted in Uncategorized
Tagged deferred computation, denominations, extending patterns, math class, models, naming, unlearning
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Notes on Fractions
I worked with a 7th grader the other day who was solving a “proportion problem”. He had set it up as and then solved it by reasoning that 30 was 5 times bigger than 6, so the scale factor was … Continue reading
Posted in Uncategorized
Tagged deferred computation, denominations, math class, models, naming, representations
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Notes on Deferred Computation – the Pythagorean Spiral
The following figure is quite interesting: Imagine you start out home, in the center at the bottom, and move a distance of 1 to the right to A. At A, you have traveled a total distance of 1, and you … Continue reading
Posted in Uncategorized
Tagged deferred computation, extending patterns, math class, models, recurrence relationship, representations
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