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Tag Archives: deferred computation
Mathematical Notation and Schools – 14
Functions: Variant Notations In this series, we’ve done a review of mathematical notation, with an eye on how each notation helps or hinders student learning. In the prior posts, we started to explore function notation, which in middle school and … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, denominations, education, equivalence, math class, models, naming, notation, representations
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Operators, Functions, and Properties – part 20
In this series, we started out by looking at operators as little boxes that have a value going in and a value coming out, and that can be chained together in interesting ways, ways that allow us to illustrate key … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, equivalence, extending patterns, models, representations, reverse engineering
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Operators, Functions, and Properties – part 19
In this series, we have been playing with the notion of a state machine: a machine that changes states depending on what buttons are pressed, and this has led us to look at the mathematics of operators in an interesting … Continue reading
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Tagged black box, deferred computation, extending patterns, models, representations, reverse engineering
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Operators, Functions, and Properties – part 18
In the latest post in this series, we looked at modeling a simple four-function calculator as a state machine where key presses invoke operators that operate on the current state of the machine, producing a new state. Missing from this … Continue reading
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Tagged black box, deferred computation, denominations, extending patterns, models, representations, reverse engineering
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Operators, Functions, and Properties – part 17
In this series we’ve been looking at machines with buttons, where a button press will invoke an action which we’ve called an operator. The operator operates on the state of the machine. It should be interesting to analyze the workings … Continue reading
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Tagged black box, deferred computation, extending patterns, models, representations, reverse engineering
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Operators, Functions, and Properties – part 16
In this series, we’ve been playing with operators in an attempt to make some models for an introduction to algebra that may fit modern kids’ ways of thinking better than some traditional models. A key entry point for us has … Continue reading
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Tagged black box, deferred computation, denominations, extending patterns, models, naming, representations, reverse engineering
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Operators, Functions, and Properties – part 14
In earlier parts of this series, we’ve looked at operators that take a number coming in, and produce a number coming out. We’ve looked at stringing these operators together in a chain, and we’ve looked at combinations of operators that … Continue reading
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Tagged black box, deferred computation, denominations, extending patterns, models, naming, reverse engineering
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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
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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
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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
Learning and Unlearning Math 