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Tag Archives: denominations
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
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Tagged black box, deferred computation, denominations, education, equivalence, math class, models, naming, notation, representations
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Operators, Functions, and Properties – part 40
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
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Tagged black box, denominations, equivalence, invariants, look-up, reverse engineering
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Operators, Functions, and Properties – part 39
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
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Tagged black box, denominations, equivalence, extending patterns, invariants, look-up, models, naming, recurrence relationship, representations
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Operators, Functions, and Properties – part 34
In the previous post in this series, we looked at some operators that take in two numbers and produce some kind of pair of numbers, an ordered pair, in a way that can be reversed. Here’s another way to produce … Continue reading
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Tagged black box, denominations, equivalence, invariants, models, representations, reverse engineering
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Operators, Functions, and Properties – part 33
In this series we have looked at various examples of operators, and most of our attention has been on operators where what comes out is a number, and what comes in is one or two numbers. Some examples of two-numbers … Continue reading
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Tagged black box, denominations, equivalence, extending patterns, models, reverse engineering, whole vs. parts
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Operators, Functions, and Properties – part 32
In this series, we’ve been looking at a model for presenting and analyzing operators with an intention for it to have applications for students learning math in school. In recent posts, we’ve looked for interesting aspects of school math that … Continue reading
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Tagged denominations, extending patterns, invariants, models, naming, representations, reverse engineering
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Groupings, Shopping Lists, and Vectors: The Series
This is a series on vector algebra, but it hasn’t wrapped up yet. Here are the installments as of now: Quantity – Different Kinds of Numbers: Vectors – it really all started with this post. But I didn’t know it … Continue reading
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 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 15
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
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Tagged black box, denominations, extending patterns, look-up, models, reverse engineering
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