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Category Archives: Uncategorized
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, lookup, models, naming, recurrence relationship, representations
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Operators, Functions, and Properties – part 38
In the last three posts in this series, we played with addition tables, multiplication tables, and division tables, and looked at equivalence classes and representatives of each equivalence class. As promised, a look at subtraction, but let’s look at subtraction … Continue reading
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Operators, Functions, and Properties – part 37
In this series we’ve looked at boxes that take certain inputs and then produce an output. We’ve called such boxes operators, and we’ve thought of them in many different ways. In some cases, the boxes perform arithmetic; in other cases, … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, invariants, models, representations, reverse engineering, whole vs. parts
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Operators, Functions, and Properties – part 36
In the previous post in this series, we broached the subject of equivalence classes. We did so in the context of looking at an addition table and noticing how each value in the table occurred multiple times. We drew a … Continue reading
Operators, Functions, and Properties – part 35
In the previous post of this series, we looked more closely at the mathematical notion of equivalence, through the lens of operators. Specifically, we looked at a split (pair) 213 and then looked at an operator that turns 213 into … Continue reading
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 twonumbers … 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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Operators, Functions, and Properties – part 31
In the prior post in this series, we looked at the kind of operators typically encountered in school (K12), whether or not they are called operators. Many of them are single number input – single number output, but not all. … Continue reading
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Tagged black box, equivalence, models, naming, reverse engineering, whole vs. parts
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Operators, Functions, and Properties – part 30
In many of the posts in this series we’ve shown operators that work on a single number coming in and that produce a single number coming out. This is a hugely important subcategory of operators, but singlein singleout operators aren’t … Continue reading
Posted in Uncategorized
Tagged extending patterns, models, unlearning, whole vs. parts
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