Tag Archives: models

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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Mathematical Notations and Schools – 7

Subtraction: The Dot For “Borrowing” In this series, I’ve been exploring notational issues and their impact on student learning.  So far, I’ve been hesitating dealing with the standard subtraction algorithm as taught in the USA for two reasons: 1. I’m … Continue reading

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Operators, Functions, and Properties – part 43

In the last several posts in this series, we’ve looked at cyclical patterns of behavior of numbers and operators.  For example, in the previous post we saw that when counting up, the last digit of a number consistently repeats after … Continue reading

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Operators, Functions, and Properties – part 41

In this series, we’ve pictured operators as black boxes with inputs and outputs.  In the previous post we looked at rather ordinary addition from a less ordinary perspective: we imagined the number line arranged as a cylindrical spiral, like a … Continue reading

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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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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

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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

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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) 2|13 and then looked at an operator that turns 2|13 into … Continue reading

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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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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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