# Tag Archives: equivalence

## 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

## Mathematical Notation and Schools – 13

Functions:  Standard Notation and Schools, Continued 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 previous post, we started to explore function notation, which in … Continue reading

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## Mathematical Notation and Schools – 11

Expressions and Formulas: A Larger Deviation from the Standard Notation In this series, we’ve done a review of mathematical notation, with an eye on how each notation helps or hinders student learning.  The focus here is modest: on what teachers … Continue reading

## Mathematical Notation and Schools – 10

Expressions and Formulas: Slight Variations on the Standard In this series, we’ve done a review of mathematical notation, with an eye on how each notation helps or hinders student learning.  The focus here is on what teachers can do, even … Continue reading

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## Mathematical Notation and Schools – 8

Subtraction: The Dot For “Borrowing” Can Also Denote Negative Numbers In this series, I’m looking at the impact of mathematical notation on student understanding and student learning.  In the previous installment, I looked at a notation for “long subtraction” different … Continue reading

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## Mathematical Notation and Schools – 5

The Overloaded Equals Sign: Equivalence In this series about mathematical notation and its impact on the learning of mathematics, the previous post started to look at the overloading of the equals sign – so many different meanings and uses cramped … 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

## Operators, Functions, and Properties – part 42

In this series, we’ve been looking at black boxes, where you put something in and something comes out.  From looking at its behavior, you can often propose a model for what is happening inside.  If you build the model, and … 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 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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