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Author Archives: Bert Speelpenning
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
Mathematical Notation and Schools – 4
The Overloaded Equals Sign: “Do This Now” In this series about mathematical notation and its impact on the learning of mathematics, we’ve looked so far at the raised minus sign for negative numbers, the various ways of denoting multiplication, and … Continue reading
Mathematical Notation and Schools – 3
Notations for Sequencing and Nesting (Parentheses) In this series, I’m exploring mathematical notation as it is used in schools, and how these notations help or hinder students’ understanding of mathematics. In the first installment of this series, I spoke positively … Continue reading
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Mathematical Notation and Schools – 2
Notations For Multiplication In the first part of this series, I looked at the practice in American schools to use a raised minus sign for negative numbers: e.g. ⁻7 for negative seven, in contrast to the “” in 10 – … Continue reading
Mathematical Notation and Schools: The Series
Here’s a summary of the series (thus far) of posts on mathematical notation, with links. This allows you to read them in order, from oldest to most recent. In this series, I’m investigating variations of standard mathematical notation, with an … Continue reading
Mathematical Notation and Schools – 1
Notations for negative numbers This blog entry marks the start of a series about mathematical notation and its uses in school. I intend to look in detail at aspects of the standard mathematical notations, and how these help or hinder … Continue reading
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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Tagged black box, equivalence, models, representations, reverse engineering, whole vs. parts
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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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Tagged black box, equivalence, extending patterns, invariants, representations, reverse engineering
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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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Tagged black box, equivalence, extending patterns, models, representations, state
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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, lookup, reverse engineering
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