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Monthly Archives: August 2010
Operators, Functions, and Properties – part 21
In this series we’ve been looking at operators, which we have visualized as boxes with a value (or multiple values) going in, and a single value coming out. We pictured these boxes as little machines, which sit there waiting for … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, representations, reverse engineering
2 Comments
Operators, Functions, and Properties – part 20
In this series, we started out by looking at operators as little boxes that have a value going in and a value coming out, and that can be chained together in interesting ways, ways that allow us to illustrate key … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, equivalence, extending patterns, models, representations, reverse engineering
2 Comments
Operators, Functions, and Properties – part 19
In this series, we have been playing with the notion of a state machine: a machine that changes states depending on what buttons are pressed, and this has led us to look at the mathematics of operators in an interesting … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, extending patterns, models, representations, reverse engineering
1 Comment
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
Posted in Uncategorized
Tagged black box, deferred computation, denominations, extending patterns, models, representations, reverse engineering
3 Comments
Operators, Functions, and Properties – part 17
In this series we’ve been looking at machines with buttons, where a button press will invoke an action which we’ve called an operator. The operator operates on the state of the machine. It should be interesting to analyze the workings … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, extending patterns, models, representations, reverse engineering
2 Comments
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
Posted in Uncategorized
Tagged black box, deferred computation, denominations, extending patterns, models, naming, representations, reverse engineering
1 Comment
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
Posted in Uncategorized
Tagged black box, denominations, extending patterns, look-up, models, reverse engineering
3 Comments
Operators, Functions, and Properties – part 14
In earlier parts of this series, we’ve looked at operators that take a number coming in, and produce a number coming out. We’ve looked at stringing these operators together in a chain, and we’ve looked at combinations of operators that … Continue reading
Posted in Uncategorized
Tagged black box, deferred computation, denominations, extending patterns, models, naming, reverse engineering
2 Comments
Learning and Unlearning Math 