Top Posts
-
Click here to be notified of new posts in this blog -
Recent Posts
- Mathematical Notations and Schools – 15
- Mathematical Notation and Schools – 14
- Mathematical Notation and Schools – 13
- Mathematical Notation and Schools – 12
- Mathematical Notation and Schools – 11
- Mathematical Notation and Schools – 10
- Mathematical Notation and Schools – 9
- Mathematical Notation and Schools – 8
- Mathematical Notations and Schools – 7
- Mathematical Notations and Schools – 6
- Mathematical Notation and Schools – 5
- Mathematical Notation and Schools – 4
- Mathematical Notation and Schools – 3
- Mathematical Notation and Schools – 2
- Mathematical Notation and Schools: The Series
Blogroll
- attribution
- black box
- deferred computation
- denominations
- discoverable
- education
- embedding
- equivalence
- extending patterns
- gauntlet
- graded hurdles
- invariants
- look-up
- math class
- math in the comics
- matrix multiplication
- models
- naming
- notation
- puzzle
- recurrence relationship
- representational proof
- representations
- reverse engineering
- selection
- series on math learning
- sieve
- sorting
- standing on nothing
- state
- unlearning
- whole vs. parts
Archives
- July 2011
- June 2011
- May 2011
- April 2011
- February 2011
- January 2011
- December 2010
- November 2010
- October 2010
- September 2010
- August 2010
- July 2010
- May 2010
- April 2010
- March 2010
- February 2010
- January 2010
- December 2009
- September 2009
- August 2009
- July 2009
- June 2009
- May 2009
- April 2009
- March 2009
- February 2009
- January 2009
- December 2008
Tag Archives: equivalence
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
Posted in Uncategorized
Tagged black box, denominations, equivalence, extending patterns, invariants, look-up, models, naming, recurrence relationship, representations
1 Comment
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
Leave a comment
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) 2|13 and then looked at an operator that turns 2|13 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
Posted in Uncategorized
Tagged black box, denominations, equivalence, invariants, models, representations, reverse engineering
1 Comment
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
Posted in Uncategorized
Tagged black box, denominations, equivalence, extending patterns, models, reverse engineering, whole vs. parts
1 Comment
Operators, Functions, and Properties – part 31
In the prior post in this series, we looked at the kind of operators typically encountered in school (K-12), whether or not they are called operators. Many of them are single number input – single number output, but not all. … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, models, naming, reverse engineering, whole vs. parts
1 Comment
Operators, Functions, and Properties – part 29
In this series, we’ve been looking at simple machines where pushing a button invokes an operator that changes the state of the machine. Stopwatches, coffee makers, calculators are all examples of such machines – some simpler than others. Many of … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, recurrence relationship, representations
Leave a comment
Operators, Functions, and Properties – part 28
The prior post in this series showed that we can get complex and rich behavior from combining simple operators and feeding their output back to their input (through what is called “state”, and the whole arrangement is known as a … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, recurrence relationship, representations, reverse engineering
1 Comment
Operators, Functions, and Properties – part 26
In the previous post in this series, we linked two state machines together, weakly, by arranging to press their Start buttons at the same time and to press their Next buttons at the same time. As a result, we got … Continue reading
Posted in Uncategorized
Tagged black box, equivalence, extending patterns, models, recurrence relationship, representations, reverse engineering
2 Comments
Learning and Unlearning Math 