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Tag Archives: deferred computation
Operators, Functions, and Properties – part 1
I intend to write some things on operators in mathematics, beginning in this post. Functions and properties will be brought in as appropriate. The idea of operators is absolutely basic and central to computers and computing; they are also important … Continue reading
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Tagged deferred computation, extending patterns, models, naming, representations, state, unlearning
7 Comments
Notes on Fractions – Deferred Computation
What would happen if we thought of a fraction as a division that hadn’t been done yet and that we weren’t necessarily interested in doing yet? I’ve suggested in earlier posts (e.g. here and here) that kids often don’t see … Continue reading
Posted in Uncategorized
Tagged deferred computation, denominations, extending patterns, math class, models, naming, unlearning
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Notes on Fractions
I worked with a 7th grader the other day who was solving a “proportion problem”. He had set it up as and then solved it by reasoning that 30 was 5 times bigger than 6, so the scale factor was … Continue reading
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Tagged deferred computation, denominations, math class, models, naming, representations
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Notes on Deferred Computation – the Pythagorean Spiral
The following figure is quite interesting: Imagine you start out home, in the center at the bottom, and move a distance of 1 to the right to A. At A, you have traveled a total distance of 1, and you … Continue reading
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Tagged deferred computation, extending patterns, math class, models, recurrence relationship, representations
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Notes on Embedding
“Embedding” is one of those mathematics ideas that is really simple but we manage to make it seem really complicated. Typically, the first time somebody studying mathematics hears or uses the term is well into their university studies. And yet … Continue reading
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Tagged deferred computation, denominations, extending patterns, models, naming, representations, unlearning
6 Comments
Notes on Representation – Multiplication
People who went through school in prior generations typically were sure that multiplying two quantities is harder to do than adding those same quantities. My impression is that this perception hasn’t really changed with the widespread use of fourfunction calculators. … Continue reading
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Tagged deferred computation, extending patterns, models, representations, unlearning
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Notes on Representation – Large Numbers
In our normal decimal number system for representing quantities, we can usually tell pretty easily which numbers are larger. For example, if you see 412 and 409 together, you don’t have to do a lot of work to tell which … Continue reading
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Tagged deferred computation, denominations, extending patterns, models, naming, representations
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Notes on Representation – Prime Bags
In our normal decimal number system, we represent quantity by writing down pieces that are supposed to be added together: 23 has a twenty piece and a three piece, and together that makes twentythree. The basic building blocks in this … Continue reading
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Tagged deferred computation, denominations, models, naming, representations, unlearning
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Math and Fraction Keys
I have been around computers and calculators for much of my life. I remember mechanical calculators that looked like big industrial strength typewriters, and I remember when the first electronic calculator came out that offered a – would you believe … Continue reading
Deferred computation and Bluffing
by naming something you don’t know, you can tame it. in math, you can often bluff and live another day! it’s a respectable trick, worth learning Continue reading