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

Posted in Uncategorized | Tagged , , , , , , | 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 , , , , , , | Leave a comment

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

Posted in Uncategorized | Tagged , , , , , | 3 Comments

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

Posted in Uncategorized | Tagged , , , , , | 1 Comment

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

Posted in Uncategorized | Tagged , , , , , , | 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 wide-spread use of four-function calculators.  … Continue reading

Posted in Uncategorized | Tagged , , , , | Leave a comment

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

Posted in Uncategorized | Tagged , , , , , | 2 Comments

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 twenty-three.  The basic building blocks in this … Continue reading

Posted in Uncategorized | Tagged , , , , , | 2 Comments

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

Posted in Uncategorized | Tagged , , | 1 Comment

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

Posted in Uncategorized | Tagged , , | Leave a comment