If It Ain’t Repeated Addition, What Is It?

Posted on by Denise Gaskins

[Photo by SuperFantastic.]

Keith Devlin’s latest article, It Ain’t No Repeated Addition, brought me up short. I have used the “multiplication is repeated addition” formula many times in the past — for instance, in explaining order of operations. But according to Devlin:

Multiplication simply is not repeated addition, and telling young pupils it is inevitably leads to problems when they subsequently learn that it is not.

I found myself arguing with the article as I read it. (Does anybody else do that?) If multiplication is not repeated addition, then what in the world is it?

Continue reading If It Ain’t Repeated Addition, What Is It?

Summer: Time to Sharpen Math Skills

Posted on by Denise Gaskins

[Photo by Vox Efx.]

School’s out — and what could be more fun in the lazy, hazy days of summer than to study math? Check out these articles from Maria Miller of Homeschool Math Blog:

How to Help a Student Who is Behind in Math

Keeping Your Math Skills Sharp Over The Summer

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Math Game: What Number Am I?

Posted on by Denise Gaskins

Photo by jaycoxfilm.

Math concepts: mental calculations, math vocabulary, and anything else you want to include
Number of players: any number, but I think it works best with two players who alternate asking questions
Equipment: imagination and, if necessary, scratch paper

Many years ago, I read a magazine article by mathematical music critic Edward Rothstein, wherein he described a game he invented for his daughter:

  • “What number am I? If you add me to myself, you get four.”

Rather than explaining the rules of the game, let me tell you a story…

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The Mosaic Tile Mystery

Posted on by Denise Gaskins

Dear Alexandria Jones,

We continue to excavate the ancient building complex, which I believe may have been Pythagoras’s school. Yesterday, one of our digging crews uncovered a mosaic tile floor in the courtyard. The pattern of the tiles alternates between two square designs. (See enclosed sketches.)

During your family’s recent visit, you expressed an interest in the mathematical ideas of Pythagoras. Could you or your father offer us any insight into what these tile designs may represent?

I look forward to your response.

Sincerely,
Sofia Theano, Ph.D.
Crotone, Italy

Continue reading The Mosaic Tile Mystery

Hit Me! (A Math Game)

Posted on by Denise Gaskins

Photo by paparutzi.

Math concepts: addition, subtraction, negative numbers, mental math, absolute value
Number of players: any number
Equipment: math cards (two decks may be needed for a large group)

Set Up

One player (the dealer) shuffles the math cards and deals one card face down for each player, beginning with the player on his left and proceeding in turn around the table. Then he deals one card face up beside each face down card.

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An Ancient Mathematical Crisis

Posted on by Denise Gaskins

PythagoreanCat

[When Alexandria Jones and her family visited an excavation in southern Italy, they learned several tidbits about the ancient school of mathematics and philosophy founded by Pythagoras. Here is Alex’s favorite story.]

It hit the Pythagorean Brotherhood like an earthquake, a crisis of faith which shook the foundations of their universe. Some say Pythagoras himself made the dread discovery, others blame Hippasus of Metapontum.

Something certainly did happen with Hippasus. The Brotherhood sent him into exile for insubordination, or for breaking the rule of secrecy — or was it for proving the unthinkable? According to legend, Hippasus drowned at sea, but was it a mere shipwreck or the wrath of the gods? Some say the irate Pythagoreans threw him overboard…

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Math Facts Are like Learning to Type

Posted on by Denise Gaskins

Photo by jetheriot.

One of the most common math questions on homeschooling discussion forums is, “How can I help my child master the math facts?” Unfortunately, when it comes to drilling facts, many children think math is spelled “B-O-R-I-N-G.” Worksheets are tedious, flash cards make them groan, and even the latest computer game is a yawner.

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Diagnosis: Math Workbook Syndrome

Posted on by Denise Gaskins

Photo by otisarchives3.

I discovered a case of MWS (Math Workbook Syndrome) one afternoon, as I was playing Multiplication War with a pair of 4th grade boys. They did fine with the small numbers and knew many of the math facts by heart, but they consistently tried to count out the times-9 problems on their fingers. Most of the time, they lost track of what they were counting and gave wildly wrong answers.

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The Function Machine Game

Posted on by Denise Gaskins

Math concepts: odd numbers, even numbers, greater-than/less-than, rounding off, addition, subtraction, multiplication, division, fractions, negative numbers, prime numbers, square numbers, problem solving, mental math
Number of players: two or more
Equipment: pencil (or pen) and paper for every player

Continue reading The Function Machine Game