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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Alexandria’s Dog is Now a Teacher

Posted on by Denise Gaskins


Photo by alex-s.

A reader of Indian descent has been kind enough to write to me about a difference in our cultures. In the US, or at least in the parts with which I am familiar, it is common to name one’s pet after a famous person. In India, however, to name a dog after a human is a very deep insult.

I am sorry! It was not intended that way.

Therefore, I have re-named Alexandria Jones‘s dog after a Westerner. I would like to keep the tradition of naming the characters in my Alex stories after people in math history, so I am hoping this one will not offend anyone.

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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

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How to Teach Math to a Struggling Student

Posted on by Denise Gaskins

photo by MC Quinn via flickr (CC BY 2.0)

Paraphrased from a homeschool math discussion forum:

“Help! My daughter struggles with arithmetic. I guess she is like me: just not a math person. She is an outstanding reader. When we do word problems, she usually has no trouble. She’s a whiz at strategy games and beats her dad at chess every time. But numbers — yikes! When we play Yahtzee, she gets lost trying to add up her score. The simple basics of adding and subtracting confuse her.

“Since I find math difficult myself, it’s hard for me to know what she needs. What’s missing to make it click for her? She used to think math was fun and tested well above grade level, but I listened to some well-meaning advice and totally changed the way we were schooling. I switched from using workbooks and games to using Saxon math, and she got extremely frustrated. Now she hates math.”

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Quotes XXI: How Is Logic Like Whiskey?

Posted on by Denise Gaskins


Photo by Brian – Progressive Spin.

Logic is the science of making valid deductions and proofs — and it is also a fruitful topic for blackboard quotes. Here are a few of my favorites:

You can only find truth with logic if you have already found truth without it.

— G. K. Chesterton
The Man Who Was Orthodox

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Game: Avoid Three, or Tic-Tac-No!

Posted on by Denise Gaskins

Math concepts: slope, logical strategy
Number of players: 2 or more
Equipment: 4×4 or larger grid, pebbles or other tokens to mark squares

Set Up

Alexandria Jones and her brother Leon played Avoid Three with pebbles on a grid scratched in the sand, but you can also use pencils or markers on graph paper. You need a rectangular playing area at least 4×4 squares large. The bigger your grid, the longer your game.

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Substitute Teacher Experiments with Combinatorics

Posted on by Denise Gaskins


Photo by peigianlong.

Here is a puzzle from Just a Substitute Teacher:

Lesson plan entry: “Hand out worksheet packets and have students staple before starting. They know what to do.”

Sounds simple enough! Four numbered sheets, eight total pages, printed front and back. What could go wrong?

Do you know how many possible combinations four pieces of paper can be arranged for stapling?

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