What’s Wrong with “Repeated Addition”?

Posted on by Denise Gaskins

[Photo by Alejandra Mavroski.]

Myrtle called it The article that launched a thousand posts…, and counting comments on this and several other blogs, that may not be too much of an exaggeration. Yet the discussion feels incomplete — I have not been able to put into words all that I want to say. Thus, at the risk of once again revealing my mathematical ignorance, I am going to try another response to Keith Devlin’s multiplication articles.

Let me state up front that I speak as a teacher, not as a mathematician. I am not qualified, nor do I intend, to argue about the implications of Peano’s Axioms. My experience lies primarily in teaching K-10, from elementary arithmetic through basic algebra and geometry. I remember only snippets of my college math classes, back in the days when we worried more about nuclear winter than global warming.

I will start with a few things we can all agree on…

Continue reading What’s Wrong with “Repeated Addition”?

Crazy 4 Math Contest

Posted on by Denise Gaskins

I heard of this contest in an e-mail from ClickSchooling:

Kids, share your creative math ideas! Describe how you use math in any activity you love to do — a sport, game, craft, hobby, or anything else.

Send in a description of the activity and how it uses math, as well as any drawing(s) or diagram(s). There are many great prizes to be won. Please ensure you’ve read and understand our contest’s rules and regulations before entering.

Sounds like fun! If you want to enter, act quickly. Entries must be submitted online by July 30th. Visit Crazy4Math.com for more information and to check out the winners from previous years.

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

Continue reading Summer: Time to Sharpen Math Skills

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…

Continue reading Math Game: What Number Am I?

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.

Continue reading Hit Me! (A Math Game)

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.

Continue reading Math Facts Are like Learning to Type

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.

Continue reading Diagnosis: Math Workbook Syndrome

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.”

Continue reading How to Teach Math to a Struggling Student