Writing to Learn Math II

Posted on by Denise Gaskins

[Photo by Andy Hay.]

In addition to all the funny Google searches, I get plenty of normal inquiries about math topics. People come here looking for help with fractions, word problems, and math club activities — no surprise, those — but I would never have predicted the popularity of the search topic “writing in math class.”

Last year, I compiled a variety of math journal resources, but I’ve found many more since then, especially for older (high school and college) students. So if you’re looking for new ways to get your math students writing…

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30+ Things to Do with a Hundred Chart

Posted on by Denise Gaskins

[Photo by geishaboy500 via Flickr (CC BY 2.0).]

Are you looking for creative ways to help your children study math? Even without a workbook or teacher’s manual, your kids can learn a lot about numbers. Just spend an afternoon playing around with a hundred chart (also called a hundred board or hundred grid).

My free 50-page PDF Hundred Charts Galore! printables file features 1–100 charts, 0–99 charts, bottom’s-up versions, multiple-chart pages, blank charts, game boards, and more. Everything you need to play the activities below and those in my new 70+ Things to Do with a Hundred Chart book.

Download Free “Hundred Charts Galore!” Printables

Shop for “70+ Things To Do with a Hundred Chart” Book

And now, let’s play…

Continue reading 30+ Things to Do with a Hundred Chart

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”?

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?

Math History on the Internet

Posted on by Denise Gaskins

[Image from the MacTutor Archive.]

The story of mathematics is the story of interesting people. What a shame it is that our children see only the dry remains of these people’s passion. By learning math history, our students will see how men and women wrestled with concepts, made mistakes, argued with each other, and gradually developed the knowledge we today take for granted.

In a previous article, I recommended books that you may find at your local library or be able to order through inter-library loan. Now, let me introduce you to the wealth of math history resources on the Internet.

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Hooray for (Math) History

Posted on by Denise Gaskins

Photo by Benimoto.

John Napier foiled a thief with the aid of logic and a black rooster. For this and other acts of creative problem solving, his servants and neighbors suspected him of witchcraft.

What does this have to do with mathematics?

Math was Napier’s favorite hobby. He invented logarithms to help people handle large numbers easily, and he even created a calculator out of a chessboard. [See how it works: addition, subtraction, multiplication.]

Continue reading Hooray for (Math) History

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

Subtracting Mixed Numbers: A Cry for Help

Posted on by Denise Gaskins

Photo by powerbooktrance.

Paraphrased from a homeschool math discussion forum:

“Help me teach fractions! My son can do long subtraction problems that involve borrowing, and he can handle basic fraction math, but problems like 9 - 5 \frac{2}{5} give him a brain freeze. To me, this is an easy problem, but he can’t grasp the concept of borrowing from the whole number. It is even worse when the math book moves on to 10 \frac{1}{4} - 2 \frac{3}{7} .”

Several homeschooling parents replied to this question, offering advice about various fraction manipulatives that might be used to demonstrate the concept. I am not sure that manipulatives are needed or helpful in this case. The boy seems to have the basic concept of subtraction down, but he gets flustered and is unsure of what to do in the more complicated mixed-number problems.

The mother says, “To me, this is an easy problem” — and that itself is one source of trouble. Too often, we adults (homeschoolers and classroom teachers alike) don’t appreciate how very complicated an operation we are asking our students to perform. A mixed-number calculation like this is an intricate dance that can seem overwhelming to a beginner.

I will go through the calculation one bite at a time, so you can see just how much a student must remember. As you read through the steps, pay attention to your own emotional reaction. Are you starting to feel a bit of brain freeze, too?

Afterward, we’ll discuss how to make the problem simpler…

Continue reading Subtracting Mixed Numbers: A Cry for Help

How Should We Teach Arithmetic?

Posted on by Denise Gaskins

Dave Marain of MathNotations is running a poll about how to teach multiplication, but the question has broader application:

How should we teach the arithmetic algorithms
— or should we teach them at all?

Algorithms are step-by-step methods for doing something. In arithmetic, we have standard algorithms for addition, subtraction, multiplication, and long division. Once the student masters the steps for any particular algorithm, he can follow the steps to a correct answer without ever thinking about what the numbers mean.

Continue reading How Should We Teach Arithmetic?