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Negative Numbers for Young Students

Posted on by Denise Gaskins

[Rescued from my old blog.]

Would you like to introduce your students to negative numbers before they study them in pre-algebra? With a whimsical number line, negative numbers are easy for children to understand.

Get a sheet of poster board, and paint a tree with roots — or a boat on the ocean, with water and fish below and bright sky above. Use big brushes and thick poster paint, so you are not tempted to put in too much detail. A thick, permanent marker works well to draw in your number line, with zero at ground (or sea) level and the negative numbers down below.

Continue reading Negative Numbers for Young Students

Harmonic Series Quotation

Posted on by Denise Gaskins

If you’d like to start your week with a laugh, here’s a great quote:

Today I said to the calculus students, “I know, you’re looking at this series and you don’t see what I’m warning you about. You look and it and you think, ‘I trust this series. I would take candy from this series. I would get in a car with this series.’ But I’m going to warn you, this series is out to get you. Always remember: The harmonic series diverges. Never forget it.”

—Rudbeckia Hirta
Learning Curves Blog: The Harmonic Series
quoting Alexandre Borovik

Order of Operations

Posted on by Denise Gaskins

[Rescued from my old blog.]

Marjorie in AZ asked a terrific question on the (now defunct) AHFH Math forum:

“…I have always been taught that the order of operations (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction) means that you work a problem in that order. All parenthesis first, then all exponents, then all multiplication from left to right, then all division from left to right, etc. …”

Many people are confused with order of operations, and it is often poorly taught. I’m afraid that Marjorie has fallen victim to a poor teacher — or at least, to a teacher who didn’t fully understand math. Rather than thinking of a strict “PEMDAS” progression, think of a series of stair steps, with the inverse operations being on the same level.

Continue reading Order of Operations

It’s Elementary (School), My Dear Watson

Posted on by Denise Gaskins

[Rescued from my old blog.]

From Time magazine, June 18, 1956:

“[M]athematics has the dubious honor of being the least popular subject in the curriculum… Future teachers pass through the elementary schools learning to detest mathematics… They return to the elementary school to teach a new generation to detest it.”

Quoted by George Polya in How to Solve It. I finally got my very own copy of this excellent book, so I can quit pestering the librarian to let me order it from library loan again…

Blogger Rudbeckia Hirta teaches math to pre-service teachers, and it seems that not much has changed since 1956. Hirta says the test answers shown were representative of her class — for instance, 25% of her students missed the juice problem. Too bad these students never read Polya’s book, in which he discusses a four-step method for solving problems. Step four is to look back and ask yourself whether the answer makes sense. Good advice!

Continue reading It’s Elementary (School), My Dear Watson

Our Tax Dollars at Work

Posted on by Denise Gaskins

Well, the new year has come, and it’s time to start gathering up receipts and thinking about tax forms.

Would you like to know that our tax dollars are doing good in the world? The National Science Foundation has spent many millions developing and promoting “reform” math textbooks, with encouragement from the U.S. Department of Education. Surely our public schools will now rise out of the doldrums and surge ahead in mathematical achievement, right?

Try for yourself this problem from one of the more famous/infamous of the reform math textbooks:

Can you find the slope and y-intercept of this equation?

10 = x – 2.5

And then check out this editorial[editorial has disappeared] at edspresso.com. You’ll be amazed at the answer!

Update: Checking on back-links, I discovered that this page had gone AWOL, so I’ll give you the “answer” from the teacher’s manual. The “slope” is 1 and the “y-intercept” is -2.5, according to Connected Math. Unfortunately, this equation actually describes a vertical line (undefined slope) at x=12.5 (never touches the y-axis).

Doesn’t bode well for “CMP helps students and teachers develop understanding of important mathematical concepts…”

Set Daily Puzzle

Posted on by Denise Gaskins

The spring semester of homeschool co-op classes starts tomorrow, and I still have a couple of handouts to prepare and several pages of notes to go over in preparation. So naturally, I find myself flitting from here to there on my computer, browsing new links and cleaning out the old.

As the saying goes:

“I used to be an amateur crastinator, but now I’ve turned pro.”

In a dusty pile of long-neglected bookmarks, I rediscovered this treasure:

Set Daily Puzzle

I love this game!

Why Study Mathematics?

Posted on by Denise Gaskins
by d3 Dan via flickr

[Rescued from my old blog.]

What teacher hasn’t heard a student complain, “When am I ever going to have to use this?” Didn’t most of us ask it ourselves, once upon a time? And unless we choose a math-intensive career like engineering, the truth is that after we leave school, most of us will never again use most of the math we learned. But if math beyond arithmetic isn’t all that useful, then what’s the point?

If you or your student is singing the Higher Math Blues, here are some quotations that may cheer you up — or at least give you the strength of vision to keep on slogging.

We study mathematics…

Continue reading Why Study Mathematics?

Fraction Division — A Poem

Posted on by Denise Gaskins

[Rescued from my old blog.]

Division of fractions is surely one of the most difficult topic in elementary arithmetic. Very few students (or teachers) actually understand how and why it works. Most of us get by with memorized rules, such as:

Ours is not to reason why;
just invert and multiply!

Continue reading Fraction Division — A Poem

What is a Blog Carnival?

Posted on by Denise Gaskins

The Carnival of Homeschooling is almost ready for its first birthday, and Henry at Why Homeschool is looking for submissions. So if you’re a homeschool blogger, go back over your recent blog posts and pick out a good one to share!

A blog carnival is a collection of blog posts loosely related to a given topic. Some, like the Carnival of Homeschooling, are posted weekly, while others come once a month or whenever the organizer gets around to doing it. Blog carnivals give bloggers a chance to reach a wider audience than just their regular readers, and they give readers interested in the topic a chance to access a wide variety of articles at once.

Continue reading What is a Blog Carnival?

The Game That Is Worth 1,000 Worksheets

Posted on by Denise Gaskins

Have you and your children been struggling to learn the math facts? The game of Math Card War is worth more than a thousand math drill worksheets, letting you build your children’s calculating speed in a no-stress, no-test way.

Math concepts: greater-than/less-than, addition, subtraction, multiplication, division, fractions, negative numbers, absolute value, and multi-step problem solving.

Continue reading The Game That Is Worth 1,000 Worksheets