If you are a homeschooler or classroom teacher, student or independent learner, or anyone else who writes about math, now is the time to send in your favorite blog post for next week’s Playful Math Blog Carnival.

Don’t procrastinate: The deadline for entries is this Friday, August 24. The carnival will be posted next week at Find the Factors blog.

Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to your own. Beginning bloggers are often shy about sharing, but like all of us, they love finding new readers.

Would You Like to Host the Carnival?

Help! I can’t keep the carnival going on my own.

Hosting the blog carnival can be a lot of work, but it’s fun to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival usually brings a nice little spike in traffic to your blog.

If you think you’d like to join in the fun, read the instructions on our Playful Math Blog Carnival homepage. Then leave a comment or email me to let me know which month you’d like to take.

Explore the Other Math Carnivals

While you’re waiting for next week’s carnival, you may enjoy:

CREDITS: “L.A. County Fair” photo (top) by Omar Bárcena (CC BY 2.0) via Flickr.]/span>

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

“When I began my college education, I still had many doubts about whether I was good enough for mathematics. Then a colleague said the decisive words to me: it is not that I am worthy to occupy myself with mathematics, but rather that mathematics is worthy for one to occupy oneself with.”

I would like to win over those who consider mathematics useful, but colourless and dry — a necessary evil…

No other field can offer, to such an extent as mathematics, the joy of discovery, which is perhaps the greatest human joy.

The schoolchildren that I have taught in the past were always attuned to this, and so I have also learned much from them.

It never would have occurred to me, for instance, to talk about the Euclidean Algorithm in a class with twelve-year-old girls, but my students led me to do it.

I would like to recount this lesson.

What we were busy with was that I would name two numbers, and the students would figure out their greatest common divisor. For small numbers this went quickly. Gradually, I named larger and larger numbers so that the students would experience difficulty and would want to have a procedure.

I thought that the procedure would be factorization into primes.

They had still easily figured out the greatest common divisor of 60 and 48: “Twelve!”

But a girl remarked: “Well, that’s just the same as the difference of 60 and 48.”

“That’s a coincidence,” I said and wanted to go on.

But they would not let me go on: “Please name us numbers where it isn’t like that.”

“Fine. 60 and 36 also have 12 as their greatest common divisor, and their difference is 24.”

Another interruption: “Here the difference is twice as big as the greatest common divisor.”

“All right, if this will satisfy all of you, it is in fact no coincidence: the difference of two numbers is always divisible by all their common divisors. And so is their sum.”

Certainly that needed to be stated in full, but having done so, I really did want to move on.

However, I still could not do that.

A girl asked: “Couldn’t they discover a procedure to find the greatest common divisor just from that?”

They certainly could! But that is precisely the basic idea behind the Euclidean Algorithm!

So I abandoned my plan and went the way that my students led me.

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

My son can’t stand long division or fractions. We had a lesson on geometry, and he enjoyed that — especially the 3-D shapes. If we can just get past the basics, then we’ll have time for the things he finds interesting. But one workbook page takes so long, and I’m sick of the drama. Should we keep pushing through?

Those upper-elementary arithmetic topics are important. Foundational concepts. Your son needs to master them.

Eventually.

But the daily slog through page after page of workbook arithmetic can wear anyone down.

Many children find it easier to focus on math when it’s built into a game.

Games are great for practicing math your child has already learned. But for introducing new concepts, you’ll probably want to follow your textbook.

Still, even with textbook math, there are ways to make the journey less tedious:

Most children do not need to do every problem on a workbook page, or every page in a section. There is a lot of extra review built into any math program.

You don’t have to finish a section before you work whatever comes after it. Use sticky bookmarks to keep track of your position in two or three chapters at a time. Do a little bit of the mundane arithmetic practice, and then balance that with some of the more interesting topics your son enjoys.

As much as possible, do math out loud with a whiteboard for scratch work. Somehow, working with colorful markers makes arithmetic more bearable.

Set a timer for math, and make the time short enough that he feels the end is in sight. I suggest no more than thirty minutes a day for now. And whenever the timer rings, stop immediately — even if you are in the middle of a problem.

The Timer Can Be a Life-Saver

Doing math in short sessions helped us avoid the emotional melt-downs my daughter used to have.

Thinking is hard work, and if I asked for too much, she would crash.

Because I sat with her and worked together every problem, I knew what she understood and when we could skip a problem. Or sometimes even jump several pages. Which meant that, even with short lessons, we still got through our book on time.

Arithmetic Is Like Vegetables

But as I said before, textbooks include a whole lot of repetition.

Too much repetition deadens the brain.

So we also took long breaks from our textbook program. Entire school-year-long breaks, just playing with math. Letting “enrichment” activities be our whole curriculum.

As healthy as vegetables are, you would never limit your son to eating just lima beans and corn.

Similarly, be sure to feed him a varied math diet.

For example, you can follow his interest in geometry beyond the standard school topics.

Building Lego scenes is a practical application of 3-D geometry. He might even want to try stop motion animation.

Talk about how math works in real life. Ponder the choices on John Stevens’s “Would You Rather?” blog or try some of the challenges at Andrew Stadel’s Estimation 180 website. Many of these require three-dimensional reasoning.

A Blogging Challenge

This is my second contribution to the blogging challenge #MTBoSBlaugust.

I’m aiming for at least one post each week. A simple, modest goal. But if I manage it, that will be four times the pace I’ve set in recent months.

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

Check out the new playful math blog carnival at Three J’s Learning blog. Joshua put together a great collection of math games, activities, and teaching tips:

The carnival features a “square dancing” puzzle, strategy game discussions, divisibility rules, fake theorems, and mathematical oceans in disguise. And much more!

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

It’s carnival time again. Activities, games, lessons, hands-on fun — if you’ve written a blog post about math, we’d love to have you join our Playful Math Blog Carnival.

Posts must be relevant to students or teachers of school-level mathematics (that is, anything from preschool up through first-year calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

Don’t procrastinate: The deadline for entries is next Sunday, July 22. The carnival will be posted at Three J’s Learning blog.

Have you noticed a new math blogger on your block that you’d like to introduce to the rest of us? Feel free to submit another blogger’s post in addition to your own. Beginning bloggers are often shy about sharing, but like all of us, they love finding new readers.

Need an Idea-Starter?

If you haven’t written anything about math lately, here are some ideas to get your creative juices flowing…

Talking Math with Kids: Children often have surprising insight. Even when they’re confused about math, their point of view can open our adult eyes to new understanding. Share your kids’ stories.

Games or Activities: Do you have a game, activity, or anecdote about teaching math to young students? We’d love to play along.

Lesson Ideas: This section is for arithmetic explorations, geometry puzzles, trig investigations, contest-preparation tips, and more. Can you make math topics come alive, so they will stick in a student’s mind?

Teaching Tips: Other teachers’ blogs are an important factor in my continuing education. The more I read about the theory and practice of teaching math, the more I realize how much I have yet to learn. So please, fellow teachers, don’t be shy — share your insights!

Mathematical Recreations: What kind of math do you do, just for fun?

Explore the Other Math Carnivals

While you’re waiting for next week’s carnival, you may enjoy:

CREDITS: “Two Bloggers, after Norman Rockwell” sketch (top) by Mike Licht (CC BY 2.0) via Flickr.

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.