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This fall, my homeschool co-op math class will play with math journaling.

But my earlier dot-grid notebooks were designed for adults. Too thick, too many pages. And the half-cm dot grid made lines too narrow for young writers.

So I created a new series of paperback dot-grid journals for my elementary and middle school students.

I’m sure we’ll use several of these activities in my homeschool co-op math class this fall.

Noticing and Wondering

Learning math requires more than mastering number facts and memorizing rules. At its heart, math is a way of thinking.

So more than anything else, we need to teach our kids to think mathematically — to make sense of math problems and persevere in figuring them out.

Help your children learn to see with mathematical eyes, noticing and wondering about math problems.

Whenever your children need to learn a new idea in math, or whenever they get stuck on a tough homework problem, that’s a good time to step back and make sense of the math.

Kids can write their noticings and wonderings in the math journal. Or you can act as the scribe, writing down (without comment) everything child says.

For more tips on teaching students to brainstorm about math, check out these online resources from The Math Forum:

Problem-solving is a habit of mind that you and your children can learn and grow in. Help your kids practice slowing down and taking the time to fully understand a problem situation.

Puzzles Are Math Experiments

Almost anything your child notices or wonders can lead to a math experiment.

For example, one day my daughter played an online math game…

A math journal can be like a science lab book. Not the pre-digested, fill-in-the-blank lab books that some curricula provide. But the real lab books that scientists write to keep track of their data, and what they’ve tried so far, and what went wrong, and what finally worked.

Here are a few open-ended math experiments you might try:

Explore Shapes

Pick out a 3×3 set of dots. How many different shapes can you make by connecting those dots? Which shapes have symmetry? Which ones do you like the best?

What if you make shapes on isometric grid paper? How many different ways can you connect those dots?

Limit your investigation to a specific type of shape. How many different triangles can you make on a 3×3 set of dots? How many different quadrilaterals? What if you used a bigger set of dots?

Explore Angles

On your grid paper, let one dot “hold hands” with two others. How many different angles can you make? Can you figure out their degree without measuring?

Are there any angles you can’t make on your dot grid? If your paper extended forever, would there be any angles you couldn’t make?

Does it make a difference whether you try the angle experiments on square or isometric grid paper?

Explore Squares

How many different squares can you draw on your grid paper? (Don’t forget the squares that sit on a slant!) How can you be sure that they are perfectly square?

Number the rows and columns of dots. Can you find a pattern in the corner positions for your squares? If someone drew a secret square, what’s the minimum information you would need to duplicate it?

Does it make a difference whether you try the square experiments on square or isometric grid paper?

I’d love to hear your favorite math explorations or journaling tips!

Please share in the comments section below.

P.S.: Do you have a blog? If you’d like to feature a math journal review and giveaway, I’ll provide the prize. Send a message through my contact form or leave a comment below, and we’ll work out the details.

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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.

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“As we go through each lesson, it seems like my daughter has a good handle on the concepts, but when we get to the test she forgets everything. When I ask her about it, she shrugs and says, ‘I don’t know.’ What do you do when your child completely loses what she has learned?”

Forgetting is the human brain’s natural defense mechanism. It keeps us from being overwhelmed by the abundance of sensory data that bombards us each moment of every day.

Our children’s minds will never work like a computer that can store a program and recall it flawlessly months later.

Sometimes, for my children, a gentle reminder is enough to drag the forgotten concept back out of the dust-bunnies of memory.

Other times, I find that they answer “I don’t know” out of habit, because it’s easier than thinking about the question. And because they’d prefer to be doing something else.

And still other times, I find out they didn’t understand the topic as well as I thought they did when we went through it before.

No matter how we adults try to explain the concepts, some kids want to be answer-getters. They don’t want to do the hard work of thinking a concept through until it makes a connection in their minds. They want to memorize a few steps and crank through the lesson to get it over with.

In all these cases, what helps me the most is conversation.

My children and I always talk about our math. I ask questions like “What do you think? What do you remember? Can you explain the question to me? What are they asking for?”

And, whether the child’s answer is right or wrong, I practice my poker face. Trying not to give anything away, I ask, “How did you figure it out? Can you think of a way to confirm your answer?”

Talking Math with Your Kids

Not sure how to talk about math with your children?

If you have preschool and elementary-age kids, read Christopher Danielson’s inspiring book and blog:

For middle school and older students, check out Fawn Nguyen’s wonderful collection of Math Talks. Be sure to read the “Teachers” page for tips and talking points:

“You don’t need special skills to do this. If you can read with your kids, then you can talk math with them. You can support and encourage their developing mathematical minds.”

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.

I’ve been following Sonya’s Arithmophobia No More blog for a couple of years, and I love the work she is doing. But this month, she’s teamed up with Lacy at Play, Discover, Learn (another great blog to follow!) to offer a humongous bundle of playful math.

You get math journaling pages, games, creative task cards, thought-provoking worksheets, and video training resources to help you build your child’s understanding of math from arithmetic to early algebra. Wow!

These activities are perfect for homeschooling families or anyone looking to supplement their child’s current math curriculum with effective discovery-based activities. If you’ve ever wondered what to do with those Cuisenaire rods you picked up on sale way back when, this bundle is for you.

I’m so looking forward to using some of these ideas with my elementary homeschool co-op kids next year!

If you’ve been reading my blog for very long, you’ve probably seen how much I love the blog, books, and classes available from the Natural Math folks.

Their newest book is just off the presses — Funville Adventures, a math adventure chapter book.

And until December 20, they’re having a holiday sale. Make your own bundle of any Natural Math books. Playful algebra, calculus for 5-year-olds, inquiry problems and more: Great deal!

(US customers only: We’re sorry we can’t offer bulk discounts for our international readers, but the complexities of international duties and tax laws are too much for this very small family business.)

Do You Know of Any Math Deals?

If you’ve seen a great deal or holiday price on a math resource you love, please share!

Add your deal to the comment section below, so we can all take advantage of the math joy this season.

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.

You want your child to succeed in math because it opens so many doors in the future.

But kids have a short-term perspective. They don’t really care about the future. They care about getting through tonight’s homework and moving on to something more interesting.

So how can you help your child learn math?

When kids face a difficult math problem, their attitude can make all the difference. Not so much their “I hate homework!” attitude, but their mathematical worldview.

Does your child see math as answer-getting? Or as problem-solving?

Answer-getting asks “What is the answer?”, decides whether it is right, and then goes on to the next question.

Problem-solving asks “Why do you say that?” and listens for the explanation.

Problem-solving is not really interested in “right” or “wrong”—it cares more about “makes sense” or “needs justification.”

Homeschool Memories

In our quarter-century-plus of homeschooling, my children and I worked our way through a lot of math problems. But often, we didn’t bother to take the calculation all the way to the end.

Why didn’t I care whether my kids found the answer?

Because the thing that intrigued me about math was the web of interrelated ideas we discovered along the way:

How can we recognize this type of problem?

What other problems are related to it, and how can they help us understand this one? Or can this problem help us figure out those others?

What could we do if we had never seen a problem like this one before? How would we reason it out?

Why does the formula work? Where did it come from, and how is it related to basic principles?

What is the easiest or most efficient way to manipulative the numbers? Does this help us see more of the patterns and connections within our number system?

Is there another way to approach the problem? How many different ways can we think of? Which way do we like best, and why?

What Do You think?

How did you learn math? Did your school experience focus on answer-getting or problem-solving?

How can we help our children learn to think their way through math problems?

I’d love to hear from you! Please share your opinions in the Comments section below.

CREDITS: “Maths” photo (top) by Robert Couse-Baker. “Math Phobia” photo by Jimmie. Both via Flickr (CC BY 2.0). Phil Daro video by SERP Media (the Strategic Education Research Partnership) via Vimeo.

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.