Homeschooling

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 hope you enjoy them, too!

Click here for more information

Math Journaling Prompts

So, what can your kids do with a math journal?

Here are a few ideas: 

• Make up their own word problems. See this blog post for examples.

• Enjoy a living math book, and then diagram the story.

• Play with some of Don Steward’s investigations of grid geometry.

• Sample the essay prompts from my Writing to Learn Math and Writing to Learn Math II posts.

• Try a set of math puzzles from the Julia Robinson Festival.

• Or explore Don Cohen’s Map to Calculus for Young People.

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:

• Beginning to Problem Solve with “I Notice/I Wonder” (PDF)
• Noticing and Wondering with Older Kids

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?

Or Try Some Math Doodles

Create math art. Check out my math doodling collection on Pinterest and my Dot Grid Doodling blog post. Can you draw an impossible shape?

How Would YOU Use a Math Journal?

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

Please share in the comments section below.