Playful Family Math on Facebook

Want to help your kids learn math and enjoy it? Check out my new Facebook discussion group called Playful Family Math.

Join Playful Family Math on Facebook

This is a positive, supportive discussion group for parents and teachers — and grandparents, aunts and uncles, caregivers, or anyone else — interested in talking about math concepts and creative ways to help children learn. A place where you can ask questions, share articles about learning math, tell us your favorite math games, books and resources.

Let’s make math a playful family adventure!


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Dot Grid Doodling

What can you DO with a page full of dots?

Yesterday, I mentioned my new series of paperback dot grid notebooks, and I promised to share a few ideas for mathematical doodling.

Doodling gives our minds a chance to relax, wander, and come back to our work refreshed. And though it goes against intuition, doodling can help us remember more of what we learn.

Math doodles let us experiment with geometric shapes and symmetries. We can feel our way into math ideas gradually, through informal play. Through doodles, our students will explore a wide range of mathematical structures and relationships.

Our own school experiences can make it hard for us to teach. What we never learned in school was the concept of playing around with math, allowing ideas to “percolate,” so to speak, before mastery occurs, and that process may take time.

—Julie Brennan

I like to doodle on dotty grid paper, like the pages in my math journals, but there’s No Purchase Necessary! You can design your own printable dot page at Incompetech’s PDF generator, or download my free coloring book (which includes several pages of printable dot and graph paper).

Patterns in Shape and Angle

To make a faceted mathematical gemstone, start with any shape you like. Then build other shapes around it. What do you notice? Does your pattern grow outward from its center? Or flow around the corner of your page? How is each layer similar, and how is it different?

Arbitrary constraints can lead to mathematically interesting doodles. For instance, create a design out of 45-45-90 triangles by coloring exactly half of every grid square. How many variations can you find?

Symmetry Challenge

Play a symmetry puzzle game. Draw a line of symmetry and fill in part of the design. Then trade with a partner to finish each other’s doodles.

Make more complex symmetry puzzles with additional reflection lines.

Math Doodle Links

  • Who can talk about mathematical doodling without mentioning Vi Hart? If you’ve never seen her “Doodling in Math Class” video series, you’re in for a treat!
  • See if you can draw a rotational-symmetry design, like Don’s “Order 4” graphs.
  • Or experiment with the more flexible rules in John’s “Knot Fun” lesson.
  • And my latest obsession: the “ultimate” tutorial series on Celtic Knotwork, which explores the link between knots and their underlying graphs.

Inspirations: A Recreational Mathematics Journal
Reflections: A Math Teacher’s Journal
Explorations: A Math Student’s Journal
Contemplations: A Homeschooler’s Journal

Also available through: Barnes-Noble-logo CreateSpace-logo


Feature photo (top): Sommermorgen (Alte Holzbrücke in Pretzfeld) by Curt Herrmann, via Wikimedia Commons. [Public domain]

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and you’ll be among the first to hear about new books, revisions, and sales or other promotions.


Dot Grid Journals with Coloring Pages

My newest book project began with a few simple coloring pages for my homeschool co-op kids. You may recall when I collected those into a downloadable coloring book last December. Well, I kept tinkering with the designs into January. And then it was time to buy a new planner…

The problem is, I’m not a naturally organized person. I like making lists and plans, but sticking to them is tougher. And I’ve never found a planner or organizational system that I could follow for longer than two weeks at a go. That is until I heard of bullet journaling.

But journaling requires a journal — a notebook of some sort. And I couldn’t find any that I liked. Either the pages were too narrow and felt cramped, or the thing didn’t fit even in my oversized purse. Or the fancy, hardcover binding made it heavy to lug around. Or the lines were too dark, or too widely spaced. Never quite what I wanted.

So I decided to make my own.

I started with dot-grid pages for flexible layouts and for doodling. I scattered some of my favorite math and education quotations through each book. And then I added several of my most flexible geometric coloring pages (based on Islamic tessellation designs).

And I had so much fun I couldn’t stop with just one. So let me introduce my Dot Grid Notebook with Coloring Pages series:

Inspirations: A Recreational Mathematics Journal
Reflections: A Math Teacher’s Journal
Explorations: A Math Student’s Journal
Contemplations: A Homeschooler’s Journal

Also available through: Barnes-Noble-logo CreateSpace-logo

With 170 roomy pages, each book gives you plenty of space to record memories, plan projects, and keep track of tasks. The dot grid makes it easy to draw graphs or diagrams. Take notes, jot down ideas, copy your favorite quotations, or doodle to your heart’s content.

  • Light gray dots at 5 mm spacing provide guidance for flexible page layouts.
  • 11 geometric coloring pages allow a multitude of artistic possibilities.
  • 31 favorite quotes offer a vision for creative math education.
  • 6 × 9 inch (about 15 × 23 cm) pages are wider than many journals, yet still fit comfortably into a large purse or bag.
  • Paperback binding makes the journal sturdy but lightweight. Carry it anywhere!

Prevent cracked spines: How to Break In Your New Math Journal.

The ebook edition features all 124 quotations (31 from each journal) about mathematics, education, and problem solving. Read through for your own pleasure, post them by your workspace, or use them as writing prompts for yourself or your students.

Yes, all of the ebooks are the same, so there’s no point in buying more than one. And at Amazon, if you buy a paperback journal, you can download the companion ebook for free!

But, what can you DO with all those nice, dotty pages?

Of course, you can use them for bullet journaling. That’s why I originally created the books, because I couldn’t find planners that fit my personal style. My bullet journal is basically an anthology of To-Do lists, bound together so they don’t get lost in the clutter. It’s the only planner system I’ve been able to stick with for more than two weeks at a go.

Or you could use the dotty pages for a commonplace book. That’s my favorite kind of journaling. Like a magpie, I collect shiny tidbits from books, websites, conversations overheard, and more. Passages. Definitions. Poems. Recipes. Proverbs. Things I’m wondering about. Cute kid sayings. It all goes into the mix.

And math puzzles, of course! Below, I’m playing my way through Paul Lockhart’s Measurement. I use the cloud-like labels in the outer margins of each page for keywords that identify what I’m writing, because someday I’ll need to skim back and find an old note.

But where dot grid pages really excel is at doodling — I’m sure you noticed the faceted design filling the lower half of my journal page above and the gem almost overrunning my February calendar. So watch for tomorrow’s blog post featuring a variety of ways to create your own mathematical doodles.

Best wishes, and happy mathing!


P.S.: Do you have a blog? If you’d like to feature a Dot Grid Journal review and giveaway, I’ll provide the prize. Leave a comment below, and we’ll work out the details.

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and you’ll be among the first to hear about new books, revisions, and sales or other promotions.


Education Bloggers: Share Your Post!

photo by Omar Omar via flickr[Image by Omar Omar (CC BY 2.0) via Flickr.]

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 Math Teachers at Play (MTaP) math education blog carnival.

Click here to submit your blog post

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.

Don’t procrastinate: The deadline for entries is this Friday, March 24th. The carnival will be posted next week at Let’s Play Math blog.

Need an Idea-Starter?

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

  • Elementary Concepts: As Liping Ma showed, there is more to understanding and teaching elementary mathematics than we often realize. Do you have a game, activity, or anecdote about teaching math to young students? Please share!
  • Arithmetic/Pre-Algebra: This section is for arithmetic lessons and number theory puzzles at the middle-school-and-beyond level. We would love to hear your favorite math club games, numerical investigations, or contest-preparation tips.
  • Beginning Algebra and Geometry: Can you explain why we never divide by zero, how to bisect an angle, or what is wrong with distributing the square in the expression \left(a + b \right)^2 ? Struggling students need your help! Share your wisdom about basic algebra and geometry topics here.
  • Advanced Math: Like most adults, I have forgotten enough math to fill several textbooks. I’m eager to learn again, but math books can be so-o-o tedious. Can you make upper-level math topics come alive, so they will stick in my (or a student’s) mind?
  • Mathematical Recreations: What kind of math do you do, just for the fun of it?
  • About Teaching Math: 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!

Would You Like to Host the Carnival? Please?!

Hosting the blog carnival is fun because you get to “meet” new bloggers through their submissions. And there’s a side-benefit: The carnival often 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 Math Teachers at Play page. 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 Math Teachers at Play carnival, you may enjoy:


howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and you’ll be among the first to hear about new books, revisions, and sales or other promotions.


Beauty in Math: A Fable

Have you ever wondered what mathematicians mean when they talk about a “beautiful” math proof?

“Beauty in mathematics is seeing the truth without effort.”

George Pólya

“There’s something striking about the economy of the counselor’s construction. He drew a single line, and that totally changed one’s vision of the geometry involved.

“Very often, there’s a simple introduction of something that’s not logically within the framework of the question — and it can be very simple — and it utterly changes your view of what the question really is about.”

Barry Mazur
The Moral of the Scale Fable


CREDITS: Castle photo (top) by Rachel Davis via Unsplash. “A Mathematical Fable” via YouTube. Story told by Barry Mazur. Animation by Pete McPartlan. Video by Brady Haran for Numberphile.

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and you’ll be among the first to hear about new books, revisions, and sales or other promotions.


FAQ: Homeschool Burnout

“Spring cleaning has made my desk look worse than before. Nobody feels like studying. The kids would rather be outside, and their mom would rather take a nap. If I line everyone up on the curb in the morning, do you think the yellow bus will take them?”

Homeschool burnout — it’s a perennial problem. If you’re suffering from lethargy and can’t face another day of school work, here are some ideas that kept me going long enough to graduate almost-five kids (my “baby” finishes homeschooling this spring!):

(1) Re-read the homeschooling books on your shelves, or get some new ones from the library. Write down your favorite quotes as you read. Try to read about one a month, to help get your enthusiasm back. And then read at least one new homeschooling book per year to help you stay inspired.

(2) Connect with other homeschoolers. Meet with friends for tea, or have a Mom’s Night Out while Dad babysits. Talk about substantive things, like educational philosophy — what you like about homeschooling, and what you’d like to change. Share your dreams for your children. Remind each other why you’re doing this.

(3) Attend support group meetings. I find that after so many years, I let the meetings slide. I think, I already know everything they are going to say. But being with other homeschoolers is encouraging. And if you find out that you can help a new homeschooler with advice, that gives you a boost, too.

(4) Find one or two forums where you can become one of the resident experts, and answer posts as often as you can. As with number 3 above, being able to give advice (and being appreciated for it) can give you the energy to keep on going.

(5) Go to a homeschooling convention, if you get the chance. The speakers are stimulating, and you may find some new book or tool that sparks your imagination.

(6) Do school anyway. It may seem impossible when you’re stuck in the doldrums, but once you get going, you may find it easier. The light of understanding in a child’s eyes can give Mom quite a lift!

(7) Try something completely different. If you have always used a textbook program, then set it aside for a month and just read library books. If you have read lots of great literature, then try some hands-on projects, or get out those science experiments you keep putting off, or visit all the museums within a two-hour radius, or… I’m sure you can think of something that has been lingering on your good-intentions list. I never could stand to teach the same old thing every year, and none of my five kids got exactly the same education. Happily, there is always another way to approach any homeschooling topic. How about Gameschooling?

(8) Figure out what your students are able to do on their own, and let them do it. Encourage them to develop as much independence as possible.

(9) Use some of your children’s independent time to learn something new for yourself. Have you always wanted to try painting, or crochet, or woodworking? Be an example of life-long learning.

(10) Start (or join in progress) a group class or co-op. You may be able to trade around with some other families: you teach history and others teach math or cooking, or whatever arrangement fits for you. This is especially helpful for those time-consuming projects that always seem to get put off, like art or science experiments.

(11) Try some of these intensely practical Tips For Coping With Homeschool Burnout.

(12) And are you a Christian homeschooler? Then pray! Your Father knows what you need, and Immanuel is with you always. Try praying your way through 1 Corinthians 13 (or this homeschooling version).

If you have any other ideas for beating the burnout blues, please share!

Homeschooling is not always peaches and cream. If anyone promised you that, they lied. But be assured that it homeschool burnout is not a terminal condition. You will recover your joy in sharing your children’s education.

I learned one thing from every story I’ve ever read: adventures never run smoothly.

And what greater adventure could there be than to introduce your child to all the wonderful things in God’s world?

homeschooling


CREDITS: “Scream” photo (top) by greg westfall via Flickr (CC BY 2.0).

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and you’ll be among the first to hear about new books, revisions, and sales or other promotions.


Visualizing Word Problems with Bar Model Diagrams

A friend emailed me, frustrated with her child’s math lesson on bar diagrams: “Why do they have to make it so complicated? Why can’t we just solve the blasted problem?”

I told her bar models themselves are not the goal. The real question for parents and teachers is:

  • What can you do when your child is stumped by a math word problem?

To solve word problems, students must be able to read and understand what is written. They need to visualize this information in a way that will help them translate it into a mathematical expression.

visualizing-word-problems

Bar model diagrams are one very useful tool to aid this visualization. These pictures model the word problem in a way that makes the solution appear almost like magic.

It is a trick well worth learning, no matter which math program you use.

Visualization

https://www.youtube.com/watch?v=HKsYDzQK8Zw

“Visualization is the brain’s ability to see beyond what the eyes can see, and we can develop visualization in many ways.”

The Bar Model Explained

https://www.youtube.com/watch?v=I6Ipio8JntU

“A bar model is a way to represent a situation in a word problem using diagrams — in particular, using rectangles.”

https://www.youtube.com/watch?v=i7LAHc1qvig

“This is one of the ideas that children learn in mathematics: the use of diagrams to represent quantities, especially quantities which are unknown.”

Word Problems from Literature

I’ve written a series of blog posts that explain bar model diagrams from the most basic through to solving multistep word problems. Check them out:

I’ve started working on a book about bar model diagrams, and I’d love to hear your input. Have you tried using them? Do they help your children? What questions do you have?


CREDITS: Videos and quotations from Dr. Yeap Ban Har’s YouTube channel. “Girl doing homework” photo (top) by ND Strupler and “math notebooking equal fractions” by Jimmie via Flickr (CC BY 2.0).

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and you’ll be among the first to hear about new books, revisions, and sales or other promotions.


Playful Math Carnival #105 via Mrs. E

mtap-105Check out the new carnival of playful math for all ages at Mrs. E Teaches Math. Each month’s carnival brings you a great new collection of puzzles, math conversations, crafts, teaching tips, and all sorts of mathy fun.

This month’s post features algebra tips, geometry proofs, Fibonacci rabbit trails, math art, and much more.

Click Here to Go Read the Carnival Blog!

Past carnivals are still full of mathy treasure. Check them out:


howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and you’ll be among the first to hear about new books, revisions, and sales or other promotions.