The more years we spent homeschooling, the more I appreciated Charlotte Mason’s work and tried to incorporate her ideas into our laid-back, eclectic, not-quite-unschooling program.
We never fit the typical Charlotte Mason mold. Mosquitos and natural laziness limited our nature walks, and our version of narration was much too informal.
But those are just techniques, methods.
What really interests me in Mason’s writing is the philosophy behind the methods. Two points resonated: That we must respect our children as persons in their own right. And that we must provide a generous, wide-ranging feast to their minds.
Striving to live out those principles had a profound influence on our day-to-day homeschooling.
I love my new paperback math journal series. The books are sturdy, inexpensive, and fit nicely in my purse.
But as with any paperback book, these have one problem. How do I use them without cracking the spine?
When we exercise, we need to warm up our bodies with a bit of stretching to prevent injury. In the same way, we need to warm up a new book to protect it. The process is called “breaking it in.”
It only takes a few minutes to break in a paperback book:
Step by Step
Never force the book but help it limber up gradually, and it will serve you well.
Because my journals are working books, I take the breaking-in process a bit further than shown in the video:
(1) Set the book on its back and follow the process above. Press down each cover, but not completely flat — let it bend at the fold line, about 1 cm from the actual spine. Then press a couple pages at a time, alternating front and back, down flat on each cover.
(2) Flip through the pages of the book forward and backward to limber them up.
(3) Repeat the steps of the video. This time, gently lean the main part of the book away from the part you are pressing down. Aim for a 130–140 degree angle.
(4) Flip through the pages again. For paperbacks, you can even roll the whole book back and forth a bit — gently curving the cover and pages almost as if you’re trying to fold the book in half — to encourage flexibility.
(5) Optional: Repeat the breaking-in process one more time. This time, fold each section back as close to 180 degrees as it will go.
And you’re done!
The pages will still curve in at the fold line, where they connect to the spine of the book. You want that because it makes the book strong. But now they’ll also open up to provide a nice, wide area for writing or math 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.
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!
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.
Finally, check out my Math Doodling board at Pinterest.
My favorite knot doodle so far.Inspirations: A Recreational Mathematics JournalReflections: A Math Teacher’s JournalExplorations: A Math Student’s JournalContemplations: A Homeschooler’s Journal
In addition to all the funny Google searches, I get plenty of normal inquiries about math topics. People come here looking for help with fractions, wordproblems, and mathclubactivities — no surprise, those — but I would never have predicted the popularity of the search topic “writing in math class.”
Last year, I compiled a variety of math journal resources, but I’ve found many more since then, especially for older (high school and college) students. So if you’re looking for new ways to get your math students writing…
Do you ever take your kids’ math tests? It helps me remember what it is like to be a student. I push myself to work quickly, trying to finish in about 1/3 the allotted time, to mimic the pressure students feel. And whenever I do this, I find myself prone to the same stupid mistakes that students make.
Even teachers are human.
In this case, it was a multi-step word problem, a barrage of information to stumble through. In the middle of it all sat this statement:
…and there were 3/4 as many dragons as gryphons…
My eyes saw the words, but my mind heard it this way:
…and 3/4 of them were dragons…
What do you think — did I get the answer right? Of course not! Every little word in a math problem is important, and misreading even the smallest word can lead a student astray. My mental glitch encompassed several words, and my final tally of mythological creatures was correspondingly screwy.
But here is the more important question: Can you explain the difference between these two statements?
Math journal entries can be as simple as class notes, or they can be research projects that take hours of experimentation and pondering. Students may use the journal to store their thoughts as they work several days to solve a challenge problem of the week, or they might jot down quick reflections about what they learned in today’s math class.
Denise Gaskins' Let's Play Math 
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