Art and Math · Arts in Education

Paper, Books and Math Workshop

There’s this overlap of paperfolding, bookmaking and math that’s been in my sights for sometime now. Next month The Center For Book Arts has me on the schedule to share my interest with educators.

It’s a natural fit: Fold a piece of paper in half a couple of times and you’ve got a book. There you have it, all this things I’ve been thinking about in one sentence.

Bookmaking by Paula Beardell Krieg

 

Why math and book arts, you might ask? CBA asked me to propose a course for educators. Over the years I’ve taught classroom bookmaking dozens of times, though my focus during those years was literacy. In recent years it has occured to me, as I visit many schools and work with hundreds of different students each year, that teachers have loads of support for teaching literacy.

Teaching math, on the other hand, can be more challenging. In my desire to stay relevant, the hands-on projects I’ve been designing for classrooms had evolved towards supporting math curriculum and math thinking. And, oh yeah, I love this work.

Everyone folds paper, many people teach math, less people make books. Not too many people have a strong relationship with all three, Basically, I want to be teaching this workshop because otherwise I doubt it will exist.

Here’s what I know about offering a workshop for teachers:

  • They want content that they can use on Monday.
  • They do not have time to do special prep which requires more than the school copy machine.
  • They don’t have easy access to special materials.
  • They like having a handy resource folder.
  • They want their students to be learn and be happy.
Equivalent Fractions
Equivalent Fractions

Here’s how I know about math:

  • I play with math kind of obsessively….never got the memo about math being scary
  • I went through K -12 math three times, once as a student, twice as a parent.
  • I’ve been working in schools, discussing math projects with teachers and math coaches. We discuss standards and curriculum goals, and I talk to students about the math they are learning.
  • I’ve been rather passionately working on deepening my math knowledge in workshops, conferences, and connecting with math educators through their writing and through the #MTbos and #iteachmath communities on twitter as @PaulaKreig

In this one-day PD workshop I plan on focusing on deepening connections, doing hands-on, classroom friendly projects that address areas of math that will help students create strong foundation for future learning.

For instance, we’ll be working with number lines in a way that is both interactive and which illuminates patterns. I’ve been working out ways of presenting number lines in ways which delight kids. The sounds of discovery that come from students when they start seeing what I show them has been one of the most beautiful sounds of my career with kids. I will also have hands-on ways of showing the number line that moves from natural numbers to negative numbers and beyond.

Since the number line stays with children, evolving from finger counting through the coordinate plane (and beyond) my focus here in not only to use the number line, but also to elevate it as an important tool that they have reason to embrace. One of my favorite responses, which informs my work with number lines, was from a first graders who told me that they looked at number lines earlier in the year and now they were done with that.

How to make an origami Pocket by Paula Krieg
Click to enlarge for reading or printing

We’ll also be doing some work with perimeter and area. What frustrates me about students’ learning here is that they often mix up perimeter and area, not remembering which is which. One of the projects we’ll be making is a perimeter-pocket. We’ll make an origami pocket, which in itself is a wonderful lesson as is goes from being a square to a triangle to a trapezoid to a pentagon. But this perimeter pocket will have a ruler embedded in the structure and a string in the pocket to use to measure around things. Then there will be an area-rug book, with lift the flap peek-a-boo images hiding under the area rugs. Fun, easy, memorable!

I love that shapes are part of school curriculum at an early age. There are numerous projects I have in my toolbox that compose and decompose shapes.

I have some nice peek-a-boo projects that address the same composing and decomposing concept with numbers.

Symmetry will also get the attention that it’s due. Sure, we’ll talk about lines of symmetry by way of making pop-ups, but we’ll also look at the idea of symmetry as a it relates to equations, which can be seen as numerical symmetry. One of my exciting discoveries has been how naturally young kids grasp the idea of symmetry, and how well they they can connect it to equations.

 

A one hundred cents flower
A one hundred cents flower

We’ll even do some hands-on play with play money. I do these one-hundred cents designs with kids which gives then lots of practice with money, as well as practice counting by fives and tens and twenty-fives.

I could go on and on here, but I think you get the idea. And, actually, that’s part of my aim for the day, not just to present projects that can be immediately used by teachers in the classroom, but also that the idea of making the curriculum more hands on will inspire teachers to create their own simply made projects.

This is a rich, wide open inquiry into what we can do together to make math real.

The Center for Book Arts, NYC, Saturday, October 26

 

 

Books Made from one sheet of folded paper · How-to · origami pamphlet · simple book binding

Four Books Students Can Figure Out How to Make on Their Own

Origami-Base-for-Star-Book-and-Cascading-Book
PDF version

For years, until she retired, I worked with an enthusiastic classroom teacher named Anna who loved seeing her students make books. Instead of teaching bookmaking skills she created a bookmaking corner in her classroom that included a little display of books that I had taught her how to make. These books were accompanied by written directions and a stack of paper. Anna’s third grade students had a great time making books independently.

Last week I received a note from Lana, a teacher in Canada who I follow and who always has insights that I value. Here’s what she wrote:

I started a personal history project with my kids today, with  the big idea that our histories are different but we learn about each other because we are a community. Students start with creating a personal history of 5-10 important events in their lives. What if I open it a bit and let kids work with paper in 3 dimensions? Someone wants a line, someone else a book, a spiral, a tree, a flexagon?

I was wondering if there are some formats that you could recommend that don’t require too much pre-teaching. Ideally kids can follow template/video.

Origami books made from a multiple folded papers, to create a Star Book and a Cascading Book, aka Origami Caterpillar Book
Origami books made from a multiple folded papers, to create a Star Book and a Cascading Book, aka Origami Caterpillar Book

Thinking about Anna’s bookmaking corner, I want to suggest a few books to Lana.

I decided to take this opportunity to finally get around to creating the StarBook/Cascading Book tutorial (at the top of this post) with video accompaniment:

This modular origami book can be tricky, but it is totally doable, The folding needs to be done precisely, folds need to be sharp, and it’s important to pay attention to the orientation of the modules as they get glued together.

Fact is though, that it looks tricker than it is. It’s a structure I highly recommend because it’s so dynamic.

Bookmaking by Paula Beardell Krieg

The next book I want to highlight is the Origami Pamphlet. This is the #1 book that I would like every person in the world to know how to make. Here’s the link to my post https://bookzoompa.wordpress.com/2009/11/30/how-to-make-an-origami-pamphlet 

Another set of these directions that I like belongs to Tim Winkler, and can be viewed at http://pictureengine.net/?p=7960

Mike Lawler made a 24 second video -Voila!- showing a piece of paper transform into the origami pamphlet  https://www.youtube.com/watch?v=APfeGF0HqvY 

Books made from one or two pieces of paper

The biggest problem with the origami pamphlet is that if you’re using regular copy paper, the book will be rather small,  If this bothersome there are two good variations that result in a larger book (other than just finding a larger sheet of paper):

You can link two of the structures together with a rubber band. That’s what’s going on with the lilac/blue booklet above. Well, I guess it’s not actually a larger book, it’s just longer.

Making a larger origami pamphlet by linking two halves together
Two Book Bases linked together to make an origami pamphlet

A way make a larger origami pamphlet is to use two sheets of paper to make two halves, then attach them together (use glue, tape, paper clips, staples? whatever ) like in the photo above.  I call this half-or-an-origami pamphlet a book base.

An advantage of making a book this way is that, if composition paper is used, the lines will be going in the correct direction for writing on.

There are so many fabulous inventive book structures students can make, but sometimes it’s great to just fold a bunch of papers in half, secure them together, and be done with it. The problem here is that it is not obvious how to secure the pages together. A doable no-needle way to sew pages together in a classroom setting is to use a bit of string or yarn to do a modified pamphlet stitch.

Modified Pamphlet Stitch
Modified Pamphlet Stitch

There you have it, four books:

  • the Star Book,
  • the Cascading Book,
  • the Origami Pamphlet (with two variations) and
  • the Modified Pamphlet Stitch book

Lana’s note mentions a spiral. I’ve been playing with some spiraling pages lately, and I have something wonderful that I want to share, but the spiral deserves its own post: which will hopefully show up here in the near future.