Arts in Education

Recalculating a Failed Workflow

Each year, as part of a bookmaking project with sixth graders, I bring in my impressive assortment of paper punches, and let the students decorate their handmade books with a colorful array of  items which include stars, crescents, hearts and creatures. It can be a wild free-for-all, with some students slapping on their paper-punched creations willy-nilly, and others making carefully thought out arrangements. It’s generally a messy, high-energy class period, with bits of paper and glue being  put down with excitement and delight.

Reflection, translation, glide-reflection
Reflection, translation, glide-reflection

Last year it occurred to me to rein in some of this excitement and introduce the students to different kinds of symmetry that would enhance their designs, Things seemed to go pretty well last year, so I tried it out again this year.

Paper Punch Symmetry
Paper Punch Symmetry

While some good things happened, it was clear to me that my own  ideas about teaching something new came at a cost: students didn’t do nearly as much decorating as in previous years, and much of the excitement had been sucked out of the project.

Naturally, what I want is the excitement AND to be able to teach something new and valuable.

My experience with the sixth graders was weighing on my mind this past week when I was working with second graders on cut-paper project.

Rhombi as the ready
Rhombi as the ready

What I think had been my biggest misstep with the sixth graders was that I dampened their paper-punching enthusiasm before they ever got a chance to indulge in the novel activity I was laying out for them. I depend on the  use of unusual tools and colorful materials to engage students,  but I hadn’t  given these kids a chance to experience their excitement before laying out the conditions which seemed to challenge and dampen their spirits.

In hindsight, I think things would have gone much better if I had laid out the materials, let the students create their collections of paper punched bats, balloons, dragongflies etc. and then, only after they had gathered together these personalized treasures, I could then proceed with the references to symmetries.

Cutting out Rhombi
Cutting out Rhombi

 

Now, this week, working with second graders, I tried to learn from what happened during my time with the sixth graders.  I had an agenda, which is to use rhombuses to construct plane shapes, such as trapezoids, hexagons, and triangles. This is supposed to be an exciting activity, full of experimentation and discovery. I didn’t want to do anything suck the joy out of playing with the rainbow of colors in search of wisdom.

The students needed to cut out rhombuses from a packet of colorful  printed strips. I decided not to tell them exactly what we’d be doing with the rhombuses. Instead, after the rhombuses were cut, I encouraged to students to slide them around on their desk, and organize them into piles or shapes that appealed to them.

Rhombuses on the run
Rhombuses on the run

This exploration time took only a few minutes, and, as different students finished their cutting at different rates, it kept everyone busy.

Stars
Stars

I traveled around the room, showing some kids how to use these shapes to make all sorts of arrangements.

Hexagon, Cube, Star
Hexagon, Cube, Star

It’s worth mentioning that they were notably impressed that three rhombuses could look like a hexagon, or like a cube in perspective, with color choice playing a significant role in creating the illusion that these same shapes were different.

playing with Rhombi
playing with Rhombi

It was only after this time of playing around that we got down to the business. I tried to keep them in discovery mode by asking them to take just a few pieces in their hands (which at this point included some rhombuses that had been cut in half to form two equilateral triangles) and to try to figure out how to make a trapezoid or a triangle or a hexagon, or a scaled up rhombus.

Plane Shapes
Plane Shapes

It all worked out.

More Plane Shapes
More Plane Shapes

At no point did I feel like my agenda had sucked the air out of the room. Whew.

My note for next time is to remember to let the kids feel the excitement and let them create their own relationships with the materials before I overlay my lessons into the moment.  Whereas I had hijacked their enthusiasm before, I think that this different approach enriches their enjoyment, and hence their learning.

 

 

 

 

 

 

Art and Math · Arts in Education

100-Book for Kindergarten, Trying it Out

Rubber Bands books to use for Hundred Book
Rubber Band book for 100-Book

About a month ago Simon Gregg posted a string of images about 100-books that were assembled by his class of 5 and 6 year olds.  On each of page there was a group of items that added up to 10.  That’s 10 pages of with 10 items, so it’s a 100-book. I want to do this project with 5 and 6 years olds! I ‘ve been in kindergarten classrooms all this week, doing a literacy based book project, but I noticed that there was one 40 minute block of unscheduled time in my schedule so I asked one of the teachers if I could try out this project with her class.

cover of 100-Book
cover of 100-Book

40 minutes was just enough time to get this book started, to get a feel for it. I assembled books for the whole class, just to expedite getting to the content. Although I didn’t realize about how this project would be received, the bottom line is that the kids enjoyed it, were enthusiastic to continue working on it, and seemed to be making some new connections. I debriefed with the teacher the next day and we agreed it’s a project worth developing. She is continuing the book without me: her kids are demanding to finish!

 

five plus five equals ten
five plus five equals ten

I wanted this to be a tactile book, and one that combined objects and finger counting. I brought in lots of foam, sticky-backed items. Students put a number of items on the page, hopefully in an arrangement, then traced the number of fingers they would need to make the total of items and fingers equal ten.

Eight plus two equals 10
Eight plus two equals 10

When there were less than five fingers to trace, the finger image looked rather odd, but the kids didn’t seem to mind.

Our first page, which I don’t have a photo of, was two tracings of hands, so that was five plus five equals ten. I noticed, when looking through the books afterwards, that a few of the kids wrote  5 + 5 = 10 on every page: these kids were not connecting the items on the page to the number sentences.  When I talked to their teacher about this she said that having them assemble the items, make them equal ten, and writing the number sentence was probably too much to do so quickly.

If I get a chance to properly do this project, these are the things I’d change or keep in mind:

  • I’d say we should do groupings of items on all of the pages as being one step (rather than finishing each page completely before moving on)
  • Next step would be going back to figure out how many fingers it would take to make ten and then creating the tracing of the right number of fingers.  Even though the fingers looked funky, I really like including them in this book.
  • Last step would be to revisit each page for a third time, this time to write the number sentence that describes the page.
  • I’d slow down and make sure kids were putting their items in groupings that could be recognizable to them.
Six and four make 10
Six and four make 10

Given enough time, I think that I would have the students make each page on single sheets, then bind them together with a simple pipe-cleaner binding, kind of like this one :  https://bookzoompa.wordpress.com/2011/12/18/pipe-cleaner-bound-scrapbook

I’d probably have the kids make a big origami pocket to store all their pages in before they are bound together.

The three traced fingers
The three traced fingers

I like the idea of using items in the book that are slightly 3D, like these foam sticky-back pieces, but I’d think it would also be great to have other things, like cotton balls or popsicle sticks, that the kids glue in. I like having them work with glue.

The kids that Simon Gregg worked with included some playing cards in their books. This is something I’d like to do. My local thrift store sometimes has used sets of playing cards that I can pick up cheaply.

Hopefully I’ll be writing more about this project as I get more of a chance to do it with more kids.

Do take a look at this twitter thread that got me thinking of this project. The videos towards the end of the thread are precious.

 

 

Art and Math · Arts in Education

Making more Beautiful Letters with Pre K

The Letter T
The Letter T

Each time I do this project with 4 year olds I understand better how to approach it and how it is a valuable activity. The images that these children create are so gorgeous that it’s easy to feel they don’t need any justification. Beauty for beauty’s sake is great, but I’m happier if there is more going on.

Seems to me that this activity supports spatial reasoning skills, the value of which you can read about at https://www.kqed.org/mindshift/43090

These 4 year olds are practicing precise finger control, which  is discussed in this long article     https://www.researchgate.net/publication/320697211_You_Can_Count_on_Your_Fingers_The_Role_of_Fingers_in_Early_Mathematical_Development

Students sort items, which is discussed at http://msue.anr.msu.edu/news/matching_and_sorting_are_early_stages_of_math_development

Preparing Materials to fill in letters
Preparing Materials to fill in the letter H

Basically, what we do is use materials to fill in the letters of the alphabet, which this age group is still learning to identify. Although there are no hard and fast rules about what I use, basically the three categories of materials we used this year for the assemblages are:

  1. Fresh natural materials, such as flower petals (rose and others), carrots, fresh greenery, red potatoes, but also used pine cones, and small Indian corn (for letters A- H)
  2. Dried materials, such as dried yarrow, Japanese lanterns, artemisia, globe amaranth, nigella,and statice, along with some cedar ( letter I, J and S – X) and
  3.  Items students picked out from the classroom, including lego pieces, rubber bands, jigsaw pieces, small building blocks, crayons and dominoes (the rest of the letters).
Dried Materials
Dried Materials

We absolutely spent time talking about the materials, naming them, smelling them, familiarizing the kids with their properties. Oh, and we avoided using white and black items, as both of these colors are problematic in photographs.

 

The Letter M
The Letter M

The letters are outlined on papers that I provide. After the children fill in the letters,  I take a picture, then the students re-sort the items back into bins before startomg the next letter. Children worked in groups of two. We had some good chunks of time to work on these, so no one was rushed. We encouraged the students to take their time, work precisely, be inventive, and keep adding materials. Occasionally these kids would make a beautiful letter then immediately deconstruct it before it was photographed, so we had to be attentive!

The Letter E
The Letter

I brought the digital versions of these letters home with me, put them into Photoshop, got rid of the background with cropping tools and color range selections, and tinkered with the highlights, saturation and shadow.

The letter J
The letter J

When all the letters were done I assembled the letters into a PDF that became little booklets, so each student has their own alphabet book to keep.  Finally, on my last day with these kids, we were able to project the pages of the PDF on a large screen, and did the magnificent “Which One Doesn’t Belong” activity, aka #WODB which is discussed at http://wodb.ca/ 

Which One Doesn't Belong
Which One Doesn’t Belong

There are no right or wrong answers in the Which One Doesn’t Belong activity. To get the kids started, we went through the letters one by one, stating reasons why is could be said that each letter might not belong in the grouping. Because there is such an emphasis at this school on inclusion, I think it made the kids a bit uncomfortable to think about exclusion. However, seeing that a case could be made to exclude every letter is, in fact, a lesson about inclusion.

So, that’s it, this year’s alphabet book.

 

 

 

 

Arts in Education

Funville Adventures, book review

Funville Adventure, by A.O. Fradkin & A.B. Bishop
Funville Adventure, by A.O. Fradkin & A.B. Bishop

There’s a seven letter F word that the mere utterance of which drives away the numerically faint-hearted, while, at the same time evokes warm and fuzzy familiarity to those fluent with the lingo of the mathematician. I‘m fearful to even print this F word yet, as I don’t want you, dear reader, to flee.

This F word describes an idea that can feel dangerous, yet  it’s a vital concept that is at the heart of math.  When there is a relationship to examine, the F word enters.

Funville Adventures by A.O. Fradkin and A.B. Bishop is a book that offers an easy slide in to the world of relationship thinking. We live in a culture that is mostly bereft of innocence, levity, and humor when it comes to deciphering the threshold ideas around math. No problem: Fradkin and Bishop let us leave this world behind and offers us a clean slate to experience ideas in a whole new way.

In the tradition of Mary Pope Osborne’s Magic Treehouse books, Funville Adventures allows us to follow a big sister and her brother into a place where they never expected to be, but where they follow their curiosity while being open to noticing, to wondering, and to making connections.

Breaking with tradition, what Fradkin and Bishop have done in their book is to anthropomorphize concepts. Instead of being introduced to numbers and independent variables which describe relationships we meet children that seem magical. When I realized that this was what was going in on their book I had to put it down for a while and let my head stop spinning. The evolution of mathematical ideas is full of stories of brilliant, serious giants of thought. But here is a world of math populated with purple dogs, ice-cream that doesn’t melt, upside trees and children with super powers. The magic that is wielded by these children leave us asking, what’s going on here, how do they do that? We are led to notice things that are done can be undone, unless that the undoing erases everything. We see children making wheels turn. We come to understand the incredible, enviable power of making everything stay the same.  Here Funvillians wow us with each of their unique transformative powers.

Numbers don’t have a place in Funville. Personally, I love numbers, but I recognize that a lack of ease with numbers often, for many people, obscure the underlying ideas that numbers are supposed to illuminate. Funville Adventures lets the reader experience relationship ideas, with both their range and their limitations. The idea here is to grasp the concept, let the notation, the lingo, the f word, function, come in at another time, but not here, not now.

Two children unwittingly slide into Funville. You can slide in with them. We all can be trapped inside this world forever: turns out the secret to getting out becomes obvious once you understand the ideas this world has gifted you. Maybe you can figure it out before the kids realize the trick to that particular bit magic.

Then, out here in the real world, we can hope for a series books giving us more adventures in Funville.