January 5, 2013
…or talking to teenagers about Geometry
I’ve been having conversations with some high school students about things having to do with math. I thoroughly enjoy these conversations, as I am intrigued by the way students make sense of the sometimes elusive concepts of algebra, geometry and trig. While looking over some problems I asked a young man Andrew if he knew the definition of a polygon. After letting him flail a bit I resorted to Latin. I know that sounds bizarre, but it seems to me that kids have a knack for making and retaining connections if can connect to the root of a word. So I put forth the question ‘do you know what poly means” The answer was no. Hmmm…”Well, do you know what polygamy is?” It turns out that nearly all teenager do have a general (though not precise) understanding of polygamy as having many wives. Great…poly, therefore, means many. A polygon, therefore, must be a shape with many wives…well, not exactly, but I suspect that this is a close enough definition to help a teenager remember that a polygon is a shape with more than two angles and more than two sides.
A discussion of Isosceles Triangles delighted me beyond measure. When I asked my young friend Lucy about an isosceles triangle, she defined it to me as the one with the two lines. I knew exactly what she was talking about: each time students see an isosceles triangle in their math books, there are lines on the two equal sides (like on the orange triangle in the drawing above), which is math nomenclature for “hey, look, these two sides are equal.” It turns out that some kids don’t really know that these little lines are code that math people use to show that line segments are equal, or that you can have an isosceles triangle without having those two lines drawn.
It’s a good thing that I didn’t have to resort to Latin to explain isosceles, as the word isosceles comes to us from Greek, and can roughly be translated as “equal legs.’ I mentioned this to my daughter and she declared,
“I’m an Isosccles!” I suppose it might be more correct to say, “I have isosceles”…?
Thankfully, Equilateral Triangles are Latin-friendly, translating into something like “equal sides.” But this makes me pause and consider some other thoughts about math. Think about this: math is supposedly elegant and logical, however, the name for a triangle with three equal sides comes from Latin, the name for a triangle with two equal sides comes from Greek, and to meaure their lengths the we use Arabic numerals (our 1,2,3,4, 5, etc.), which actually originated in India. No wonder math can be such a challenge! Not only does it seem like a foreign language, fact is, it is many foreign languages!
That said, an understanding of bookbinding (much of which has its roots in Chinese and Japanese cultures) is supported by having a good understanding of geometry.
A bit late, but all the same, I wish you peace in the New Year and may you make connections that support and enrich your life.
June 6, 2012
Each season that I am involved with classroom bookmaking students nudge me into making discoveries about how to think about bookmaking. This year one of the lessons that I walk away with is how satisfying it can be to bond with the bookmaking process through a personalized book-figure. Okay, that’s not a real term, but I don’t know what else to call it.
What I noticed was that once a child created an image for their book that they could sort of anthropomorphize they seemed to connect and care more about their subject matter and their book. For instance Brianna’s Flower (above) became a personal extension of herself, so her project became very much her very own, rather than just another assignment.
This connection seemed to be made if it was a fantasy flower, an extinct animal….
…or endangered animals. When I started to noticing how students made connections to their books through these figures I began to encourage them to feel free rein while enhancing them through color….which led to some extravagant and lovely results.
I can’t remember who the ladies are in the photo above, but I like their taste in clothing.
Here’s the president and his wife, as created by the hands of second graders who were researching famous people.
By the time I worked with first graders on their chick project I had figured out that the first thing we should do is cut out a chick (everyone had the same chick pattern to cut out). I knew enough to encourage each child to give their own chick a personality by making an expressive eye, giving the beak some color and shape and considering the shape of the wing. If a chick became temporarily misplaced before we attached it into the book, the student would look for it as if she were looking for a personal friend, and it was a sweet reunion once the chick was found.
When I worked with second graders on their flower and plant book I told them not to worry about making a particular flower, but , instead to create a flower according to their own ideas about what would attract the kind of bee they want to be visited upon. I loved the flowers that these students came up with! The most interesting thing that happened, though, was that as these book-figures developed I realized that, through these book figures, even I was connecting to the students books in a more personalized way. One day I had to make a stop at a school sometime after my residency ended. The completed projects were on display, and I had time to take a look at them. One of the books housed the lady in the pink pillbox hat, shown in the first photo of this post. She was such a character that I had to go back again with my camera to make sure I had a record of her. Fortunately, by the time I caught up with the teacher, Mr. Terri -who also happened to be the teacher who came up the concept of this project- the pink hatted lady was still in the classroom. I would have been truly despondent had she gone home without my photographing her. Just a couple of days ago I showed her image to my friend, Ed. I was absolutely delighted that he immediately and correctly guessed her identity.
Here she is again, my book-figure friend Jackie Kennedy saying good-bye for me as I am about to sign off on classroom bookmaking for the 2011-2012 school year.
April 14, 2012
There is generally one project that I am most smitten by each year. This year’s dinosaur project, which first grade teacher Mrs. Kaveny and I put together, is my star of the season.
We folded two 11″ x 17″ cover weight papers, a blue paper for the background, and a white paper for the foreground. Using pre-pressed score lines, students folded the sides of the white paper in 4.25″ on both sides, so that the paper closed like a set of french doors. We added a pop-up on the left fold, and cut curvy mountain ranges on the top edge. The blue paper was folded just a bit differently than the white so that the papers overlapped in an interesting way.
For me, the highlight of the project was bonding to our dinosaurs. Students were assigned a specific dinosaur. The librarian, Mrs. Fields, downloaded line drawings of dinosaurs from the Enchanted Learning website then students colored in their dinosaurs. Mrs. Kaveny and I both agreed that no one really knows what colors bedecked the dino’s bodies, so these 7-year old artists used colors at their own discretion. After the coloring was done, I took their drawings home, scanned them into my computer, then copied the image three times, doing some shrinking and stretching, so that I was able to hand back three dinosaurs -a family!- to grace inside of the book.
Of course we needed to insert the research writing. There are two books within this book. On the right hand panel there’s a folded page which contained “fast facts.” In the center of the book there is a pocket which contains another book, which is filled with complete sentences and paragraphs.
Here’s what the pages for the writing looked like in my sample. After the part of the project that I facilitated was done, my time at the school was over, so I didn’t have a chance to see the project completed. Students did the writing and the rest of the landscape decoration with their teacher.
The finishing touch to the book was Mrs. Kaveny’s title for the book, Dino Details. We cut out the title in the shape of a dinosaur egg and made a crack. The students were talking about adding a baby dino on the cover too. Wish I had thought of that!
April 13, 2012
Nine years ago Kathy Pike, a seasoned Scholastic author of educational books, asked if I would like to be a co-author on a book that has been entitled 25 Totally Terrific Social Studies Activities: Step-by-Step Directions for Motivating Projects That Students Can Do Independently. I did my work, received an advance, and for years and years that was the last I heard of the book. It seemed to have been shelved and forgotten. A couple of years ago I discovered that it had been published. Scholastic sent me ten copies of the book. It was a thrill to have the book in my hands. Now I’ve unexpectedly received a few hundred dollars of royalty money in the mail. I guess the book is selling…as well it should .
First, let me say there’s nothing fancy about this book. On the other hand, it’s only $9.00 and it’s full of really accessible projects. When I first saw the book I was sad that it wasn’t one of those full color glossy bookmaking books, but when I took the time to really look it I have to say that it’s diamond in the rough. The title references social studies projects, which is just fine, but it’s really a great resource about making books in the classroom.
The picutes in the book are all in black and white, but I still have some of the orginal color photos from my old camera. Here’s a color photo of one of the projects.
I bribed my children into doing the writing and making the images for this sample book as I wanted it to look authentic.
No one asked me to look over the way that the publishers presented the directions in the book, so some of the directions are not quite on target. Here’s a tip: if you buy the book and want to make the Origami Pamphlet you can print up a better set of Origami Pamphlet directions right here.
Here’s another page. I’m showing this because it describes a clever structure, submitted by one of the other authors Jean Mumper. I’ve never made it this one, but I keep meaning to try out.
At the time that we were working on the manuscript Kathy directed me to a group of students who had made this folded circle book. I took some photos which (hopefully) give a sense of the circular way that the pages of this book open.
This circle is about the size of a coffee can lid.
The title fully shows only when the book is fully closed.
When each quarter of the book is opened, a picture is revealed, and, as an added bonus, there is room on the folded piece to write a caption. The books that I saw were made with layers of circles so that there are more than four quarter pages to the book.
These folding circle books had some fun sculptural possibilities.
It was a good experience to write my part of this book. It was a real pleasure to get a surprise check many years later. I want to say, though, that the best part of putting a book into the world is that I was able to write a dedication. While my children were young their nursery school teacher and day care provider, Becky Potter, was an angel in my life. There is no way I could adequately ever thank her for the support and care and wisdom my family found in her generous spirit. I was so happy to dedicate my part of the book to her.