Curriculum Resource: Art, Science, Math, Art

We were having a discussion during our homeschool coop this week about our belief that one of the great benefits of homeschooling is our ability to study things in an interdisciplinary way.  Whereas in schools, usually what you are studying in English has no connection with what you are doing in History or Science, we can spend our time in Language Arts reading literature of the era that we are doing in History, plus we can supplement with Art History/Art projects and Music History and sometimes History of Science, etc.

When I stumbled upon the Fong Qi Wei's website for Exploded Flowers, it immediately made me think of this multidisciplinary approach to life.  Qi Wei is a photographer, apparently living in Singapore.  In the Exploded Flowers series, he carefully takes apart a flower and photographs it with all its stems, petals, pistons, and other components spread apart.  Here are some examples of his work:

Copyright © 2011 Fong Qi Wei

Copyright © 2011 Fong Qi Wei

Copyright © 2011 Fong Qi Wei

Copyright © 2011 Fong Qi Wei

Copyright © 2011 Fong Qi Wei

For all of these beautiful photos, or to buy a print or card of one, visit his website here.

I love these, because they are obviously beautiful art.  But they also help us learn about science, particularly what exactly goes into a flower.  I think it could help us explain to our students the components of the flowers and what pieces perform what functions in the whole plant reproduction process.  

However, it also lead to me to math, and the patterns of the petals and other parts.  I've written a number of posts about Fibonacci numbers, and my son and I have spent quite a bit of time looking for those Fibonacci sequences in nature.  But in real life, it is often hard to tell exactly how many petals there are in a flower, or segments in a pine cone, and such (believe me, we've tried).  So actually taking it apart and counting that way--that might be one way to solve the problem.  I have to admit, though, that I counted many of the petals in the photographs, and I didn't find too many examples of Fibonacci numbers.  But there were lots of interesting patterns to consider, once it was separated enough that you can definitely count different items.

But it doesn't just stop there.  Eventually, it occurred to Qi Wei that all those individual petals were similar to individual brush strokes in a painting.  So he created several of what he calls "floral paintings" out of petals.  For example, consider this one, which was inspired by a woodcut print called The Great Wave off Kanagawa, one of the most famous pieces of Japanese art:

Veronicas, Hyacinths, Pom Poms, 2011, All Rights Reserved Qi Wei

I think that is incredible.  But I have to admit that my favorite of this series, which mostly reflects Asian art, is one inspired by a Western artist, Van Gogh:

Van Gogh Sunflower Remix, All Rights Reserved Qi Wei

So, so lovely and interesting!  And so we go from art to nature, and then from nature to art.  This makes me really want to go get some flowers and try re-creating some of our favorite paintings in petal form.  And thus these pictures extend into Art History, and even Social Studies, as we consider the difference between Asian art and Western art....

That how I think life really is--one topic and/or subject flows into another, which suggests another.  I'm just really glad that we can run with that in homeschooling in a way that traditional educational classes can't.  But even if your children attend a traditional school, this could be a fantastic project to do with them at home!

Math Trek and Fib Poems

Yesterday was the last session of this academic year's version of the Math Treks, sponsored in the Triangle NC area by Natural Math.  The idea behind the Math Treks is to "grow math eyes" by trying to find math concepts, such as fractals and tessellations and golden ratios and such, in nature, or at least among the landscapes in which we live.  These concepts are captured in photography and shared via Flikr, and help students connect abstract math concepts with the concrete reality in which they live.  It's a really great program, and I'm so grateful that we were able to participate.

Since yesterday's session was the last one, it was a culmination of many of the treks that came before.  Find all of the items on the list, and you were designated as a "Super Treker."  We were looking for these items at the Arboretum at NC State, which was a rich place for both photography and natural math (and which I've written about before in this post).  Maria D. of Natural Math and I ended up working together, and eventually found all the items, winning ourselves the title of "Super Trekers."

One of the things we had to do was write a Fibonacci Poem, also called a Fib (which I've explained before in this post), which has syllables in the Fibonacci sequence.  So I wrote this Fib Poem:

Math
Trek
Super
Edition.
Find Nineteen Items.
Then You Are a Super Math Geek!

So here I am--a designated Super Math Geek!  Who would have thought it (especially given that Math is not my strongest discipline)?

My son did his own quest with other students of his age, so I didn't see his items until everything was over. However, as we were walking out, he did show me this thing that he had created:

Start of my son's Fib poem

Not only was it a public declaration (at the very entrance of the Arboretum), but it was the opening syllables of his Fib poem.  Here is his Fib:

My
Mom
Is The
Best Mother
In the Universe.
I Think that She Is Really Great!

So we all had a great day playing with math and photography on a beautiful day in a gorgeous setting, with a little bit of sadness mixed in because we were ending something that we've really enjoyed.  But I think I was probably the happiest mom leaving, thanks to the poetic tribute from my son.

Pi Day Celebrations

Man, yesterday was a red letter day here with all the interdisciplinary math we had going on during Pi Day 2011!  In the morning, my son and I worked with Maria Droujkova of Natural Math on a one-page book showing division of fractions that I am writing and my son is illustrating (both of us with Maria's wise counsel, of course).

In the afternoon, we did some of our other work, but then we kicked off the evening with our traditional (well, at least we've done it for the past couple of years since Maria has introduced us to Pi Day) Pi Day dinner of Pizza Pi(e)s.  Each one of us had our own pies with varying degrees of pi-ness.

My husband's pizza was pretty typical, with pi mostly being represented by rounds of sausage:

Mine was more of a celebration of circles.  I began with a circle of ricotta cheese (an idea I took from a recent Cooking Light magazine), then a circle of organic basil, then a circle of feta cheese, then another circle of basil.

I then layered that with circles of onion, then layered tri-circles red and green pepper on top of that.

My son had the most Pi pie, though.  He cut his pepperoni and mushrooms into the shape of pi.

It was a fun and delicious way to mark Pi Day.

Then, after dinner, we had a wonderful discussion with author Joe D'Agnese about ways to use his book Blockhead:  The Life of Fibonacci in exposing students to a variety of math ideas, but also in relating math to both history and real life.  Thanks to those who joined us for the talk.  If you missed it (or want to review it), you can access the recording of the discussion through this link.

Finally, after midnight, we had the Random.org number generator pick for the winner of the Blockhead book giveaway.  The lucky winner is Ann Murphy!  Ann, please email me at ccross@mindspring.com and let me know what dedication you would like on your autographed book (if any) and the address to which to send it.  It is kind of fitting that Ann won, because she got an extra five entries because she posted the information about the contest and webinar through her social network.  So I kind of like the fact that someone with a statistic advantage actually won the Pi Day giveway--although, as I said, I left it up to the random number generator to pick the winning number.

Congratulations to Ann--let us know how you use the book once you get it.  And I will be posting the list of suggested books in a forthcoming blog post.

Special Pi Day Webinar by Author of Blockhead: The Life of Fibonacci

In yesterday's blog post, I announced our March Giveaway of an autographed copy of the book, Blockhead:  The Life of Fibonacci by Joseph D'Agnese, in honor of the celebration of Pi Day on Monday, March 14.  However, this month we have an extra treat.  The author of the book, Joseph D'Agnese, has agreed to do a special webinar about this book on the evening of Pi Day itself (although, just to be clear, he will not be speaking about math that relates specifically to Pi or Pi Day activities).


Therefore, at 8:00 PM US Eastern Time (GMT -5.0), Mr. D'Agnese will give us some insight into his book and how to use it to teach match concepts to our students.  Joe will go beyond merely talking about the sequence and pattern of Fibonacci numbers to illustrate other ways to use the book to talk about such mathematical concepts as different numeral systems (Roman, Arabic, etc.), the value of place values, what is a number, numbers in nature, using an abacus, and many other related topics.  For the book lovers in the audience, he will also describe some of his inspiration and research for the book, and display the wonderful pictures in the book that convey these mathematical concepts, sometimes subtly, sometime more directly.


To participate in this seminar, which is being offered as part of Maria Droujkova's Math 2.0 series of math-related computer-based discussions, all you need is a computer and an internet connection, although it is helpful to have a built-in computer microphone so you will be are able to speak.   For the details on how to join in the webinar, please visit the event webpage on the Math 2.0 wiki.


UPDATE:  In response to a question, let me add that we will be recording this webinar for people who can't participate at the designated time.  I will have a link to the recording on my March 15 blog post.

March Giveaway: Blockhead: The Life of Fibonacci

Another month, another book giveaway.  This month's book is in honor of a March holiday that I went for WAY too many years without celebrating until I was informed of it a couple years ago by Maria Droujkova of Natural Math.  That holiday is Pi Day, which is celebrated on March 14 in recognition of the Pi number of 3.14159265.....well, click here for the first million digits of Pi.

Regular readers of this blog will not be surprised that the book I'm giving away this month is Blockhead:  The Life of Fibonacci by Joseph D'Agnese.  I love this book, as I've attested in my review on my blog; we've used it not only for math, but for a variety of subjects ranging from cooking to poetry.  As I explained on my blog post, Picture Books for Middle Schoolers, that while the book is written for an elementary school audience, I think middle schoolers--and perhaps older--can find deeper levels in the books than the younger students, making it appropriate for a wide age range of readers.  But you can make your own judgement for your children by viewing parts of the book at its own website.

However, as wonderful as the book is itself, the copy we will give away will be extra special because it will be signed by the author himself!  So you want to be sure to enter.  To become eligible for the drawing, you need to add your name to the comments below.  Although it is not a requirement, I would love you to also include in your comment the title of a math-related picture book that you and/or your family recommends.  This will allow us to create a list of other math picture books to share with readers of this blog.

You can also earn additional entries by helping me to spread the word about this contest.  So if you post an announcement about this on your blog, your Facebook page, or your Twitter account, email me at ccross@mindspring.com to let me know, and I will give you an additional five entries to the one you get by entering a comment.

To get an idea about the beautiful graphics in this book, please watch the following two-minute trailer:


Good luck to all applicatants.  The winner will be chosen after midnight on Pi Day by Random.org through a random number simulation process.  Be sure to check back here on March 15 to find out if you are the lucky winner!

UPDATE:  We have now scheduled a free webinar with the author!  Check this blog post for details.

Hanukkah Book Review: The Extraordinary Mark Twain (According to Susy) by Barbara Kerley

Now, for a change of pace, I thought I would write not about a humorous book, but about a book on a humorist.  The Extraordinary Mark Twain (According to Susy) is an unusual twist on a biography; it is a description of the great 19th century American writer, Mark Twain, as told by his 13 year old daughter, Susy.  The author, Barbara Kerley, is a renowned writer of biographies and other nonfiction books for children.  She had considered writing about Mark Twain for years, then stumbled upon a reference to a biography that Twain's adolescent daughter had written about him.   So Kerley tells the story of Mark Twain, but intersperses the pages with little cut-out pages from Susy's biography, where she reflects on this famous man from a personal perspective.

At first glance, this is a pretty simple book; the reading level is more for the elementary school level than for middle schoolers.  But like another of the picture books I reviewed earlier, my beloved Blockhead:  The Life of Fibonacci by Joseph D'Agnese (another point of light in 2010), I think it can also be appropriate for early adolescents.  For one thing, Susy is herself 13, so middle schoolers can relate to that.  I personally think a first reading of Tom Sawyer, or particularly of Huckleberry Finn, is more appropriate during middle school, so this could go nicely with reading some of Twain's most important books.  It contains a page with tips for writing biographies, and demonstrates more middle school-level biography techniques, like using a particular anecdote to illustrate a larger truth about the subject, rather than a mere recitation of facts that is more common to elementary school.  But more importantly, read carefully, this book explores some of the issues that tweens wrestle with in middle school, like the difference between how others see us and how our family sees us, our public and our personal personas, and accepting our weaknesses along with our strengths.

The illustrations by Edwin Fotheringham are also quite lovely, and are not too juvenile for middle schoolers.

My son picked it up and read it on his own, and he enjoyed it.  But I plan to read some Twain later in the year, and expect to return to this book again then.

And while we are on the subject of biographies about humorists...
Last week, my son read the book Sir Charlie:  Chaplin, the Funniest Man on Earth by Sid Fleischman, and declared that it was one of the best books he had ever read.  I haven't read it myself, so I can't vouch for it personally.  But Fleischman won the 1987 Newbery award for his book, The Whipping Boy, so chances are that this book is pretty well written.  And Sir Charlie is definitely for a middle school level or higher.  Or if you want to continue the Mark Twain theme, Fleischman also wrote a biography on Twain entitled The Trouble Begins at 8:  A Life of Mark Twain in the Wild, Wild West.  It's definitely on my list to read when we roll around to that point in our history and literature studies.

Lesson Plan: Writing Fibs (Fibonacci Poetry)

In today's poetry class, we learned the fine art of writing fibs (of course, when I announced that, all the students were intrigued).  But in this case, fibs is short for Fibonacci Poetry.  They are named after Fibonacci, the mathematician who discovered the Fibonacci sequence of numbers (the Fibonacci sequence is a series of numbers where each number is the sum of the previous two numbers).  If you are not familiar with Fibonacci numbers, which occur in all sort of natural growths (pine cones, pineapple, leaves on trees, the nautilus shell, etc.), check out this book from one of my previous posts.

Fibs are six-line poems in which each line contains the number of syllables in the initial Fibonacci sequence--1,1,2, 3, 5, and 8.    I wrote the following two Fibs to explain them to the students by example:

One
Sound.
Then Two.
Next Comes Three.
Fifth line has Five sounds.
Wrap it up with an Eight sound line.


A
Fib
Poem
Has six lines
With syllables that
Grow in Fibonacci sequence.

We paired Fibs with writing Haiku, which also have a set syllable structure.  However, the traditional Haiku form also has various rules--it is supposed to be about a scene in nature, it is supposed to have a word that connects the poem to a particular season, and the final line is supposed to be about the emotion that scene evokes.  Fibs are a more recent poetic form, and have fewer restrictions about content, etc. 

I like Fibs because they are new to most students and so have them thinking in different ways.  I also like them because they are contemporary (which I think is important to students) and because they connect poetry to math (and I love creating connections between disciplines).  Plus, Fibs are just fun!

Here is one last Fib that I wrote for the students in my class:

This
class
has been
so much fun!
Your poems are great.
The poets are even better!

Math For Dinner

Today is a one-in-a-lifetime (presumably...although I'm holding out for a medical breakthrough...) event--10/10/10 day.  My new age friends say that it is a time of great energy convergence, and my math friend, Maria D of Natural Math, says that it is a mathematical holiday called Powers of Ten day, and recommends that everyone celebrates by watching this video.

At our house, we didn't focus on the exponents of ten, however, looking more at the fact that there were three tens.  So we created a dinner based on threes.

We started out with a vegetable platter with hummus for dip.  There were three types of crudites:  carrots, three colors of bell peppers, and three-sided pita chips. 

However, we didn't use just any hummus; it was Trader Joe's Three Layer Hummus:

We had three three-sided vegetarian dishes.  They were Spanakopita,

Samosas,

and Marsala Burger Wedges.

Our last dish was our attempt at "Fibonachos."  We took three colors of corn chips:

Laid them out in a Fibonacci sequence with altering colors (although it is hard to tell the blue corn chips from the red corn chips, so we put the yellow corn chips in between them):

Then covered them in three ingredients:  chili, salsa, and cheese.

Dessert was (at least) three varieties of chocolate.

What a fun and delicious way to celebrate 10-10-10 day!  But since that isn't coming around again for another hundred years, maybe we'll recycle this idea for the 3rd of March.

Book Review: Blockhead: The Life of Fibonacci by Joseph D'Agnese

While I was searching the picture books section of my local library for a pornographic Eric Carle book (see this blog entry for more info), I found this wonderful book:  Blockhead:  The Life of Fibonacci by Joseph D'Agnese.  Earlier this year, I met Joe and his partner (in writing, sometimes, but in life, always), Denise Kiernan, when they came to talk to our homeschool group about their fabulous book, Signing Their Lives Away:  The Fame and Misfortune of the Men Who Signed the Declaration of Independence.  (Not to get off topic, but this is a great resource for middle schoolers who are studying the American Revolution, because it has interesting child-oriented stories about all 56 signers of the Declaration--the famous and the forgotten. )

Anyway, I knew this book was coming out from talking to Joe, and knowing the quality of his work, I expected it to be good.  And now that I've seen it, I'm happy to report that I was not disappointed.  It does a great job of presenting the Fibonacci sequence of numbers in a way that can be easily understood by elementary students.  But I think it is so well written, and the illustrations are so glorious, that I believe it is still appropriate to middle schoolers, especially those who are visual learners who have not yet learned to love the the numeric precision of mathematics.

The illustrator is John O'Brien, whom I don't know, but now would love to, because I think he did a great job.  He managed to create beautiful and modern pictures that evoke the feeling of medieval wood carvings (at least to me).  But most of all, he fills his pictures with all sorts of subtle depictions of Fibonacci numbers--Fibonacci curves and swirls, Fibonacci numbers captured in leaves, fruits, animals, and even landforms.  This is part of the reason I think the book also works for older audiences; if they are already familiar with the Fibonacci sequence, they can be engaged in searching out the patterns drawn on each page.

However, there is another message in the book.  In D'Agnese story (admittedly, a fiction based on scanty information about the real man), Fibonacci is called a "blockhead" by his contemporaries because he is so fixated by numbers--and so, doesn't see things like everyone else.  The book also provides a supportive commentary to other children who are different, telling them to follow their passions, even if their peers don't understand them.   As Fibonacci's mentor counsels him, after the child mathematician tells him that numbers are what make him happiest, "Then you should learn all you can about them.  That way you will always be happy."  What great advice that is for all of us!

My middle school son and I read it today, and at first he thought it was simple.  But when he looked at it again, he found more and more layers to the pages.  Then, when we went to spend time with my dear friend, math educator extraordinaire Miss Maria, we found ourselves searching out Fibonacci numbers in the rows of the pine cones we were throwing.

However, don't take my word for it.  See the video that Denise created for the book at the book's website.  Also, if you happen to use the book in a class or group setting, I can attest that Joe is a great speaker to students--engaging them at their level while still providing valuable content.   Even if you don't have a budget to have him come speak in person, he does Skype visits for even nominal tax-deductible contributions to Heifer Internation (a charity that I have given to personally) as part of the Fibonacci Giving Project.