Curriculum Resource: Greg Tang Math Puzzles

Yesterday, Maria Droujkova of Natural Math had a web seminar with Greg Tang, the author of math poetry/puzzle books such as The Grapes of Math,  Math-terpieces:  The Art of Problem Solving, and other similar books.  His books are really geared towards elementary students, mostly the 6-10 year old crowd, I believe.  So while my son had enjoyed reading his books when he was younger, I hadn't really thought about Greg Tang for several years now.

But I tuned into the webinar, and discovered that Tang now has a website with some resources that I think are appropriate for middle schoolers.  It appears that lately Tang has spent less time writing and more time programming some of the games and puzzles into interactive exercises on his website (which is apparently about to be taken over by Scholastic, which is also the publisher of his books).

The games on there, so far, at least, still focus on mastering basic mathematical computational skills.  However, I know my son can still use some work on recalling those math facts quickly and accurately.  But they are fun games, even though they based on simple mathematics.  Some of them are kind of like Sudoku, where you have to figure out the right selections of numbers, but you have to add, subtract, multiply, or divide to choose the right one.   I found them kind of fun and interesting to do as an adult, but my son enjoyed doing them as well.

Our favorite was a game called Kakooma, in which you are given a series of hexagons with six numbers in them, and you have to figure out which number can be created by adding, subtracting, or multiplying two of the other numbers in the hexagon.  So it doesn't require a math savant, but you are racing against the clock and other players, a bunch of whom have figured out all seven problems in a set in less than 10 SECONDS!  Unbelievable!

Anyway, if you buy a subscription, all the games have a bunch of different levels to make the game harder or easier, but there is a free version of each game that has been challenging enough for us so far.

So if your family likes math puzzles, or if you are just looking for a fun way to practice some basic computational skills, check out GregTangMath.com.

If you are interesting in finding out more about how Greg Tang develops the math books, games, and other materials he creates, you can access a recording of the entire webinar at:
http://mathfuture.wikispaces.com/GregTangMath .

Math Trek at the North Carolina Museum of Art

Our Math Trek series has started up again for the new year.  This is one of the creative math activities organized by Maria Droujkova of Natural Math.  It is a multi-aged program where students of all levels take quests to find and photograph different math concepts.  We then share them with each other, whether by discussion, acting them out, or posting them on the web.

This week's Trek took place at the North Carolina Museum of Art, which has so many wonderful things to look at, whether mathematical or not.  Maria's colleague, Brad Herring, was there to capture the action on film, so that we could share it with other similar groups around the world so they could have their own Math Treks:

Our intrepid leader, Maria Droujkova

Our videographer, Brad Herring

Maria have the students various "quests" to find and photographs, including recording examples of fractions, proportions, and fractals.  Then we came together to discuss and recreate some of our favorite mathematical concepts/photographs:

Recurring Circles

Acting out the proportions of seats in a circular amphitheater

Making a human fractal

As always, it was a fun and educational outing.  Plus, the weather was beautiful this weekend.  But to see students discovering math in settings all around them--that was even more beautiful!

Math and MBTI Psychological Type

Happy Math Storytelling Day!  This is an event in honor of my dear friend, Maria Droujkova of Natural Math, whose birthday is it today.  The idea is that we share our stories about math with each other.

So my story involves math education and psychological type as measured by the Myers-Briggs Type Indicator (MBTI).  This past winter, I taught an online class through P2PU on the Psychology of Math Learning.  The idea of the class was to look at various psychological theories, including MBTI personality type theory, to see if it would give us insight on why math can be such a struggle to so many learners.  (For more details on the class, you can read my original blog post about it).

The structure of the class was that each week, we would take an online test about one of these theories, then post our "score," such as our MBTI type, which in my case is ENFP (Extravert, iNtuitive, Feeling, Perceiving).  Then we would reflect on our experience learning math, and see if we noticed any ways that our test results might have helped or hindered our math education.

The class didn't work out quite like I planned, because even though this approach was explained in all the class descriptions, and had a couple dozen people sign up, the only students who ever posted their scores or their reflections on the theory and their math experience were the Extraverts!  So, we ended up with a skewed sample of respondents.  But we Extraverts had a great time talking about things between ourselves.

However, it was an eye-opening revelation for me.  Math had always been my worst subject at school; worst NOT in the sense of grades, since I was the kind of student who would do whatever I needed to do to get an A, but in the sense that I knew I didn't really understand the answers I was regurgitating back on my graded work.  And that wasn't usually the case for me--generally, I understood the concepts behind all my other subjects.  So I never liked math, thought I wasn't good at math, and never took any academic math classes past my required Algebra II/Trig in my junior year of high school.

But by looking at MBTI, I could see at least part of the reason why.  Because the way I was taught math was EXACTLY opposite to my personality style.

• Math was taught as a completely I (Introvert) subject.  You stayed in your own seat, stuck to your own paper, came up with your own answers.  Any working together on a problem wasn't collaboration, it was cheating.  Even in Science, we at least had lab partners when we worked on experiments, and did lots of group projects in the Arts and Humanities (my favorite subjects).  But in math, I don't ever remember working with another student.
• Math was taught as a million different discrete problems that built up, bit by bit, to larger concepts--which is a very S (Sensing) approach.  Everything had an order and a sequence that eventually led to a comprehensive explanation of the subject.  But N (iNtuition) people like to see the big picture first, so that they understand why they are doing all the individual problems.  N people also usually don't fare very well in the high-sequenced, "show all steps of your work" approach that was used in my academic math classes.
• Why subject could possible be more T (Thinking) than math?  What does F (Feeling) have to do with whether 2 plus 2 adds up to 4, or that the area of the circle is Pi times the radius squared?  I was presented math as a completely abstract, logical, impersonal subject, which isn't something that we emotional, subjective, relationship-oriented F people particularly like.
• Finally, I was taught math as a very black/white, right/wrong, only one right answer kind of way, which is what MBTI calls J (Judging).  P (Perceiving) people like open-ended answers, multiple possibilities, and options.  But I was never given any of those shades of gray in my math classes.

Let me make two things clear.  First, I'm not saying that any of those approaches are "bad" or "wrong."  The whole basis of MBTI is these different preferences, which we are born with, are not better or worse than each other.  They are just different.  I doubt I had bad math classes, because I went to good schools and I'm sure I had good math teachers.  That was just how math was taught in those days.  And I'm sure that approach works brilliantly for some people--just not for me and my personality style.

Secondly, I now know that math doesn't have to be that way.  Math education has come a long way since then, and there are many more ways that math is presented these days in schools.  I am also so thankful that I met Maria, and through her, all the people on the Natural Math loop who have shown me math as a rainbow, not just a black and white subject.  For example, Math Mama Sue Van Hatten just recently had a blog post about how her students work together in groups.  The wonderful math-rich puzzles presented by Math Pickle encourage students to find many answers to the same problem.  Maria is constantly presenting math as fun, and as beautiful, and as creative, and as a vehicle for individual expression.  And I could go on and on about the wonderful new math educators who are diversifying the experience of this important field.

So my story has a happy ending.  Maria and others have helped me to "grow new math eyes" so I can appreciate math in a way that works for my personality.  But I think my story also has a moral, which is that math instruction (and all instruction, really) needs to meet the individual's personality and style, at least to some extent.  If you are a teacher or a parent or a homeschooler (some of my readers are all three), and your math teaching isn't working, consider the personality of the student who is having problems.  It is easy for us to get so caught up in our own MBTI preferences that we don't even notice that we are only giving open-ended exploratory problems to students who do better with more structure, or refuse to even consider a response from our creative thinkers that is different than the one in the answer key, which we find so reassuring.

Post Updates, AKA Good News

I wanted to let everyone know the good news about a couple of my recent blog posts.

Most recently, I wrote a couple of posts--the original Eliminate Math Anxiety post and then the popular Mobius Marinara post--about my friend Maria Droujkova of Natural Math and her attempt to raise $6,200 through Tipping Bucket to extend her work on teaching significant math topics to children from 0-5 years  into a book and online community that could reach many more people.  The deal with Tipping Bucket is that people pledge money to projects they want to support, but if the organizers don't attract all the money they need to make the project work by a set deadline, the pledges are returned to the donors.

However, I'm happy to report that Maria's Moebius Noodles received its full funding!  So the project is now a go, thanks to many generous donors (including, I'm proud to say, my son, who gave a full week's allowance to support this effort).  If you want to find out about developments on this project, follow Maria's blog, Math Accent (which is a font of wonderful information about all sorts of different math topics, not just those related to our youngest learners).

And speaking of our youngest...at the end of last month, I also posted about one of our local homeschooling families who, unfortunately, had lost both of their twin babies.  On top of the terrible loss of their infant girls, they had a lot of bills to deal with, so we were having an online fundraising effort to support them financially.

In this case, it is still a sad story.  However, I am happy to report that this Internet effort between friends, and friends of friends,  and friends of friends of friends of...., well, it resulted in raising $8,372.32 for the family.  I know that the family really appreciates every gift, not only for helping them deal with their financial issues, but as a vote of confidence in their ability to survive through the worse circumstances that a family ever needs to confront--a loss of one (or, in this case, two) of their beloved children.

Both of these remind me of one of my favorite quotes from Mother Teresa, who once said:

"What we are doing is just a drop in the ocean.  But if that drop was not in the ocean, I think the ocean would be less because of that missing drop."

Both of these projects show what is possible when a lot of ordinary people give just a little to a good cause.  It is easy to think that what you can afford--$1, $5, $10--can't make a difference.  But you put all those drops together, and it creates an ocean.

I also heard from several readers of this blog who said they had supported these efforts.  So I want to thank you personally for your support.  I know many will reap benefits from your gift, and I'm glad that you were part of our ocean.

Curriculum Resource: Edible Mobius Strips

There is only one day left in the fundraiser for my friend Maria of Natural Math, who is trying to raise $6,200 for a community-based initiative to help parents, caretakers, and preschool teachers to introduce deep math concepts to children from infants to age 5.  Since the deadline is so near, we kind of have mobius strips on the brain (because the name of the project is Moebius Noodles).   We are thinking, breathing, and eating mobius strips...

And I mean that literally:

Yes, tonight's dinner consisted of edible mobius strips, made out of handmade pasta, courtesy of my brilliant son.  He is the one who had the idea of showing our support for the Moebius Noodle projects by making mobius strips out of actual noodles!

So we made some dough and pulled out the old pasta rolling machine:

Then we rolled out the dough, cut them into strips, and joined the ends of each strip together in that paradoxical inside/outside form that is the mobius strip:

It took quite a while, and it seemed like we had made 6,200 pieces of pasta, although I imagine it wasn't quite that many:

I had also made a homemade tomato sauce out of the fresh tomatoes and peppers from our local farmers market, combined them with some turkey meatballs, and VOILA!

Mobius Marinara!

And I share all this, not only because it is fun, but because it demonstrates the potential of the Moebius Noodles project.  First, I doubt my son would ever have had this idea without his exposure to Maria, because let's face it--cool things like Mobius strips aren't covered that much in traditional math curricula. Secondly, it illustrates the way that Maria makes math fun and concrete and real life in a way that works for children of all ages.  Sure, my son is a middle schooler, but toddlers could enjoy making a meal of mobius strips just as much.  Finally, Maria's concept for Moebius Noodles is to make it a community project, not just her personal product.  She wants to publish the ideas under a Creative Commons license, which means it would be free for others to use and adapt.  She also wants to make it a open web-based program where everyone can contribute ideas and resources.  So my son came up with this project, which was fun and worked out really well and which we are glad to share with others.  But what might you or your children come up that would not only work for your family, but might really benefit others--if you had a way to get it to them.  THAT is the idea behind Moebius Noodles--not simply a book or a commercial product, but a vehicle by which we can all access and add to the community of ideas about teaching even our youngest how to use and enjoy math.

So as of the time I'm writing this (10:00 PM on Monday, September 19), we only have 24 hours to raise the remaining $2,500 for this project (remember, with Tipping Bucket, if the entire sum isn't raised, all the money goes back to the donors).  So if you have been meaning to donate, but haven't gotten around to it, now is the time.  And whether you donate or not, stay tuned to developments with the Moebius Noodles project.  Maria wants your educational ideas and experience as much, if not more, as she would like your money.

What If We Could Eliminate Math Anxiety?

What is it about math?  We all have subjects that we are better at or are worse at, or that we like or don't like as well.  But no one ever talks about having "history anxiety" or "grammar anxiety."  Math, however, is a whole different matter, at least for thousands....no, let's be honest...millions of us (of all different ages).  If there is any topic that our children (or, again being honest, ourselves) are likely to say that they hate or just don't get or just try to avoid, it most often math.

But what if we could eliminate that for the next generation of students?  Wouldn't that be worth a few dollars to you?



My friend Maria of Natural Math has some great ideas about how to raise children so that they love, rather than fear and resist, math.  Through Maria's eyes, math is a language or an art form through which to view, understand, and communicate about life, not a series of incomprehensible formulas to be memorized and worked over and over again.  And Maria believes that, just like language, basic math concepts--even those that form the basis of calculus--are best absorbed when the human brain is young and plastic....say, up to five years old.  After that, according to Maria's research and experience, it is harder to children to learning the basic mathematical building blocks, just as it is harder for older brains to hear and repeat the distinct sounds of a different spoken language.

I am one of the privileged few who lives close to Maria, and has had the benefit of her experience in teaching my son about math.  Since math was my toughest subject as a child--I'm definitely one of those who continued to suffer from math anxiety into adulthood (although, thank goodness, my husband is really strong in math)--I attribute my son's recent confidence and high performance in math to what he has learned from her, not from me.  But she is only one person in one place, and the problem is so much larger than what one person can do.

So here is what we are doing to try to make Maria's expertise available to a larger population.  Maria has a fundraising effort going on at Tipping Bucket, a cool new social media fundraising vehicle.  Tipping Bucket takes proposals from worthy efforts, checks them out to make sure they are legitimate and have a reasonable plan, and then selects some to support through their website.  Each project has about a week to present their case to the world.  People check it out, and if it speaks to them, they pledge money.  HOWEVER, their pledges only count IF the project reaches its desired goal.  If it falls short, all the money is returned.

Maria is seeking $6,200 to turn her expertise about introducing math concept to infants and toddlers into a book, which could then be made available to everyone.   So we are trying to mobilize hundreds or thousands of us who care about children and the math education they receive BEFORE they ever get to school to give just a few dollars to make this project a reality.

If this speaks to you, please use the button below to go to Tipping Bucket to donate:



Then, spread the word among your communities.  Each of us may only be able to give $1, $5, or $10 dollars.  But if we share this educational opportunities with our friends and colleagues, and ten of them choose to give as well, that raises another $10, $50, or $100.

However, there is a short deadline on this project.  We must raise the entire $6,200 by Wednesday, September 21, or all the money is returned to the donors.

So if you would like to be part of the effort to raise our children to embrace and create with math, rather than to dread and dislike it, please act right away.

If you want more information, visit Maria's blog post about the project, or see the Tipping Bucket page.

PS:  If you would like to post a button on your own blog or website, please copy the HTML code below:

<a href="http://tippingbucket.org/projects/moebius-noodles">

<img src="http://www.naturalmath.com/blog/wp-content/uploads/2011/09/MoebiusNoodlesFundraiserBadge2.jpg" 

alt="Moebius Noodles Fundraiser Badge" width="200" height="174" /></a>

The Math of Art

My dear friend Maria of Natural Math has a life mission of showing people the art of math.  But last night at Cary's monthly Art Loop (or Final Friday, as we usually call it), I got to see examples of the math of art.

Unfortunately, there were very few people enjoying this month's Art Loop, presumably because most were at home preparing for Hurricane Irene.  But that was a shame, because there was some lovely art and artists, and the evening ended up being perfectly calm and beautiful.

While I always enjoy all the galleries, one that particularly struck me was J.J. Jiang's exhibit at the Page-Walker Art & History Center entitled "Hometown Waters-From Suzhou, China to Oriental, North Carolina."  Jiang, a professional architect and illustrator who was originally from China, somehow came to settle in the Eastern Carolina town of Oriental, and the show features pictures of boats and other water scenes from the two places.  This particularly struck me because Oriental is where my husband keeps his boat (and thus was down there on Thursday securing it from the hurricane).  Oriental has a theme of dragons (to connect its name to China), and you can wonder through the town finding dragon eggs in various parks and such.  But I had never seen a Chinese response to this North Carolina town.  You can see some of the pieces in this show on his website under the Galleries, then Art Portfolio.  The artist is a gifted and interesting man.

But then I wandered over to the Cary Town Hall, and there I found two other captivating artists.  The first I was Elke Brand, formerly from Germany but now working in the area.  She has a Planet series made of digital photography with a very symmetrical focus.  You can see my bad photos below, but can see her work more clearly on her blog:

I really, really liked her three pieces "Planets We Are One" that are shown on her "Legends, Heroes, Leaders" post on her blog.  We've done some similar things with Maria in Natural Math by reflecting art in mirrors, but her's were much more professional and interesting, of course.

But then I came to an exhibit that made me think even more about Maria:  an exhibit entitled "Baskets:  Billie Ruth Sudduth Meets Fibonacci."  You can't get much more math-y than that!  The Fibonacci sequence (the number plus the number preceding it, such as 1, 1, 2, 3, 5, 8, 13...) occurs naturally in the wild and often unconsciously in human art and living.  Sudduth, who is based in North Carolina but is becoming a world-renowned basket weaver/artist, weaves her baskets deliberately using Fibonacci sequence number in such pieces as the one below, which I believe was called Fibonacci 3:

Fibonacci #3? Basket

Signature Basket

Once again, you can see much better pictures of her work in the Gallery on her blog.  Her middle school connection is that she came up with this idea when she was teaching a middle school class called
Math in a Basket, which is now available for sale as a book on her website (scroll down towards the end of the page to see it).

Anyway, it really made me think of Maria and all the others who are exploring Math as not just manipulation of numbers on a worksheet, but as a language that informs all sorts of other field--including math.  But they are beautiful things to go see, even if you don't want to make them into a mathematical exploration.

Curriculum Resource: Who Wants to Win (REAL) $1,000,000--Math Edition

Yesterday we talked about a science game based on the TV show, Who Wants to Win $1,000,000?  Today, we are talking about a site that is offering $1,000,000 (to be split with their most inspirational math teacher) for people who solve 13 great math questions, one for each K-12 grade level.

Just one caveat--the sponsors of these competition, Math Pickle and the Pacific Institute for the Mathematical Sciences, haven't yet gotten the funding for the puzzle winners.  But I guess they don't have many people claiming to be winners yet, either, so perhaps they've got a while to raise the money.

Here is a video that presents the unsolved problem for the 8th grade, which is based on the ancient Greek myth of the Minotaur in the labyrinth:



Even if you don't expect to win $1,000,000, you should definitely check out Math Pickle.  It has a bunch of different videos, all geared to specific grade level, about ways to spice up your math teaching.  In particular, it features puzzles, exploratory questions, and hands-on activities that draw students into problem-solving and applying the math they are learning, rather than doing rote exercises.   The problems and ideas are quite interesting, and I've tried a few of them with my own son.

It is this kind of approach to math (also a hallmark of the work we have done with Maria Droujkova of Natural Math) that has turned around my son's attitude towards math, which he used to hate but now thinks is neat.  And that is worth more than $1,000,000 to me.  So it is worth your while to visit Math Pickle and pick up a few ideas for getting your students engaged in math problem solving.

Lesson Plan: Sufi Tughras and Name Snowflakes

For the past couple of weeks in our World Religion class, we have been looking at Sufism, an offshoot of Islam.  A graphic symbol for many Sufi orders, which have a much more universal or interfaith approach than most practices of Islam, is the winged heart:

Another tradition in Sufism is to create the winged heart shape as a tughra, which is a calligraphic rendition of the name of the master teacher of that Sufi order (and/or words describing him/her).  So, for example, the tughra of the Sufi orders that come from the tradition established by Hazrat Inayat Khan (the predominant strand of Sufism in the United States), looks like this:

These are beautiful works of art, but not something easily done with a middle school class, since it requires both calligraphy skills and knowledge of arabic.  So instead, I drew upon something we had done years ago in Math Club with my friend Maria of Natural Math, who in turn learned it from another friend and homeschooling mom, Chrissy Akers--namely, Name Snowflakes.

To create Name Snowflakes, you fold up a piece of paper like you would to cut normal types of snowflakes that many students do in elementary school.  However, instead of just cutting out shapes, you draw the name or other word in big block letters that stretch from top fold to bottom fold and that stay attached to each other, and cut out the spaces outside the word.  If you do it right, you have the word repeated number times in different directions, which can look quite lovely.

Here is one I did with my name, Carol:

which, when unfolded, looked like this:

Here is one made from the word SUFI:

Here is the one my son did from the word WUG (chosen primarily because it didn't have any interior spaces that had to be cut out, which is the hardest part of cutting):

So they aren't nearly as lovely or as significant as a tughra, but they can turn out pretty well and at least help students understand the concept of tughras, especially since they can't distinguish the arabic letters.

Our crew had fun with them, as you might be able to tell from this picture:

Curriculum Resource: Where Does Pi Come From?

This evening I attended an absolutely fantastic webinar that was part of the Math 2.0 series that my friend Maria of Natural Math runs.  If you have a middle schooler (or even a high schooler) taking Geometry, you and your child should check out the recording of this hour-plus educational lesson.

The session was called "Pi in July," and featured two mathematicians:  David Chandler, a mathematician who teaches at a California public charter school that supports homeschooling families and offers supplemental instruction to major high school math textbooks at Math Without Borders ; and Allison Krasnow, a mathematics teacher at Willard Middle School in Berkeley, CA.  The two have been working together to develop ways to explain to students where the number Pi actually comes from.

Chandler began by explaining, using geometry and especially the Pythagorean Theorem, how the approximation of the number Pi was originally derived by Archimedes in ancient Greece.   He started with a simple graphic that demonstrates why Pi is between 3 and 4, and not 10 or 7 or some other random number.  Krasnow then took his idea and modeled it in GeoGebra, a free open source software for creating geometric figures.   Finally, Chandler worked through the process that Archimedes used to figure out this key mathematical number--except that he used a spreadsheet to crunch the numbers up to millions of points.

I'm not doing the talk justice, but it really is a brilliant process.  My 12 year old son participated and was able to follow everything step by step, and really got the concept of why Pi is what it is.  I think that is so much better than when I learned geometry, when I was just given the value of Pi to plug into formulas with no idea where it came from or why I should believe it.

For more information on the webinar and the presenters, or to access the recording of this session, see the Pi in July page in Math 2.0.

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.