Thursday, September 30, 2010

Made My Day

There is a YouTube TED presentation put on by math teacher Dan Meyer that describes in the opening sentences the plight in which math teachers often find themselves:

"Can I ask you to recall a time when you really loved something - a movie, an album, a song or a book? And you recommended it whole-heartedly to someone you also really liked, and you anticipated that reaction, you waited for it, and it came back and the person really hated it. So by way of introduction that is the same state in which I've spent every working day of the last 6 years. I teach high school math.


That's a tough spot!

I shared a couple of posts ago how I try to work to "create wonder" in my classes. Given the above, it's a tough prospect, but when it works it is a joyful thing for me and my students.

Today, in two situations, I saw the wonder, and it was beautiful!

One of these things was a student coming to office hours today who is in my Math for Liberal Arts class - basically a Math Appreciation class - just as there are Music Appreciation classes and Art Appreciation classes. We do something similar, sampling a wide variety of topics. I try to bring in the topics that are the most beautiful (tessellations and fractals) and that are the most different from arithmetic and algebra but are very applicable (topology/graph theory and logic). It was so cool talking with this student today, because he saw how much of the purpose of class was to develop a new way of looking at things, a mathematical vision that lends itself to a bigger picture of life and also new problem solving techniques that stretch the brain to envision things and approach them in new and productive ways. YES!!

Another situation was with another Math 101 student. One aspect of this class is math history, and the students will be teaching that part. They each need to select a mathematician on whom to do a presentation. This student had interacted with me a bit, debating which one to choose. She finally decided on Piet Hein. That's a name that appears regularly on my blog because he is a poet as well as a mathematician (as well as a scientist, inventor, game creator, and designer). He created a type of poetry that is one of my favorites: Grooks. For example, one Grook that has come to my mind a lot lately (in the face of the dilemma described in the opening lines of this post) is one that I've posted before:


Sometimes, exhausted
with toil and endeavour,
I wish I could sleep
for ever and ever;
but then this reflection
my longing allays:
I shall be doing it
one of these days.

In sending me her official request to have Piet Hein as her mathematician, this student wrote the following:

I'll speak of Hein's mathematical psalms,
Although, I must add this caveat:
I admit to having some qualms
About choosing the teacher's favorite!


I've had a smile on my face all evening from these two interactions. Teaching math is not easy, but sometimes it has some pretty rewarding moments, and today I had not just one but TWO of them that made my day!

Wednesday, September 29, 2010

I Need More

I need more than a truth to believe
I need a truth that lives, moves, and breathes
To sweep me off my feet
It ought to be

More like falling in love
Than something to believe in

More like losing my heart
Than giving my allegiance
Caught up, called out...

...all religion ever made of me
Was just a sinner with a stone tied to my feet
It never set me free
It's gotta be

More like falling in love

(from More Like Falling in Love by Jason Gray)

Friday, September 24, 2010

Working to Create Wonder

Finally, can you not change the world through working to create wonder?

I came across this statement today on a student philosophy forum I am following. It caught my attention because of a recent NPR Science Friday program that touched on wonder (in math) - and because of a question I was asked this week by a fellow juror - and because of a conversation I had with a friend this morning in which we touched on topics of physics, faith, Beethoven and mathematics.

What was beautiful about that conversation was a sense of wonder.

What I try to convey in my teaching is a sense of wonder.

I'm often asked (not only by students but by acquaintances and even strangers) why people need to learn math and whether or not anyone EVER USES algebra.

Certainly we all have likes and dislikes. I'm a very picky eater and don't like or appreciate comestible delicacies that others savor and rave about. I would love to appreciate a wider variety of foods, because the ability to appreciate is a gift and enriches life.

I think the same is true of just about everything from sports to wine to academics to music to art to nature.

We can approach any of these things with a "What's it good for and how can I USE it?" attitude. But to only validate things for their USE to us seems to me to diminish the experience of the whole of life.

Yes, for most people math is intimidating or at least not inviting.

No, most people don't use algebraic formulas in their daily life or in their work.


Though I would say, other than reading, math CAN BE one of the most readily applicable topics we learn in school and is useful in everyday life in everything from balancing checkbooks to determining gas mileage to cooking to splitting the bill at a restaurant to deciding on purchases to remodeling to making appropriate logical decisions after hearing political arguments. Of course you can avoid using math in this by not balancing your checkbook and by ignoring whether or not you get good gas mileage and by letting someone else figure out how to split the bill. So do you NEED math in your everyday life?


It's also applicable through the technologies we have that people who understand math have figured out for us - computers, televisions, satellite dishes, airplanes, medical imaging technology, and so much more! But here too, we can just say, "I'll leave that to someone else who likes math and knows how to do it. I don't care how these things are made - just so they work."


But math isn't just about producing a product.

One other thing math (algebra and beyond) is about is training the mind to think. It's about logic and abstraction and strengthening that brain "muscle."

Another thing math is about is having a fuller understanding of the universe we live in, in all its aspects. Galileo said, "Mathematics is the alphabet with which God has created the universe." He also said that the universe "cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word." So if you want to go a little deeper in understanding how the world and universe hold together, you need to know a little math. You don't have to explore deeply the wonder of creation; you can take it or leave it, but here we are ALIVE and in the middle of an amazing world and universe, which is a really cool thing to explore and savor while in this short life we have the chance to do so!

Some people, including my favorite poet, Emily Dickinson, have expressed that mathematizing things makes them sterile and ruins the wonder. Dickinson says: "Arcturus is his other name. I'd rather call him 'Star.' It's very mean of science to go and interfere."

But does knowing the math or science of something really diminish it's wonder or beauty? I love Emily Dickinson, but I prefer Richard Feynman's view when approached by a friend who thought science diminished the beauty of a flower: "[There are] All kinds of interesting questions [for] which the science knowledge only adds to the excitement, the mystery and the awe of a flower. It only adds. I don't understand how it subtracts."

Another Feynman quote that gets to the heart of the matter, and for which I would insert "math" just as much as physics, is:

"Physics is like sex. Sure, it may give some practical results, but that's not why we do it."

When people ask me about learning math, they want to know how they can USE it, and I feel trapped in a corner because the question already presupposes that the only reason we might learn math is for how we will APPLY it in life or work. If we go about all our learning in this way - history, geography, chemistry, physics, math, literature, music - honestly, no one HAS TO USE any of these things in their everyday lives.

A third reason to learn math is because, just like music and art, it is (when viewed and presented properly) beautiful in its own right.

A significant part of education is to open eyes to see wonder.

I understand, not everybody is going to like math. I get that. I don't like blueberries - even though people think that's crazy. But I'd sure like to move the focus away from thinking EVERYTHING we learn has to be OF USE and on to at least trying to find the beauty and sense of wonder in things we encounter in life - whether they be Beethoven's Symphonies, food, galaxies, fine wines - or even - math!

The student comment I opened with was: "Finally, can you not change the world through working to create wonder?"

That is what I try to do with math in my classes and in my conversations. It is my hope that people will allow themselves to be open to the wonder - rather than shutting it down with the seeming coup-de-grace, "How am I ever going to USE it?"

And maybe I'll even give blueberries another try!

Tuesday, September 21, 2010

What Would You Do?

I got home today from a long day of jury duty (three week trial!!), office hours and then teaching a 3-hour-long night class. I was tired, and there were some frustrating things that happened today beyond that. So, as I was griping once I finally got home after 10pm, my husband said, "Tell me one good thing that happened today."

I had to think a bit.

But what I realized surprised me.

The good thing that happened today was reading my students' homework.

This is for a Math for Liberal Arts Class. We were discussing higher dimensional geometry - including time as the fourth dimension. One of their homework questions was:
"If a time machine were invented and you were allowed one round trip, would you travel to the past or the future? What would you do with this one chance, and why would you make that choice?"
I found some of the answers really intriguing. Here is a sampling:

1) I would go to the past and tell my self things not to do and then not do them.

2) I would go to the past, before this current recession, and put all my money in gold.

3) I would go to the past and prevent the Library of Alexandria from being destroyed; just think of where we could be now if we had not lost all that knowledge then.

4) I would go back and relive my good childhood memories.

5) I would go to the future to see my great-grandkids.

6) I would go to the future, about 200 years, and see what new technologies there were, especially in the health field.

7) I would go to the past and hear Jesus give the Sermon on the Mount.

8) I wouldn't travel in time to the past or the future, because I wouldn't want to mess anything up like can happen with the "butterfly effect."
So, now I leave you, reader, with the same question. If a time machine were invented, and you got to take one round trip to the past or the future, which direction would you go and what would you do?

Sunday, September 12, 2010


There are symbols that transcend language and can be understood by all (or nearly all) people. Often road signs are designed this way, allowing travelers who do not speak the language of the country they are in to drive safely nonetheless.

Here are a couple of examples of symbols that seem to work well universally:

Such "universal," language-free symbols are also included on products, on assembly instructions or on tags of products that are sold in a variety of countries.

Today I had to wash an item I had not washed before. I looked at the tag, and it only had symbols on it. I had no idea what they meant. Thank goodness for Google and the internet! I was able to cross-reference the symbols and find out if the item was supposed to be washed hot or cold or what. I'm curious. Do you know what the symbols below mean? I am posting the answers in the comment section. No fair peeking until you've taken the "quiz."

Do people other than, say, dry cleaners or other professional launderers really understand these symbols? How did you do on the quiz?

Wednesday, September 08, 2010

Hard Times, Holy Water

When through the deep waters I call thee to go,
The rivers of sorrow shall not overflow;
For I will be with thee thy trials to bless
And SANCTIFY to thee thy deepest distress.

When through fiery trials thy pathway shall lie,
My grace all-sufficient shall be thy supply;
The flame shall not hurt thee; I only design
Thy dross to consume and thy gold to REFINE.

So shall each fear, each fret, each care
Be turned into a song,
And every winding of the way
The echo shall prolong;
So shall no part of day or night
From SACREDNESS be free,
But all my life, in every step,
Be fellowship with Thee.

(from the hymns "How Firm a Foundation" and "Fill Thou My Life" for a dear one going through deep waters right now - may they be made holy to you - and may you be blessed.)

Wednesday, September 01, 2010


My apologies to all family and friends to whom I may seem to have fallen off the planet. I've got the perfect storm going on over here, and we are in survival mode. We're in good spirits, and all is well, but we are only managing the necessities of life. I haven't even had time to follow up "A Mother's Therapy (Part 1)" with a Part 2!

It's so crazy it's almost funny.

Last week we got Anthony all set to go, and, as we should have expected, unexpected extra errands came up. We began processing the emotion of sending a child off to college for the first time. My new semester of work began (with all the requisite inservices and meetings) - so I had to put my emotional processing on hold. David is in Michigan for college orientation with Anthony, so I'm "single-parenting." And, hey, why not, we threw in some extra social activities over the weekend. Oh, and I had a birthday in there somewhere too.

And then I got sick!!!! (which made my 9:35am to 9:05pm teaching day yesterday a bit of a challenge)

It's kind of a fun challenge though - to have all that in the works - and to make it work - just as long as I don't have to do it too long!

Did you hear that David? COME HOME SOON!!

I got a message from Anthony this morning that has had me smiling all day in the midst of our "storm" over here. It looks like he's got some great people in his room and suite and floor. At least two of them play Magic! YEA! And he not only got classes he needs but the ones he was most hoping for - Honors Calculus III, Fundamental Questions in Philosophy, Introductory Physics: Mechanics and Gravity, and Biblical Literature and Theology. His brain is going to be so happy! And that makes his momma happy too! I've had a goofy grin of happiness on my face all day!

And, by the way, David, COME HOME SOON! :-)