Checking In

Posted Friday, April 17th, 2015 @ 12:08 am by Kathryn
Categories: Arts, Domestic Arts, Journal, Miscellaney, Poetry

When I feel at loose ends, sometimes I pull this series of questions out and check in.

Outside my window the street sounds fade. Cool air settles on the grass and patio, bringing a gentleness with it. Distant yips and howls tell me the coyotes are roaming.

I am thinking about what I just heard on the news about the sardine population collapsing, which has prompted a halt on fishing season for them. Officials say over 90% of seal pups died this year because of starvation; they had no sardines to eat. I eat sardines often and feel both guilt and selfish concern about what this will do to price and availability. This news coincides with my having finished a book — captivating and dire — called The Sixth Extinction, by Elizabeth Kolbert. Human activity has triggered enough environmental change that we may be moving into a new epoch, from Holocene to Anthropocene.

I am thankful for ordinary life. My neighborhood cat-who-is-not-quite-my-cat whom I feed and pet; Claire’s marvelous and spirited self; social media connections; quietude; coffee, and books.

I am wearing black jeans and a black shirt, which is unusual for me, and it feels like too much of one color.

I am creating new connections in my brain now that I’m playing more with numbers. I’m also writing poetry, and making a little art.

I am hearing the hum of silence; my laptop hard drive, the refrigerator, a distant car motor, the high pitch of plugged-in electronics. It has a walled-in aspect to it, and is vastly less restful than the silence of camping outdoors.

I am remembering twenty years ago. My father recently sent me letters I’d written to him in 1995, after I moved to Austin. In these letters I talked about the growth of the Internet, and how that would create major change in the world. I was on a search for a new career, and very torn about my varied interests.

I am going to feel some regret in the morning for staying up this late.

I am reading poetry by Lucille Clifton and Gwendolyn Brooks, and I’m about to dive into a novel, The Diamond Lane.

I am hoping to motivate myself to clear my workspace so I can make some more collages.

On my mind is the fact that I’ve committed to co-leading the Project Cornerstone program at school next year, and I have many ideas as to how to increase community awareness and involvement with it.

Noticing that I’ve been avoiding exercise again, and indulging in more food, and forgoing tracking this.

Pondering these words: growth mindset and fixed mindset, coined by Carol Dweck.

One of my favorite things is snuggling in bed with Claire at the end of the day, singing a lullaby to her.

From the kitchen I’ve been cooking a variety of crockpot meals: chicken tortilla soup, pork roast, red beans, pot roast.

Around the house I’ve been culling items that get little use and trying to stanch the flow of paper that floods us weekly. I’m also still unpacking and sorting from the camping trip.

A few plans for the rest of the week: Friday will be an errand day. Saturday I have a SoulCollage® session from 9:30 a.m. – 1:30 p.m., after which I will take the car to get a smog test. Sunday is church, and then the Mighty Daring Girls will meet to make masks. Then I’ll roll into the next week with training at Project Cornerstone, taking Claire to choir practice, and all the usual routines of the school week.

Here is picture I am sharing of an ATC I recently made.

ATC abstract

Math Before Coffee

Posted Thursday, April 16th, 2015 @ 10:01 am by Kathryn
Categories: Education, Journal, Science, Technology

Tupper's Self-Referential FormulaMath is a language. You can learn bit by bit, or you can learn by immersion. I suspect the former is a more successful process. However, this morning my brother tweeted about “fun with math” and linked to a video about the “everything” number. It’s about Tupper’s Self-Referential Formula.

Link here.

Thus began my introduction to a “simple” formula that can plot itself on a graph. It can also be used to draw any other two-dimensional image.

I mentioned this to Hub, and who looked up the term; this led to a comment, “He’s cheating! He’s using mod and floor.” WTH does that mean?

Now, this is usually where I start feeling dumb and intimidated. But I admitted not knowing, and thus learned that “mod” is short for modular. Basically, it is the remainder in a long division problem. The mod (modular operator) of 5 divided by 2 is 1. Modular arithmetic — who knew?

On to floor and ceiling. Floor refers to mapping a real number to its next lower integer: the floor of 7.1 is 7. The floor of 7.8 is also 7. Ceiling refers to mapping a real number up to its next higher integer: the ceiling of 7.1 is 8. The ceiling of 7.8 is 8. This is different function from rounding. If I round 7.1, the answer is 7; if I round 7.8, the answer is 8. I am told this is used in computer programming and math.

As for the formula, it’s related to computer graphics. Hub went on to tell me about SIGGRAPH, which stands for Special Interest Groups on GRAPHICS and Interactive Techniques. It’s a group of computer professionals who spend their time creating the graphics you see on your computer, phone, tablet, movies, robotics, in emerging technologies, as well as what is used in research. He also suggested I look up the Utah Teapot and Lenna.

Martin Newell, a graphics researcher, created a mathematical model of an ordinary teapot in order to create a 3D computer model. It has since become a standard reference object in the graphics community. Go look at it. I’m amazed.

As for Lenna… it is an image of a woman looking coyly over her shoulder, and it is used as a standard test image for high resolution color image processing experiments. Its detail, shading, texture, and flat regions make it a good subject. As for the source of the image? It’s from a Playboy centerfold. Some controversy is associated with the use of the image because of the underlying sexism. Read more here.

I can’t say I learned actual math this morning, but I did come away with new knowledge. And all before I’d had my morning coffee. (Which I still haven’t had, because I just had to sit down and get this out of my head.)

For the Love of Math

Posted Wednesday, April 15th, 2015 @ 12:45 pm by Kathryn
Categories: Education, Journal, Motherhood, Quotes, Technology

As a child, I loathed math. From the very earliest — first grade — it confounded and intimidated me. I felt stupid. My father, being an elementary teacher, sought to bolster my learning by doing flashcards for addition and subtraction. In order to perform and please him, and my teacher, I memorized the cards. I didn’t really understand 7 + 4 = 11. And so I didn’t understand the process of numbers. In later elementary grades I remember struggling with area and perimeter, multiplication and long division. I felt utterly unintelligent.

In ninth grade, I fought with algebra. It didn’t help that the teacher was an older woman who radiated vulnerability, which meant the students disrespected her and little teaching happened. I began to skip class. I would go to the resource center after school for help. When we got to word problems, I discovered I was able to do them with help from the resource teacher, and I felt a measure of accomplishment.

In tenth grade it was geometry. The teacher was a gruff old man who terrified me. I’d look at the book and none of it made sense. I couldn’t understand, and the fact that I struggled reinforced the feeling of failure. And so, I began skipping that class too. Except the school sent home a letter to my parents. I was required to stay after school to work in a small group with the teacher. And to my surprise, I found him less scary, and I began to understand a bit more. But math remained oblique to me.

I remember cramming for the Geometry Regents exam with my brother-in-law the weekend before the exam. I feared failing it, since that meant I’d have to do summer school, which would mess up the family camping plans. If I failed, I assumed the wrath of my father would obliterate me. I took the exam. I struggled. Afterward I cried, certain that I hadn’t passed. The next day, the teacher proctored the Biology Regents exam. He roamed down the rows of kids, and as he came to me, he leaned over and whispered, “You passed. You got 65%.” Oh, glory! Bless him for sparing me the torment of waiting to find out.

In our state the requirement for math was a minimum of two years. In my senior year I took “practical math,” also considered math for dummies. It was basic arithmetic, percentages, fractions, and so on. I did it to fill out my schedule.

And after that I ran from math as far and fast as I could for many years. In my mid-20s, I returned to college full-time to finish my B.A. in psychology. My first semester included a statistics course that met three times a week at 8 a.m. The teacher gave a weekly “quiz” — 30 multiple choice questions that were actually very challenging. My first one came back with a grade of D.

I panicked. I needed to pass this! So I decided I would get all the help I could. His office hours were from 7-8 a.m. So before the next test, I was in his office with questions. He patiently helped me, and suddenly the heavens opened and the light of understanding beamed upon me — wait, no. Not really. But I understood more, and I got a B on the next test. There were 14 tests in that class. I read the text, calculated the problems, and studied diligently for each test. When I received the grade of B at the end, I was really proud of myself.

The following semester I took a general math class. I learned about the Euler method, and sequencing, and a bunch of other stuff I’ve forgotten now. I worked hard in that class, and I earned an A.

Since then, I haven’t needed much math. And I’m still daunted by it. I can’t do basic calculations in my head; I still use my fingers, or write things down. But as a parent, I have kept my mouth shut about this. I have not talked about my dislike of math, or my struggles with it, because I believe that math can be learned. It takes effort. I know that now, and I proved in the college courses I could do the work.

The other day, Claire said, “I HATE math!!” Oh, dear. In the past we had done Bedtime Math, which she enjoyed and felt confident doing. But we got lazy about it. Upon returning to it, I noticed she was distracted, not really trying to understand the questions. She would then sense my frustration with her (for not trying) and quit, saying, “I’m stupid.”

Claire has a streak of perfectionism in her and a tendency to conclude that if she doesn’t understand something, the problem is inherent to her. She assumes math ability is a fixed quality — she is just not good at math, period. How interesting, because she is actually very bright, and learning has always been fun in our family. According to her teacher, she is performing well in math. I look at her worksheets and see correct answers. So, what is going on?

I made a comment on Facebook, and a friend of mine who is a teacher contacted me privately. She offered me some suggestions worth sharing.

First, she commented that Claire doesn’t see me doing math. I’m her biggest role model. I read avidly, but never do math puzzles, for example. Hmm.

Next, it is not uncommon for girls to absorb attitudes about math from other people — at school, peers have a lot of influence.

Then she told me about some resources:

  • I can download Noyce problems of the month from Inside Mathematics and try them myself. Last year, our school offered the Problem of the Month for kids to work on, and Claire enjoyed it. From the website, it says,
    “Problems of the Month are non-routine math problems designed to be used schoolwide to promote a problem-solving theme at your school. Each problem is divided into five levels of difficulty, Level A (primary) through Level E (high school), to allow access and scaffolding for students into different aspects of the problem and to stretch students to go deeper into mathematical complexity.”

    So, she can do the beginning levels with me, and I can take on the rest. Hey, I might even enjoy them!

  • Greg Tang Math: who on earth is Greg Tang? From the Scholastic book website, his biography says,
    “Greg Tang was tutoring math in his daughter’s class when he noticed something interesting about the dominoes they were using. Each white dot had a pencil mark on it, which meant the children had been counting them one at a time. Mr. Tang taught them to look for patterns instead, and to add and subtract groups of dots in order to calculate the dominoes’ value quickly. From there, he developed a new method of teaching arithmetic in a visual and spontaneous way. His method teaches both computational and problem-solving skills, and is so fun and challenging that children forget they are learning math! He believes that all kids are capable of doing well in math, and he has a mission to make math a natural part of every child’s life. He has successfully taught his method to children from ages five to ten.”

    Greg has a number of cleverly titled math workbooks for kids, such as The Grapes of Math, Math Potatoes, and Math-terpieces. His website offers games and puzzles.

  • Jo Boaler, professor of mathematics at Stanford University. A search for her connected me to a free online course: How to Learn Math: for Students. (There is one for teachers and parents as well, to help them provide support, but it costs tuition.) The description says, “If you have had past negative experiences with math this will help change your relationship to one that is positive and powerful.” So I enrolled Claire. She is very excited to be taking a course at Stanford University!

I read a lot of griping about Common Core math on social media and in the news. Yet the way I was taught did not teach me to understand at a deeper level. I memorized functions and did not learn connections. I learned to do without understanding the reasons. When I saw this video, Common Core Math Explained, I could see the appeal. It is my hope that I recover from my past negative encounters with mathematics by re-learning math as Claire learns.

When Claire was five months old, we started going to Music Together classes. Prior to this, I could not carry a tune. I couldn’t start a song on key without music leading me. But we listened — over and over and over, hundreds of times, to the CDs. As a result, I internalized the sounds. I learned audiation, which “takes place when we hear and comprehend music for which the sound is no longer or may never have been present.” Now I can sing pretty confidently. I accomplished growth in the area of music, and I’m looking forward to the same with math.


Posted Sunday, April 5th, 2015 @ 1:45 pm by Kathryn
Categories: Buddhism, Community, Quotes, Spirit

This captures the essence of spiritual life for me.



Posted Monday, January 12th, 2015 @ 11:55 am by Kathryn
Categories: Aenigmas (My Poems), Arts, Journal, Poetry

For Swap-bot, I joined a project that required writing a sestina.

According to the Academy of American Poets:

“The sestina follows a strict pattern of the repetition of the initial six end-words of the first stanza through the remaining five six-line stanzas, culminating in a three-line envoi. The lines may be of any length, though in its initial incarnation, the sestina followed a syllabic restriction. The form is as follows, where each numeral indicates the stanza position and the letters represent end-words:

(envoi)(tercet) BE. DC. FA.
The envoi, a tercet, must contain two of the repeated words per line.”

So, here is what created itself within me. After I wrote it, I noticed it is technically incorrect. The tercet is wrong. But I’m leaving it as it is, for now, until I feel moved to edit.

The Dance

There I stood, waiting for the express
While pondering ways to renew
my flagging spirit, which struggled to climb
life’s mounting challenges, when I saw you, serene,
your hands moving in the air, a kind of dance —
the glorious joy on your face making you rich.

Gazing around, I noticed the world’s colors were rich.
In each person I sensed the soul’s desire to express,
to enter into the dance.
I felt that I could summon the energy to renew
and make myself serene
like an arbor trellis with those roses that climb.

To reach far, to stretch toward goals that require I climb —
this makes life worthwhile, and I feel rich.
In these moments, my heart beats serene.
I vibrate with life and tremble to express,
to evolve, to embrace impermanence and thus renew
life’s eternal dance.

So, which steps will we choose to dance?
Will it be the hustle, the two-step, the fandango climb?
Or maybe a slow waltz, to allow our breathing to renew
while rhythmically moving to the beat, slow and rich.
Perhaps we will lean in to share a kiss, to express
what tantalizes us as we attempt to appear serene.

We might do this under the silver light of the moon, serene
in the movement of the dance
and the people watching — their murmurs will express
how desire steeps, distills, intensifies, like the climb
of mercury trapped in a glass tube, the red rich
like blood, like the lungs give oxygen to renew.

And after we untwine ourselves, we turn within to renew
the relationship with the One who never leaves, the serene
companion who understands money does not make one rich;
nor does having it guarantee an invitation to the dance
and that life is often one painful, slogging climb
to an illusory summit that cannot contain all we express.

It is a koan to puzzle: that form and emptiness express
all that is, removing the need to delve or climb.
Just accept, wisdom says, so you can surrender to the dance.
As I move, I offer my life to you, to heal and renew
in the hope of erasing the wrinkled brow, leaving it serene
and a soul well-fed, feeling sated and rich.

–Kathryn Harper


Be Kind

Posted Monday, January 12th, 2015 @ 8:42 am by Kathryn
Categories: Journal, Social Science, Spirit

It bears repeating.

Here’s the link if the video doesn’t work.

How to Fall in Love

Posted Saturday, January 10th, 2015 @ 9:21 pm by Kathryn
Categories: Journal, Quotes, Social Science, Spirit

I know the eyes are the windows to the soul or whatever, but the real crux of the moment was not just that I was really seeing someone, but that I was seeing someone really seeing me. Once I embraced the terror of this realization and gave it time to subside, I arrived somewhere unexpected.

I felt brave, and in a state of wonder. Part of that wonder was at my own vulnerability and part was the weird kind of wonder you get from saying a word over and over until it loses its meaning and becomes what it actually is: an assemblage of sounds.

So it was with the eye, which is not a window to anything but a rather clump of very useful cells. The sentiment associated with the eye fell away and I was struck by its astounding biological reality: the spherical nature of the eyeball, the visible musculature of the iris and the smooth wet glass of the cornea. It was strange and exquisite.

Mandy Len Catron

Easier Said Than Done

Posted Tuesday, January 6th, 2015 @ 10:32 am by Kathryn
Categories: Journal, Quotes, Spirit

“We say to the confused, Know thyself, as if knowing yourself was not the fifth and most difficult of human arithmetical operations, we say to the apathetic, Where there’s a will, there’s a way, as if the brute realities of the world did not amuse themselves each day by turning that phrase on its head, we say to the indecisive, Begin at the beginning, as if the beginning were the clearly visible point of a loosely wound thread and all we had to do was to keep pulling until we reached the other end, and as if, between the former and the latter, we had held in our hands a smooth, continuous thread with no knots to untie, no snarls to untangle, a complete impossibility in the life of a skein, or indeed, if we may be permitted one more stock phrase, in the skein of life.”

– José Saramago


Posted Monday, January 5th, 2015 @ 11:53 am by Kathryn
Categories: Arts, Buddhism, Journal, Spirit

This song by Hozier is gorgeous, poetic, and haunting to me. Take a listen (click here if the embed doesn’t work).

SoulCollage® December

Posted Monday, December 15th, 2014 @ 11:50 pm by Kathryn
Categories: Arts, Journal, Spirit

SoulCollage® Committee Suit: Feline Familiars

I am one who is soft and curvy, and I am one who is fierce. I am one who enjoys pleasure and will communicate. I am one who is a mystery. I am one who is subtle. And I am one who is primal.

What is your gift or message for me?
Remember to indulge in things that give you joy, comfort, and pleasure.

What do you want me to do?
Watch things. Take your head and eyes out of your computer and watch kitty television, which is watching the world. Be curious about everything around you.

Why did you show up today?
It’s been almost a year since Stella died. She was a good friend for 17 years and she is still with you.

If you have a shadow, what would it be? Or, what light do you offer?
The shadow is a tendency to laziness and to sneakiness. The light is the magnificent pleasure of being.

Feline Familiars_Committee