Category Archives: Quotes

For the Love of Math

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, Bean 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.”

Bean 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 Bean 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 Bean 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 Bean. 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 Bean learns.

When Bean 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.

How to Fall in Love

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

“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

Some Knowledge

“And so seated next to my father in the train compartment, I suddenly asked, “Father, what is sexsin?”

He turned to look at me, as he always did when answering a question, but to my surprise he said nothing. At last he stood up, lifted his traveling case off the floor and set it on the floor.

Will you carry it off the train, Corrie?” he said.

I stood up and tugged at it. It was crammed with the watches and spare parts he had purchased that morning.

It’s too heavy,” I said.

Yes,” he said, “and it would be a pretty poor father who would ask his little girl to carry such a load. It’s the same way, Corrie, with knowledge. Some knowledge is too heavy for children. When you are older and stronger, you can bear it. For now you must trust me to carry it for you.”

–Corrie ten Boom, The Hiding Place

The Reason I Love to Bake

There is another reason for the priority of pastry: pastry chefs are the only ones in the kitchen who are alchemists by necessity. Where the rotisseur or the man with the sauté pan does his best work when he does least, it is in the nature of pastry-making that you begin with ingredients that don’t at all resemble what you end up with. It is de rigeur for the fish chef to say that he wants his fish to shine through, but the cake maker does not want his cake to taste anything like the flour that constitutes it. Baking is always making new.

–Adam Gopnik

No Matter

“Listen to me, your body is not a temple. Temples can be destroyed and desecrated. Your body is a forest — thick canopies of maple trees and sweet scented wildflowers sprouting in the underwood. You will grow back, over and over, no matter how badly you are devastated.”

–Beau Taplin

How the Universe Thinks

“I will argue that modern science, traditionally considered guilty of reducing our existence to a pointless accident in an indifferent universe, is actually saying the opposite. While it does say that we are an accident in an indifferent universe, it also says that we are a rare accident and thus not pointless.

As we look at planet Earth and the factors that came into play for us to be here, we quickly realize that our planet is very special. Here is a short list: the long-term existence of a protective and oxygen-rich atmosphere; Earth’s axial tilt, stabilized by a single large moon; the ozone layer and the magnetic field that jointly protect surface creatures from lethal cosmic radiation; plate tectonics that regulate the levels of carbon dioxide and keep the global temperature stable; the fact that our sun is a smallish, fairly stable star not too prone to releasing huge plasma burps. Consequently, it’s rather naive to expect life – at the complexity level that exists here – to be ubiquitous across the universe.

Even if there is intelligent life elsewhere and, of course, we can’t rule that out, it will be so remote that for all practical purposes we are alone. Even if SETI finds evidence of other cosmic intelligences, we are not going to initiate a very intense collaboration. And if we are alone, and alone have the awareness of what it means to be alive and of the importance of remaining alive, we gain a new kind of cosmic centrality, very different – and much more meaningful – from the religiously-inspired one of pre-Copernican days, when Earth was the center of Creation: we matter because we are rare and we know it.

The joint realization that we live in a remarkable cosmic cocoon and that we are able to create languages and rocket ships in an otherwise apparently dumb universe ought to be transformative. Until we find other self-aware intelligences, we are how the universe thinks. We might as well start enjoying each other’s company.”

–Marcelo Gleiser, We Are Unique

Thanks to Whiskey River for sharing this.

The Dark Path to Enlightenment

“We seldom go freely into the belly of the beast. Unless we face a major disaster like the death of a friend or spouse or loss of a marriage or job, we usually will not go there. As a culture, we have to be taught the language of descent. That is the great language of religion. It teaches us to enter willingly, trustingly into the dark periods of life. These dark periods are good teachers. Religious energy is in the dark questions, seldom in the answers. Answers are the way out, but that is not what we are here for. But when we look at the questions, we look for the opening to transformation. Fixing something doesn’t usually transform us. We try to change events in order to avoid changing ourselves. We must learn to stay with the pain of life, without answers, without conclusions, and some days without meaning. That is the path, the perilous dark path of true prayer.”

—Richard Rohr, Everything Belongs: The Gift of Contemplative Prayer

The Definition of My Life

Oh, best of intentions! You know where they lead. I’d planned to focus more on the blog this year and it’s languished.

I’ve got many irons in the fire. And I’ll explore them here later. Meanwhile, of late this quote has been my email signature. It resonates.

“I may not have gone where I intended to go, but I think I have ended up where I needed to be.”

–Douglas Adams

Look Inside

One of my daughter’s favorite performers are Peter, Paul, & Mary, and one of her favorite songs by them is called Inside.

Tonight I was scanning Facebook and came across a link from A Mighty Girl. A Mighty Girl is an excellent resource of zillions of ideas, toys, book titles, articles and more to help girls to grow up confidently. They shared a link from the Huffington Post of a letter from a father to his daughter about society’s hyper-focus on physical appearance.

In the article, Words From a Father to a Daughter (In the Makeup Aisle), Flanagan wrote:

When you have a daughter, you start to realize she’s just as strong as everyone else in the house — a force to be reckoned with, a soul on fire with the same life and gifts and passions as any man. But sitting in this store aisle, you also begin to realize most people won’t see her that way. They’ll see her as a pretty face and a body to enjoy. And they’ll tell her she has to look a certain way to have any worth or influence.

But words do have power and maybe, just maybe, the words of a father can begin to compete with the words of the world. Maybe a father’s words can deliver his daughter through this gauntlet of institutionalized shame and into a deep, unshakeable sense of her own worthiness and beauty.

He concludes by asking, “Where are you the most beautiful? On the inside.” The article is worth reading, bookmarking, printing to share. A Mighty Girl also posted links to resources on their Facebook page; I’m sharing them here:

To help girls understand more about the impact of the media messages they encounter related to beauty and body image, check out “All Made Up: A Girl’s Guide to Seeing Through Celebrity Hype to Celebrate Real Beauty” for ages 10 to 14 and “Body Drama” for ages 15 and up.

For a diverse selection of body image-related books for Mighty Girls of all ages focused on fostering a positive self-image, visit our “Body Image” section.

For books for parents that address body image issues, including the helpful guide “101 Ways to Help Your Daughter Love Her Body,” visit our “Body Image / Self-Esteem” parenting section.

And, to learn about a few of our favorite books that celebrate the special father-daughter bond, visit our post “A Father’s Love: A Mighty Girl Celebrates Fathers”.

And to reinforce the message (and because it’s a fun song), I’m sharing Inside here.


The link to the video is here.

Presence and Silence

I’ve been thinking about something for a long time, and I keep noticing that most human speech – if not all human speech – is made with the outgoing breath. This is the strange thing about presence and absence. When we breathe in, our bodies are filled with nutrients and nourishment. Our blood is filled with oxygen, our skin gets flush; our bones get harder – they get compacted. Our muscles get toned and we feel very present when we’re breathing in. The problem is, that when we’re breathing in, we can’t speak. So presence and silence have something to do with each other.

Li-Young Lee

I also think that Presence is magnified in natural settings, particularly primeval forests such as the Redwoods and Sequoias.

DSC00030

The Japanese term Shinrin-yoku may literally mean “forest bathing,” but it doesn’t involve soaking in a tub among the trees. Rather it refers to spending time in the woods for its therapeutic (or bathing) effect. Most of us have felt tension slip away in the midst of trees and nature’s beauty. But science now confirms its healing influence on the body. When you spend a few hours on a woodland hike or camping by a lake you breathe in phytoncides, active substances released by plants to protect them against insects and from rotting, which appear to lower blood pressure and stress and boost your immune system.

Mother Nature Network

Before Putting the Nail In

It’s pretty much impossible to feel anger at someone for driving too slowly in front of you in traffic when you’ve just come from sanding your own coffin. Coveting material objects, holding on to old grudges, failing to pause and see the grace in strangers — all equally foolish. While the coffin is indeed a reminder of what awaits us all, its true message is to live every moment to its greatest potential.

–Jeffrey M. Piehler, Ashes to Ashes, But First, a Nice Pine Box

Enclosing Nothingness

I’ve always felt that inside each of us there is profound anonymity. Sometimes I think that when you go deep inside, you meet everyone else on a sort of common ground – or you meet nobody. But whatever you meet, it is not yours though you enclose it. We are the container, and this nothingness is what we enclose. This is where Heidegger is very interesting to me. He describes the division between the world as nothing, as what he calls the “open,” and any act of conceptualizing which restores the world in a particular way.

Many of his texts are longings to experience that anonymity, the condition where we don’t have an “I” yet. It is as if we were in a room from which, paradoxically, we were absent. Everything is seen from the perspective of that absence. I suppose, in some ways, this is a mystical vision that brings to me a sense of the universe as an anonymous presence. The force of that sometimes frightens me, sometimes delights me.

–Charles Simic

This quote just touches slightly what I am exploring these days. This nothingness, or space, isn’t empty — it just seems that way to us in this dimension. The anonymity isn’t obliteration, though to the ego it feels that way. It’s so much more expansive than we can imagine, and connected too. This is a piece of what I know, what it true for me.

[Thanks Whiskey River for mining so many marvelous gems]

Rain!

Look at what we woke up to!

rain

We’re praying for much much more of it.

And, from one of my favorite poets:

A Rainy Morning

A young woman in a wheelchair,
wearing a black nylon poncho spattered with rain
is pushing herself through the morning.
You have seen how pianists
sometimes bend forward to strike the keys,
then lift their hands, draw back to rest,
then lean again to strike just as the chord fades.
Such is the way this woman
strikes at the wheels, then lifts her long white fingers,
letting them float, then bends again to strike
just as the chair slows, as if into a silence.
So expertly she plays the chords
of this difficult music she has mastered,
her wet face beautiful in its concentration,
while the wind turns the pages of rain.

–Ted Kooser, Delights and Shadows

Because He Was Himself

When a cat begins to lose his fur, it is a very humiliating and terrible thing. He looked and felt so forlorn that he lost all appetite. And about this time it occurred to him that his housekeepers might give notice, that if he became a permanent invalid, they would no longer care to look after him. He knew how much they enjoyed stroking the top of his head and now there was nothing to stroke. And how often had he heard them exclaiming about his large green eyes, which grew marvelously dark at night and marvelously pale in the morning. Now they looked at him and said humiliating things like,

“Poor puss, he does look a sight, I must confess.”

And one day Brusque Voice said, “Nobody could love him who had not known him before. But we love him, don’t we? And we won’t abandon him.”

It was she who brought a disgusting bottle of greasy stuff with a hospital smell and rubbed it into his fur twice a day. Tom Jones was by now beyond caring and had gone into a depression so deep, that he allowed her to do this, from sheer inertia. His purring machine even creaked a good deal and it hurt him to purr because it reminded him of the days when his purrs were sheer poetry and he himself a swaggering, handsome Gentleman Cat with a white tip to his tail. Ah, he thought, taking a surreptitious look, after all I still do have the white tip to my tail. And I must not despair.

…Only a strange thing was happening little by little. He was coming to understand that even if he never got well at all, his housekeepers were now more than housekeepers, they were true friends and they would not abandon him. He was really and truly safe. They did not love him for his glossy tiger coat, nor for his white shirt front and white paws, nor for his great green eyes, no, not even for the white tip of his tail. They loved him because he was himself.

-May Sarton, The Fur Person

farewell snuggles

Stella, age 17, fading

Just Doing It

I don’t know what else to title this post. Back in the early days of blogging, people started blogs as social interaction. If the blog had a steady readership, the author would feel a need to explain any gap in posting.

Then, other writers started to mock the self-importance of those posts. Who cares why you aren’t posting? Either do it or don’t.

So I tried to avoid that habit. And while this post may sound a bit like an explanation of why I haven’t posted (and maybe get picked up by Sorry I Haven’t Posted, which, um, hasn’t posted in three years), I’m also simply trying to break the mental tomb I seemed to have sealed myself into. Well, that suggests action. It’s more like mental rigor mortis.

When I first began blogging in 2002, I updated often and at length. I was engaged this way for many years. I also posted photos of my artwork and crafts, and my poetry. When my daughter was born, I wrote about my experiences with her.

And then Facebook came on the scene. Most of my social group (online and off) migrated to using that, and I started to as well. And when Bean turned four, I decided it was time to back off on writing publicly about her in detail, and that gutted my motivation to write. I’d still post about crafts we did, and other activities, but eventually I moved it all to Facebook.

In the past year, when I sit down to write here, I fumble. I grope for something to say. I might have a wisp of inspiration, yet some part of me whispers that it’s nothing new, it’s just more noise in the world. Why bother?

And yet. Writing is how I sort myself out. How have I become so disinterested in what’s going on? One voice in me says, “It’s all ego driven.” My practice is to engage fully in the moment, with the world I inhabit and the tasks I complete. I have made a judgment that to be Buddhist requires forsaking the mind. I’ve projected that judgment onto my teacher (not that I’ve told her). In my head, Maezen says this, even though she’s never uttered those words.

Another voice in me calls out, reminding me of other reasons to write. In childhood I felt a deep yearning to know more about my parents, about their childhood experiences, about what they thought of life and current events. Now, as a parent, I understand the difficulty of dredging up memories with specifics to make a good story. Bean often asks me, “Tell me a story about your childhood,” and I simply don’t have access to the memories. Writing is a pathway into them.

I’ve also a strong desire to be known, seen, heard since childhood. I want my child to know about me, if she is interested when she is older. So there is some value in writing. I’ve approached my blog as a kind of commonplace book, where one might read and see what piqued my interest. But as I read Mr. Penumbra’s 24-Hour Bookstore, I am tantalized by the idea of a Codex Vitae. What is that, you ask? In the novel…

The Codex Vitae is something that special members of this fellowship “earn” the right to create, after rising up in the ranks. When written, it’s submitted to the fellowship, approved, and encrypted. 3 copies are made of the book, 1 goes to the central library, and 2 others go to branch libraries in other parts of the world. The key to the encryption is only given to 1 person, and it remains a secret until the writer’s death.

–Buster Benson, The Way of the Duck

He thought this was a great idea, and so do I. What if I created my own book of knowledge? A blog is a living book. And perhaps no one will read it, or only a few. My daughter might have no interest. After all, it’s a pretty large resource already, having existed for 12 years. In the end, I’ll die and this blog will go someday, but isn’t there some value in scribing my journey?

The truth is, I miss myself. For now, I will close with a poem that captures my hope:

Love After Love

The time will come
when, with elation
you will greet yourself arriving
at your own door, in your own mirror
and each will smile at the other’s welcome,

and say, sit here. Eat.
You will love again the stranger who was your self.
Give wine. Give bread. Give back your heart
to itself, to the stranger who has loved you

all your life, whom you ignored
for another, who knows you by heart.
Take down the love letters from the bookshelf,

the photographs, the desperate notes,
peel your own image from the mirror.
Sit. Feast on your life.

–Derek Walcott

I want to give a nod to two long-term bloggers who in the past week have given me encouragement to try again (even if they don’t know it): Whiskey River and Euan Semple.

And a link to an article from a blog titled Thought Catalog about how and why to keep a commonplace book.

journey

Journey / 2011

In Memory of Snow

Taken last year at Yosemite… This year we are not going to the snow. There are some resorts open that are making artificial snow, and a few high peaks may have snow left from last year. But there has been no snow this season. None anywhere.

Look up at the miracle of the falling snow,—the air a dizzy maze of whirling, eddying flakes, noiselessly transforming the world, the exquisite crystals dropping in ditch and gutter, and disguising in the same suit of spotless livery all objects upon which they fall.

-John Burroughs

after the snow
snow blossoms
stream at crane flat
getting ready to go down
vivid blue sky

For comparison: photos of 2013 and 2014

The first fall of snow is not only an event, it is a magical event. You go to bed in one kind of world and wake up in another quite different, and if this is not enchantment then where is it to be found?

-J.B. Priestley

Out of Time

“But love, sooner or later, forces us out of time. It does not accept that limit. Of all that we feel and do, all the virtues and all the sins, love alone crowds us at last over the edge of the world. For love is always more than a little strange here. It is not explainable or even justifiable. It is itself the justifier. We do not make it. If it did not happen to us, we could not imagine it. It includes the world and time as a pregnant woman includes her child whose wrongs she will suffer and forgive. It is in the world but is not altogether of it. It is of eternity. It takes us there when it most holds us here.”

-Wendell Berry

Via Whiskey River