This, in itself, is remarkable.  My math anxiety is becoming a thing of the past, finally.  After 46 years.  And I find that thinking about math more flexibly is getting to be fun. 

I am also subscribing to Scientific American now, which I love, though their are huge swaths of print within it that I simply do not understand, at least not in this particular universe. 

And I keep meaning to work on more magnet stuff, and electronics, and oh, the time is so short and what I want to do is so much.  Oy.

Actually, geek-wise, a lot has been going on while I’ve been away. I ordered MAKE magazine, had my debit card hacked, finally grasped the electronic activity of magnets, and went back to American Science and Surplus to get the motor to finish making my bees fly!  PLUS, I”m gonna be in a MOVIE! How fun is that?  While I was at AS&S, there were people making a documentary about the place, and when I waltzed in asking for a discoball motor, well, they just found me irresistable!  It will be on the Discover channel, or maybe it’s the Discovery Channel?  I don’t know.  I’ll never see it. I don’t have cable.

As for magnets.  I found out that they have a north pole and a south pole, just like the earth, which makes me wonder if maybe the earth might not be just one big magnet.  Really, I found out, if you hang a magnet by a string, it will flip itself around until it’s north pole faces north.  mark that side of the magnet, and try it again,and sure enough, the marked side will flip to the north.  Why is this the case?  I have no idea, but it’s kind of cool, nonetheless. I’m sure it has something to do with electrons.

Also, I found out that if you try to get the north side of a magnet to butt up against the north side of another magnet, they will avoid each other like a fourth grade boy and a fourth grade girl. North and south sides, however, make a happy couple.  The experiment book that came with this kit is pretty weak on explanations.

I need to make friends with a physicist!  Where is s/he?  The student is ready!  The teacher should appear!

I started last night, working with first grade worksheets. Easy enough, right? Now I’m learning about “places” and doing problems that are easy, but look suspiciously like algebra, like 8 + 4 = 12 and 12 – 4 = 8, all in the same row. Now, my first question to myself is this:  WHY does this look like algebra to me?  It’s that “backwards and forwards” thing.  There’s something flexible about this, which you’d think I would like, but it rubs me the wrong way. 

One thing I noticed that I do, even in a first grade math workbook:  I assume things.  I make simple mistakes on account of these assumptions.  Otherwise known as ”stupid mistakes.”  This is a lifelong habit of not paying enough attention.  I’m not a good proofreader, either.  So this is an issue, not just in math, but in life. 

In most instances, it’s not a big deal.  In fact, when reading long novels (something I do a lot of), it’s probably an advantage.  My education professor friend tells me that most adults skip 40% of the letters on the page when they read.  But this characteristic is not an asset in the math world.  Skipping 40% of your algebra problem, or your tax return, or your bank statement isn’t such a good idea. 

So, I need to retrain my brain to look at everything on a page.  I actually have a physical sensation when I do this.  I have not quite identified it. Is it some of that old Math Anxiety popping up?  Is it my battle against dissociation? Quite possibly.  Not paying attention has been a survival strategy.  And now, I need to pay attention.  I have learned to lean on my ability to quickly and intuitively size things up.  When I have to slow down and not make my usual assumptions, I find it annoying and, in a strange way, sort of scary. Interesting.

Even thought I have a tendency to ignore the details, I did manage to ace just about every class I took in college.  The only class I dropped, as it happens, was Chemistry, which is also the only class I took that had to do, even vaguely, with math.  The only “B” I got was Logic, and then only because I couldn’t figure out deductive logic and those damn Venn Diagrams. 

My professor, David Schlaeffer, said at the time, “You think in gestalts.” He was, and is, exactly right. His suggestion was that I take a book that’s hard to understand and read it, and outline everything in it, thinking about how the chapter title links to the sections of the chapter, to the sentences.  Separating one idea from the next–breaking it apart as it were. This is the sort of process they now call “decomposing” in mathematics instruction. It sounds very grisly to me, but that’s what they call it. 

How did I get straight A’s in all of my other classes? Take gross anatomy, for instance, where a great deal of memorization was required. First of all,  there was a body involved, a “manipulative” as it’s known in math class.  Second, I totally played with gross anatomy.  I bought different colored Play-Dohs and created bones and muscular attachment points in my spare time.  I created a gorgeous notebook of drawings and diagrams. And I completely got it.  completely.  Because I immersed myself in it, and used talents that I have in making myself memorize and understand. If the subject had nothing to do with math, I was relaxed and able to enjoy the learning process through many means.

In subjects where I had to do math, but it was applied, I also had an easy time of it.  This gets me back to my friend Gail’s comment about how one can only become a reader by losing yourself in the meaning.  Well, when I was a kid, the New Math people made extra sure that math didn’t mean anything to the kids they foisted it upon.  When you apply math to something as a tool, you are using it to achieve a goal. When you become a reader, the focus isn’t on the alphabet itself, but on what you can do with it. In the same way, when you have meaningful math in aeronautics, the focus isn’t on the math itself, but on whether you can figure out the wind vector so you know how to approach your landing strip.  You lose yourself in the meaning.  I can do that with reading, and I can do it with aeronautics.  Can I do that with Math?

On another note, Jo Boaler is writing a book for adults like me who struggle with math.  She says she’s doing it because she hears from people like me all the time. Yay!

I’m also going to write to the Nova Science Now people, and see if they have any suggestions.  This reminds me of when I was in 4th grade and Kristy Biddle and I sent fan letters to various stars to see if we could get autographed pictures. We did. I lost mine in one of our basement floods, but I savor the memory.

Okay, so this Joanna person isn’t exactly Carol Burnett or Doris Day, but, still.

My Math Memories begin when I was a six year old, trying to get the difference between the greater than sign and the less than sign, which I understood, even back then were the same sign, just flipped around.  What I also understood, but that none of the adults around me comprehended was that the tiny angle that they called “greater than” was, in fact, miniscule, compared to the far larger angle that they called “less than.”  I did not see an alligator’s mouth when I looked at that wedge. I saw an angle.  A very small angle–as an adult who now has words for such things, I would call it, perhaps, a 15 degree angle, and the other angle was huge, about 345 degrees,  by comparison.  I kept telling my teacher, my parents and then the principal, “No! THIS side is bigger than that side!”  and they just thought I was being cheeky.

I remember being kept in from recess and being sent to the principal’s office to work on my greater than and less than concepts. Worksheet after worksheet after worksheet, I remember struggling, as I still do, to remind myself that everybody else in the world has this exactly backwards, but that their way is the “right” way.

Math Memory #2: Second grade, 1967, trying to learn something called “New Math,” in which we worked in something called “Base 3″ one day and “Base 8″ the next and so forth and so on, and I NEVER had a CLUE as to what Miss Leach was talking about.  Frankly, this math was so new that I don’t think SHE had a clue as to what she was talking about either.

Math Memory #3: Second grade again.  Miss Leach made us play this sadistic game called “Around the World,” the point of which was to humiliate and shame the kids in the slow math group by making us publicly guess the answers to simple multiplication questions while competing on a team with kids who actually knew their times tables.  7 x 7, anyone?  How about 6 x 8?  Of course, my guesses were always wrong, leading the others on the team to grimmace and hate me ( and the other kids in the slow math group).

Math Memory #4 When I was in 7th grade: My father taking my brother through Dartmouth College, telling him about what a terrific time my brother was going to have when he went to Dartmouth.  When I suggested that I might want to go there, too, my father said, and I quote, “You can’t come here, Honey.  You can’t do the math.”  I remember this as vividly as if he had laid a whip to my back.  I remember we were in the Hopkins Art Center, I was looking at a rusty brown metal sculpture in a corner. I remember the hallway.  I remember the light. My dad abused me emotionally, and math was one of his bludgeons.

Math Memory #5 Begging my eighth grade math teacher to give me a D- so I could go to high school. I was basically asking her to ignore the fact that I had spent the entire year with a paperback novel hidden behind my textbook because I was at that point so lost in math that I couldn’t even begin to sort out what she was talking about.

Math Memory #6 My father standing over me as I sat at the dining room table, algebra book open, with tears running down my cheeks.  I remember his breath on my head as he said, “God, this is so EASY!  Anybody can do this!  Even an IDIOT can do this!”  I flunked Algebra and had to take summer school, where I got a D-.

Math Memory #7 Taking Oceanography in high school and being able to figure out how to calculate ocean depths easily.  Taking Aeronautics in high school and being able to calculate wind vectors easily.  Wondering, “why can’t I figure this stuff out in Math class?”

After reading Dr. Boaler’s book, my struggles with math make a lot more sense.  I was introduced to math and had my nose rubbed in it in the exact wrong way. I could feel my ingrained math attitudes coming out early in the book.  She gives a classic math problem, the “Fabonacci sequence.”  It goes like this:

“A certain man put a pair of rabbits in a place surrounded by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?”

My math hater’s response is this:  first of all, rabbits give birth to more than two bunnies every time they mate, so that’s crazy to think you’re just going to get two bunnies every time.  And then, it is SO unlikely that they’re always going to breed one male and one female every time they have bunnies.  I mean, maybe the odds are, over hundreds and hundreds of rabbits that you’ll get almost a 50/50 split, but it’s unlikely that this will work out so perfectly with a smaller number.  Finally, if you wanna keep these rabbits behind the wall, you’ll have to find a way to keep them from digging themselves out from under it.  So there, Mr. Fibonacci.  Take your rabbits and stick ‘em where the sun don’t shine.

As I read further, I discovered that my response to this word problem is typical.  This does not take away from the fact that Fibonacci had something or other to do with the discovery of the “Golden Ratio,” which, as far as I knew, was an artistic concept about design proportions that are pleasing to the eye. So, I was surprised to learn that this had something to do with math.  I think artists probably had this figured out before Fibonacci.  He just figured out the math part of it.  Which is, I guess, interesting to mathematicians if not to anybody else.  See how snarky I get when it comes to word problems?

Boaler continues on.  Back in the 17th century, some guy named Fermat claimed that the equation A n + B n + C n has no whole number solutions for n when n is greater than 2. and I thought, “Well, bully for him. So what?  Who cares?”  but then I started wondering about mathematics.  The next page, Boaler talks about triangles and the sum of squares built on a hypoteneuse, and in my head I have this confusing picture of a bunch of squares in a triangle and realized she was talking about squared numbers, but I wonder WHY we called square numbers square numbers, when they don’t, at first blush at least, seem to have anything to do with squares.

This is the kind of question I would have gotten a dirty look from the math teacher for had I asked it in 7th grade math class. 

Anyway, long story short, somebody figured out the proof for this in 1994.  An exciting moment in the history of mathematics, I’m sure, but I don’t think it has actually rocked anybody else’s world.  Certainly not mine. My math cynic pops out again.

More questions begin to pop, however, as I read on.  She describes someone as an “algebraic topologist.”  What the hell is an algebraic topologist?  For that matter, what the hell is algebra?  To me, algebra is a simply a way to make mathematics more incomprehensible by deciding to throw in the alphabet.  She does define algebra as a way of figuring out changes in patterns.  I had no idea.  Really.  As the book went on, I found myself saying over and over again, “I had no idea.”

Just as I was thinking about giving up on the book,  I got to page 37. She had me at page 37. As if there are not enough “wars” going on in the world, “culture wars, Afghan war, Iraq war, blah blah blah,” some boneheads have decided to start a “Math War” in which senseless rote memorization is being pitted against actually understanding what the hell it is you’re doing when you do math.  At this point I realized that this Jo person was on my side after all.  Because THINKING about what I was doing has been my downfall in math ever since I was a six year old trying to sort out the two different angles of the so-called ”greater than” sign.  Criminy! That’s a very sophisticated concept for a six year old!  I didn’t have a math learning disability!  My educators had a math TEACHING disability!

She goes on to talk about the need for TALKING in math class.  This is not easy for me to swallow, since TALKING in math–e.g. saying, OUT LOUD  in second grade “seven times seven equals,  . . . um . . . . 37?”–made me the object of scorn and derision in my entire second grade class.  You expect people to TALK about math? Horrifying.  She says math is “more than a collection of rules and methods set out in books” (It is?????)  When students talk about math, “they realize that math is a subject that they can have their own ideas about, a subject that can invoke different perspectives and methods, and a subject that is connected trhough organizing concepts and themes.” (p49). 

This is news to me. Welcome news.

A lot of the actual math in the book I don’t understand because I operate at about a third grade level in the math department.  But she did help me understand why I DON’T understand.  Like me, she rails against “word problems” as being just plain goofy most of the time.

She also says there are connections between algebra and, say, geometry. Again, news to me. I thought if you were good at one, you were bad at the other.  I can do geometry more easily than I can algebra, which I never understood.  She slams the use of tracking, because it makes you feel stupid (yes!).  She says girls learn math differently than boys, and that sexism still exists in this area of education (yes).  She says students are given problems to do without a sense of mathematical goals. I’m not sure I was paying attention enough to absorb any mathematical goals even if they were presented, but math always did seem like tiny-minded computations thate were completely irrelevant to my life–that is, until I started living it and had to contend with my enormous math phobia and inability to perform even the simplest calculations, making me terrified of my checkbook, my taxes, my debts . . .

 One of my favorite lines: “White and Frederiksen concluded that the students were previously unsuccessful not because they lacked ability but because they had not really known what they were meant to be focusing upon.”  That’s me, to a “T”.

 She also introduces the concept of “Math compression.”  You are supposed to be able to learn this stuff and somehow “compress it” so you can call it to mind easily later as other information is added.  People like me look at math learning as a ladder, where you have all this malarkey to memorize, and there’s just more and more and more of it, piled higher and deeper.  That’s exactly how I think of math.  Just a huge pile of crap that you have to know by rote. And you’re going to forget it once you’re out of school anyway, so what’s the point?

That’s when a recent conversation I had with a friend who is an education professor came to mind.  She said that, when teaching reading, you have to help struggling readers get out of the tangled, hampering web of phonics and mechanics of reading and help them relax and “lose themselves” in the meaning of whatever it is they’re reading.  Perhaps in this way, teaching math and teaching reading should not be so different.

 It also never occurred to me that you can represent things in different ways in math.  I get this in an Excel Spreadsheet sort of way.  As in, “take these percentages and turn them into a pie chart.”  but I never thought of the pie chart as a math thing.  I always thought of it as a kind of powerpoint presentation, visual aid thing.  And graphing stuff, I remember vaguely having to do some sort of incomprehensible graphing in my failed attempts at algebra.  I had no idea that that had anything to do with representing a problem in a different mathematical way.

 Then she talks about “decomposing” and “recomposing” numbers.  New concept to me.  After coming up with the right answer to a multiplication problem on page 156 by imagining a chalkboard in my head with the numbers on it and doing the carrying and such, I turned the page (p. 157) to find a chart of different ways to solve the problem.  I had a post traumatic math moment and burst into tears.  It made no sense to me.  How could you make this math problem so complicated and call it “easier?”  Then I calmed down, blew my nose, and took a look.  It took me awhile, but I finally figured out how each solution was arrived at.  And yes, at least one of the ways to do the problem on that chart was easier than the way I had done it. My reaction was typical of people who struggle with math, I learned a few pages later, who resist more than one way to do these problems.  My take on that is, “I can barely figure out the first way you told me to do it, and now you expect me to figure out four OTHER ways to do it?”  But there I go, getting tangled up in the mechanics, rather than relaxing and losing myself in the meaning–just as my professor friend says struggling readers do.

 She then turns to a guy named George Polya.  He says that when experts solve math problems, they first attempt to “understand the problem.”  Then they make a plan. Then they work the plan, and then they look over their work.  Now, doesn’t that make sense?  He does not include any outline of how math phobics attempt to solve math problems.  When we attempt to solve math problems, we first “panic.”  And then, replaying humiliating 2nd grade moments of “Around the World” in our heads, we throw desperate approximations of answers at the problem as if we were frenetic, blindfolded darts players. And then we go hire ourselves an accountant. And if they, perchance, get it wrong, we throw any dunning letters away, unopened.

 I think I like Polya’s method better. I am going to learn Polya’s method, dammit!

 Today, simple fractions! Tomorrow, the world! (or maybe even calculus!)

As I write that, I think I must be kidding myself. ME? Calculus?  I don’t even know what calculus IS, though I can guess from the word that it has something to do with calculating something in Latin. So, occasionally, between science experiments, I will attempt to hack open the juggernaut of mathematics, algebra and beyond.

This is a learning disability.  Of course, education professors haven’t really researched this much, since most education professors apparently don’t like math and would prefer to only think of reading as something worthy of a learning disability.  PROBABLY BECAUSE THEY DON’T UNDERSTAND MATH EITHER!  I bet most of ‘em just squeaked through their stats class on the way to pick up their Ed.D’s.

So, this is still relatively unchartered territory, although some LD specialists have been suggesting, at least since the 1990′s, the possibility that a Math Learning Disability can be a seriously crippling problem that follows one throughout life. Like, my life.  Can anybody spell “I can’t balance my checkbook” or “interest compounded daily” or “credit card debt”?

First, let me apologize right now to the North Pacific Gyre for the all the plastic in this kit.  In an effort to appeal to 8 year olds, the kit is loaded with rods and wheels and pins that are full of holes, like Anti-Legos.  And the budding scientist–meaning the eight year old, or myself–must construct a variety of platforms, vehicles, etc.,  out of these Anti-Legos

in order to perform her experiments.  Hence, my potato impaling device: 

The deadly spike!

Next, you need a couple of small, roundish, raw potatoes, which I happened to have sprouting away in my kitchen.  You hold the potato up at the top rod and drop it. Tadaa!  Impaled potato.  Do it with a heavier potato and you’ll see that it gets impaled really deeply. 

The point of this underwhelming physics feat is that the more mass something has, the more it bows to gravity’s sway.  And then I read the fine print in the science manual, and really dumb basic questions started popping up for me.

The manual says there will always be a force of attraction between two  bodies.  WHY?  And why does a black hole, which is not a body at all, have more of a pull than anything that has mass?  Or does a black hole have mass?  What is a black hole, anyway?

And if there will always be a force of attraction between two bodies, that means I am being pulled toward this laptop and vice versa, right?  How do we KNOW that I am being pulled toward this laptop and vice versa? If i were on another planet with much less gravitational pull, would it be more obvious? Would my laptop follow me around?

And, coming back to this planet, why is the earth squashed at the top and the bottom? Does that have something to do with gravitational pull coming from the center of the earth? And that leads me to questions about the north and south poles. Magnetic poles, right? What about magnets and all this gravity stuff?  I never really thought about it before, but is seems to me that magnets have something to do with gravity–all that attracting and spurning each other.

And what is it about iron that makes it magnetic, anyway?  In fact, what makes a magnet a magnet? And what’s the difference between a gravitational pull and magnetic pull?  Or is there a difference?

And how much weight do I lose when I fly on an airplane? I’d love to drop a few pounds.

I did find that, if I touched one of the wires to my television set, I did get something that sounded like very faint voices on my crappy Slinky radio. 

I also found out that in WWI or II, soldiers in the field made radios like this. And if they can do it, dammit, so can I.  

But first, I need to get an old telephone and also I need someone to give me the plastic bottle from their contact lens solution, which, according to the scitoys guy, is a great base for a radio like this.    In fact, if someone would give me two plastic bottles, I could turn the other into a little steam boat. It turns out that the guy who keeps the scitoys website is the same guy that wrote the book, Gonzo Gizmos, which I purchased at American Science and Surplus when I was there last week. 

In the meantime, I have moved on to basic physics, with the help of yet another kit–the Physics Workshop by Thames and Kosmos, which I will hold forth about in my next post.

http://sci-toys.com/scitoys/scitoys/radio/radio.html