Marsbarn Designs...

What is success?

It's the beginning of report card season.

Last night, I got a phone call from the father
of a student I tutor in math.
Miss M, the student I've worked with the 
longest, just received her report card.

My goal has never been for grades.
I want my students to understand the math 
that presents itself to them. I meet too many 
adults who fear math, who hate it, and I want
to minimize that.  Numbers aren't the enemy,
any more than words are, or science is. 
Grades are nice markers, but my first foes 
are fear and loathing. My second enemy is
misunderstanding.  Grades?  With luck,
they are a nice after thought or a reward
at the end of a long term.

Miss M struggles with math.
She and I have developed a mantra when
a new section is introduced in math class:
 
"Give yourself permission to not understand.
Stay calm.  Be kind to yourself.
You won't get it the first time.
You many not get it the second time,
or the third, but you will understand it.
You have to give yourself permission not 
to understand. Stay calm.  Be kind to yourself."

When we first started to work together in 
elementary school, our main goal was to keep 
her math anxiety in check, so she wouldn't pass
out or end up at home with a migraine. 
Our secondary, pie-in-the-sky goal was for her to
pass the standardized 5th grade test. Despite a 
doctor's offer to give her a waiver, Miss M 
soldiered on.  We set about finding ways of looking
at the problems that worked for her.  We began
to map her personal strengths and weaknesses, 
and how she could build on the strong bits. 

This is her first year in high school,
and we've been meeting more frequently as she
navigates a rigorous, private high school math program.
Geometry is a course that challenges most
of her vulnerabilities in math.  She has a profound
deficit in pattern recognition, something that is
essential in geometry.  What I've seen this semester,
as we work more intensely together, is how far
she's come since we first started working together in 
elementary school.  Not only is she more capable,
she is more confident.  The fear of not knowing,
or of being wrong, doesn't have the strangle
hold it once did. These years of intense work 
are paying off in more ways that just the ability
to solve a problem in a text.  She doesn't fear
the unknown like she used to.  She is kinder to 
herself.

Miss M is away with her Mom, but her father
had to call me, because her report card had
arrived and he just couldn't stand it.
Miss M has an "A" in Geometry. 

 

Making the numbers fun

I gained another math student this January. 
He's my youngest student yet (a third grader),
and has a head for numbers (which many of my
students don't begin with).  With this student,
my task here is to keep math fun. (Yes, fun.)
His Mom was concerned that he's not engaging,
and that he's starting to complain that math 
is slow and boring, so he's cutting corners,
which means he's starting to miss things.

So, at our first meeting, after he finishes 
explaining his homework to me,
I pull out a clean piece of paper.

"If I draw two dots, how many lines can you
draw connecting them?" I ask.

"Two." He answers instantly.

"If I draw one dot, how many lines can I draw?"

"Um.. n o n e."

"Okay, lets make a chart to keep track, alright?"
He nods, game to see where all of this weirdness is 
going to end up. I draw a T chart with "Dots" and
"Lines" as the two headers, and write up "1" dot,
"0" lines; "2" dots, 1 line.

"How many lines for 3 dots?"

 "Two", he says as he draws a dot in line with our 
first pair of dots.

I redraw three dots in a triangle shape, and he quickly
draws in 3 lines and changes his answer.

"What about 4?"

"4!", he shouts out, and draws lines connecting the 
corners.

"What about diagonals? Would those break some sort 
of rule?"

He pauses, thinks, and draws an "X" connecting the 
corners. "6".

We continue to onto 5 dots, in which he spots a pentagon
with a star inside. Then we move onto 6, and then 7.
We talk about ways to work methodically so you don't miss
lines. At this point we stop and look at our chart.

"Can you tell me how many lines we'll have for 8?"

He looks at the chart.

"Do you see a pattern?  Take your time."

He looks, he thinks, "OH! The first time grows by
one, the second, by 2, the third by 3. So, if we 
add 7 to our 7th total, we'll get number 8!"

"Shall we test that out?  Shall we see if we have 
28 lines for 8 dots?"

"Yes!" he said, and started drawing dots.
And, yes, his theory worked. He then accurately 
predicted the 9th part of the pattern and tested 
that. 

When you stop to think about it, the pattern makes
a lot of sense. Every time you add a new dot, you 
connect that dot to each of the previous dots, making
a line for each preexisting dot.  So the 10th dot, would
add 9 more lines to the previous total of lines.

I think it was a good lesson. He had fun, I had fun. 
We both thought about numbers and patterns.  We 
practiced critical thinking and analyzing. I have a 
paper folding project in mind for our next meeting! 

As an aside, I did this same activity with another student,
one who doesn't see numbers as readily.  He also had  
fun drawing the lines, finding the pattern, and then
(to his own shock) predicting the next elements in the
pattern.  Good number fun, all around!

A (slightly snarky) Physics Takeaway

When people ask, "What's your degree in?"
And I say, "Physics." 
They often pull back in shock, and then say, 
"Wow.  What do you do with that?"
Followed by, "Why aren't you still doing, you know, 'Physics Stuff'?"

And while I could do the philosophical (and slightly snarky)
"All things are Physics Things!", I instead think about 
what I actually do with my wee physics degree,
now that it's been nearly 20 years since I got it stamped.

I spent 5 years getting a degree in Physics, 
and what has stayed with me? Well.  Let's see.
Shall we have some bullet points?
I learned:
-How to roll with a 90% male class.
-How to deep breath through tests that are impossible to finish.
(This is a most useful skill, as Real Life has lots of tests
you can't finish or pass.)
-The power of a grading curve. (35% for a B! YES!)
-Faith in yourself really does count for a lot. 
-A RPN calculator is a great ally.
-Write it all down. All of it. It might make sense later.
-Balance. (My minor was in Women's Studies. My classes
were either 90% testosterone or 90% estrogen.)
- Always have a back up pencil, and don't be afraid to lend it to someone in need.
-Take breaks, and walk.
-No one actually knows the answer. (Really. It's all open for debate.)
- When you hit a brick wall, wing it and keep going.

That winging it thing?  What do I mean? I mean when 
you have no inkling of what to do next, look at your tools
and try something else.  I have vivid memories of staring
at pages of homework calculations and feeling lost, 
and then starting again by making a list of "What I Know."
For example: I know the force of gravity G(m1)(m2)/r^2,
I know Force=(Mass)(Acceleration), etc.
Then I'd think about how I could use all of those elements
in a new way. "How does it look with the collar turned up?"*
With a list in hand, I'd start banging away at it again.

That "What do I know" re-hashing?  I use it all the time in
math tutoring.  When I see my students feeling lost, 
I ask them to review what they know, what they
remember, and then ask them what new things they
could try using that.  It is nice to be reminded that you
have tools at hand.

To me, physics is all about figuring out how to use what
you know to learn more things. It's a constant reassessing
of what knowledge you possess, or think you possess, 
and then trying to fit it together into some else. 
It's the ability to have a lego set, make the nifty thing
on the box, and then to tear it apart and make something
else. All the while knowing that you'll never make all the
things, and the creation you are working on might not 
ever work.  You will probably have to tear it apart again,
and start over.  

And why don't I do physic-y physics? (IE why don't I have a 
career in the field?)  Well, the physics that I loved most,
we covered in the first two years of classes.  The smaller
our physical scale became, the more theoretical the
classes, the less I loved it.  There was too much "all in my
head" stuff, and not enough "LOOK" here it is!  Also,
a bachelor's degree in physics is just the first step on a long
and difficult journey toward greater degrees (think Frodo
and Sam carrying the ring to Mordor.  A BS is just getting
to Rivendell. I'm more of a Bilbo, let's settle here! type.)

 

*That quote is a insider reference to a family member who,
when faced with a new garment in the 1980's and 90's,
would ask, "But how does it look with the collar turned up?"  
In other words, if I just tweak it a little, is it better? Worse?
Could this simple alteration be the Thing?

New Year's Day with Math on the Brain

Despite my definite lack of recent blog posts, 
bloggy thoughts have been bouncing about in my brain.

I have been having those chewy thoughts that need
to be captured in words, so I can see them better, but
time and patience and life keep getting in the way.
Absolutely all of those tough morsels of persistent 
ideas revolve around math.  Yes, I have math on the 
brain.  I believe I mentioned in another post that I 
have 5 math students this school year, and perhaps I'll
have a 6th in the new calendar year.  

Some of my students just need a nudge to make sure
they're getting the details, or perhaps they need a 
reminder that math can be fun and exciting, not a 
drudgery or something to be feared.  I want my students
to be suprised when we're out of time, not counting
the minutes until I release them.  Recently, one of them
kept saying, "This isn't fun. This isn't fun." to the algebra
we were working through, but when I said it was time to 
go, she said, "What? I don't want to go! Really? We're done?"

A few of my students seriously struggle with math learning.
Those numbers with their ways and rules, are slippery
and their brains need concentrated help to grab on and
comprehend.  It's these students that fire my deeper 
curiousity.  I want to know more, understand more,
research and learn more whys and hows.