Marsbarn Designs...

When math becomes a personality test

So, I was looking at G's math homework, and there's 
this word problem that reads:

"Susan can paint her living room in 2 hours.  Jaime can
paint the same room in 3 hours.  How long will it 
take both of them to paint the room together?"

First of all, who can paint a living room in 2 or 3 hours?
We must suspend disbelief. Okay.  I get it.

Now, the first impulse is to average their times,
but that means that it would take Susan 30 minutes
longer to paint the room with help, than doing it 
alone, and while that is possible (and not unheard of)
we are going to hope that Jaime is not a toddler, 
and is actually really helpful.

So, let's imagine we cut the room in half, and 
let each of them paint half of the room.
After one hour, Susan is done with her half,
but Jaime still has a third of his half to do.

This is the personality test portion of this word
problem.  Is Susan the kind of person who will
sit on her tush and drink whipped coffee drinks
while Jaime finishes his part of the room?
Or will she help him?

If she goes the blended drink route, it will take
1 1/2 hours to paint the room. If she decides to
help him.. well.. that's an interesting idea.
(This is the part of my thinking about the word 
problem where Big E began to groan and shake his 
head.)

So, Jaime has 1/3 of his half of the room left
to paint (this would be 1/6 of the total room).
If we cut this portion in half, (1/12 of the total
room) it would take Susan 10 minutes to paint
her half, but Jaime would still have 1/3 of the
1/12 left unpainted (or 1/36th of the entire room).
You can see that in this method of calculation, 
the room would theoretically  never be painted.
Some infinitesimal space would be left undone.
Happily, in reality, Susan would just push Jaime
aside at a certain point and say, "Dude, we're done."
With all of the reasonable times added up, it would
take them about 1 hour and 12 minutes.

But, there is another way of looking at the problem.
If we combine their rates, instead of dividing the
room, we can cut out a lot of circular work.
If we consider that Susan paints 1/2 of a living room
per hour, and Jaime paints 1/3 of a living room per 
hour, we can combine their rates:  1/3 + 1/2=5/6. 
So, together they paint 5/6 of a room in an hour. 
This means that in 6/5 of an hour, they paint a room. 
Or, in normal time speak, 1 hour and 12 minutes.

Of course, this is the type of word problem that 
gave me fits in school. Which answer is right?
Is working with Jaime worse than working alone?
Is Susan the kind of person that will just do her work
and then leave Jaime to finish up on his own?
Or, will they work, efficiently and kindly together?
Ah, the complexity of life.

It's work.

Marriage is hard work, is strong work,
just as parenting is.  Anyone who tries to tell 
you otherwise isn't doing it right.

Marriage in a police family is a special flavor of
difficult. There is the darkness, the violence,
the danger, the bullshit, and, at times, negotiating
that mine field as a spouse is like trying to tread water
with weights tied to  your feet. It's the Navy Seal
version of daily life.  

This has not been a particularly good week, in the
realm of police life.  The week started with a shift
that ran 5 hours late after a suspect fought his way
free with a knife.  No one was stabbed, but this isn't
a pleasant way to spend an evening at work.  These
are the types of events that add up, and overflow,
in both the officer and the spouse.  

The struggle, after you get home, is how to bring 
joy and wonder back into life.  How do you foster 
the idea that life is precious and can be good?
This is what keeps us together. This making light
in the dark.

The children in that link are refugees from terrible,
terrible violence. They've all known hunger, death,
war, and violence.  Bringing them a bit of wonder
is true magic.  This is how we keep moving forward.

trying to gather back the things we let go of.

I finally made time for an art gathering.  I haven't
managed to organize a Lady's Art session all school
year.

It has been hard to find time this year for art and for
friends. There have been no art classes, no children's
events (beyond the girls' birthdays), no workshops.
While Sweet G's  doctor's appointments continue to 
range outward, and (in theory) there should be more 
time for, well, life,  I find myself tired.  There 
are things I want to do. A normalcy I long for, but
this gas tank is a bit empty.  (Okay, a lot empty.)
It was difficult to let go of these things that mean 
so much to who I am, but it has been even harder
to put them back into my life. 

Things just take longer than they should.  The house is
more cluttered than I like. The messes stay longer,
and the will to push myself to get. stuff. done. is lax.

But this day with sweet people making Ukrainian eggs
was lovely.  We ate potluck loveliness and played.
It wasn't a class (although I was the only one who'd
done it before) because I didn't want the pressure of 
money and performance and production.  I just wanted
good people to play with.

We've surpassed the 9 month mark, since G's diagnosis.
Her professional care is winding down, and soon we'll
be stretching our legs in remission land.  She is doing well.
We are doing well.  But the wear is apparent on all of
us.  I need to make time for more things for me,
the dividends are worth it, but moxie to get it done
is scarce.  Perhaps there will be more umph in my
getalong come June.

It is a truth often acknowledged that a math equation may give itself airs.

My relationship with Math has been a Mr Darcy/Elizabeth
Bennett sort of affair. At first meeting, Math and I did
not get on.  I considered the subject difficult and self
serving.  It was the purview of the already in the know. 
It was language you were born to, and if it didn’t
come quickly or easily to you, it must be due to a
deficit of character.  

 
My dyslexia made sure that my first impression of Math
was particularly poor.  Beyond writing “2”, “4”, and “5”
backward, I’d read mathematical equations in reverse
as well.  Subtraction and division with its directional
dependency were my particular nemesis.  Time and
coping techniques helped to reframe the dyslexia into
a hindrance, but not a barrier, but Mathematics itself
remained an aloof foe. In a Mr Darcy fancy, it did not
ask me to dance, and scorned my attempts at
deciphering its character.  Math's good graces lost,
are lost forever, or so it seems. 

 

But then, as grade school gave way to high school,
we began to see each other in different light.  We realized
that we would always have friends in common, and that,
perhaps, we could casually co-habitate the same social
circles.  Science required Math.  A trip to the store
required Math.  Geometry was my Pemberly, my first
inkling that Math could be a good companion.  Geometry
was elegant, and so well turned out with logic I could grasp,
I could feel myself being drawn to an entity I had sworn to
scorn.

 
College was my chance to begin again, with a fresh
perspective. I began at the beginning, with pre-algebra,
and slowly made way through the introduction of
Mathematical social graces.  This time, I could see Math,
not as aloof, but as complex and multidimensional.  
I slowly discovered that aspects of Math could be seen
from different perspectives.  If something appeared,
at first meeting, to be obtuse,  I could find a different,
more amiable direction.  It was my viewpoint that made
the entity seem forbidding; I had to find a perspective
that worked for me.

Which is how I find myself currently smitten with Math. 
We are in a confirmed relationship of mutual
understanding.  As my older daughter makes her way
through the introductions of high school Algebra, I am
continually impressed by the elegance of my old foe. 
The new methods of teaching and working through
algebra help tremendously, but I think the willingness
to stop and look from a new direction plays an even
greater role. I am no longer intimidated by the subject. 
I am not afraid to be wrong, and I am confident that it
will eventually make itself clear to me.

This is how I found myself as a math tutor.  I understand
where my students are coming from. I have been there.
I know what it is to be outside of that magic society of
people who “Get It”.  I remember the frustration and
the fear of not understanding. I know how deceitful
and proud those numbers can seem, and that often,
you just need a new way to think about them.