Math

Yesterday Was Difficult. Today Will Be Better.

 

I'll start with the end:

I'm about to go purchase a filofax, which, if you're taking the SAT this year, I'm sure you have no idea what I'm even talking about.  And no, I'm not a technophobe; I've even been called an "early adopter."

But I can't survive another day like yesterday; I know I won't make it. Technology nearly (not quite) brought me to my knees.

It was an email after the 6 hours of still unresolved technology issues that finally did me in.

Some unsolicited advice from the same tutor who told me last time that students such as her "younger self" don't want even want to be in classes with people who can't answer these SAT math problems.  "They're so basic," she said.

Her follow up email to me last night made that one look like it was written by Miss Manners.

You need to choose whether you want to admit that you are ignorant about math and did not receive a proper education or whether you are simply stupid. You seem to be choosing willfully stupid route, which is too bad.  You do yourself a disservice in that you do not learn, and you also set a bad example for others.

(Does she talk to her students this way?)

I want to point out that I am not being "willfully stupid," nor am I "simply stupid."

However, I may not have received a proper education.  That part could be true. And then add to my improper education about 30 years since my last math class, and voila, you have me.

Which brings me back to my improper math education:

If you want to know how my math education may have gone so awry, read this article by Barry Garelick in Education News: The Myth About Traditional Math Education.

Given that I am above the 60th percentile with my math score, I'm clearly not alone with my math improperness.

He traces the issue back to the 40's, 50's and 60's, and discusses the changes in textbooks.

"The education establishment continues to advance faddish techniques such as a group of collaborative learning, inquiry-based and problem-based learning, while it pays lip service to traditional approaches, calling it a balanced approach."

The whole article is well worth the read if your'e interested in math and education.

Illustrations by Jennifer Orkin Lewis

 

 

 

 
42 Comments | posted November 3rd, 2011
 

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Math

Watch Your Back (That’s All I’m Sayin’)

Or "Savor the Flavor," as PWNtheSAT said to me yesterday, as I screamed with rage after being messed with, again (and again and again), by the SAT math section.

I inadvertently struck a nerve a week or two ago when I suggested that you need to know more than just solid math to do well on the math portion of the SAT.

One (anonymous) commenter even left me this message on Psychology Today:

"This idea that the test is full of booby traps is ridiculous. You simply have to READ the question, figure out what they are asking, and then answer accordingly. You need to show that you understand the basic math concepts. The questions aren't tricks. I had read a version of that assessment over and over again, and then took the test again as an adult and easily scored 800. BECAUSE I UNDERSTAND MATH AND CAN READ."

But I'm sticking with my position: Solid math basics are essential, but not sufficient. If you want to ace this test, you need to be prepared not to be messed with by a test that's trying to mess with you.

Take, for example, the following questions, all of which come from just one, lone, College Board practice SAT, and I believe illustrate the point that "solid" math knowledge alone is not enough (at least not while the clock is ticking and you've got about one minute per problem).

Exhibit 1:  

This appeared (to me) to be run of the mill parabola question, so I broke out the "Quadratic Equation" and jotted it down in the margins: y = ax² + bx + c.  Then, I did my very best to turn what they gave me, back into what I knew.

But I couldn't get past that minus sign in between the "a" and the "x²." No idea what that meant.

Well I'll tell you what it meant:

It meant that the "a" referred to in this problem (above) is not the same "a" that I learned about in "math"  -- It's just coincidentally also called "a"  -- just like the one that's usually located in the exact same position.  

But don't be confused. It's not THAT "a."

MEAN....mean mean mean. Makes me scream.

Exhibit 2:

Looked like a 30 60 90 to me.

Wrong!  "Not drawn to scale" = dead giveaway.

And don't let those (a + b)² send you down the "Pythagorean road" that you learned in math class, because it's not that either (go figure).

This would be the fanciest "Sadness Gap" question I ever did see.

(Who would have thunk. Not me, that is for sure.)

 

Exhibit 3:

So (so so so so) proud of myself, and brimming with enthusiasm at the prospect of trying out my newfound Polynomial clarification, I FOILed the thing.

In fact, I probably spent a good 2 minutes down FOIL ROAD -- never arriving at the answer until after the bell, when I went back and looked, and went "dah, I can't believe I did that."

They got me again.

Illustrations by Jennifer Orkin Lewis

 
58 Comments | posted October 19th, 2011
 

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Math

Associative Interference

A few months ago I joked, How Long Till the Polynomials?   

All kidding aside, I knew there was a pebble in my shoe around the polynomials, I just couldn't pinpoint the issue at the time.

Turns out it was more than a pebble.

Cut to a few weeks ago, and I was attempting to write my own "Solve for Expressions" question. I emailed the first draft to PWNtheSAT so he could take it for a test drive, and I got back the following message:

"I don't see how to get from what you're giving me to what you want......Is there a trick I'm not seeing?"

That was my first inkling that something was very wrong, but I checked my work and sent him my steps:

First this: (a - b)², then that:  (a + b)(a - b), etc. etc.

And then he emailed me again:

"Look at your second step!"

And just like that, in the blink of an eye, I had my polynomial epiphany.

(Incidentally, I'm baring my soul here in case there's anyone out there who might benefit from knowing that it's okay not to know everything.)

Mortified, I wrote back, "I'm scaring you now, right? I'm beyond your scope, aren't I?"

Then he told me it's a big distinction, but a common mistake (and I am choosing to believe him about the "common mistake" part, if only to maintain the courage to soldier on, and not die from embarrassment.) And, I'll try not to obsess about what other holes might be lurking.

I called my friend Catherine who attempted to console me.  "It's not you," she said, "It's called associative interference. Have you read Wickelgren?"

And then she sent me a post she'd written, from which I will quote, because it did make me feel better: Why is Remembering What You've Learned About Math Hard?

It's the similarity between the facts. That is, the fact 3 + 5 = 8 is not so different from 3 + 6 = 9. They both contain 3's; they both contain +'s, and they both contain single-digit numbers....

Thus, to a child beginning to learn such facts, the facts overlap in the brain, creating a blur that makes it easy to confuse them and difficult to remember any single answer. In cognitive psychology, this "blur" is called associative interference, which occurs when one idea, A, is linked in the mind to two or more other ideas. It's like static on the radio, which often occurs when other stations or electrical impulses interfere with a radio station's music or speech. 

Anyhoo, I adapted my "Solve for Expressions" question to incorporate all areas of confusion:

If a² = 4 and b² = 9, which of the following could equal c in the following equation:   c(a - b)² = 2(a² - b²)

A) -10

B) -2

C) .5

D) 2

E) 25

 

Hopefully, "the issue" is now resolved.  I did have a moment of satisfaction when I ran across a need to know this piece of information yesterday, while taking a full, timed, practice test.

As always, any and all attempts to answer the question above in the comments below, will make my day.

 

Illustrations by Jennifer Orkin Lewis

 
15 Comments | posted October 15th, 2011
 

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Math

The Cure For Graph Dyslexia (And It’s Not A Pretty Sight)

I don't want to count any chickens before they hatch, but I do believe I may have cured my "reading functions backwards under pressure" problem. Incidentally, my son told me lots of people have this issue, which made me feel better.

It took me a few tries, and I even double stumped myself -- but here is the most gruesome Function Notation Graph question I could conjure up:

The figure above shows the graphs of the functions f and g.  If  y = f(x), and f(4) = k,  and g(-2) = m, which of the following is closest to f(k) + g(m) - (k/m)² ?

(A)  f(-2)

(B)  f(2)

(C)  g(-3)

(D) g(-6)

(E)  g(6)

What do you think?  All answers/attempts/questions left in the comments will Make My Day.

By the way, is anyone else having a hard time finding their SAT groove? I feel like there is always something "really important" to do before I can get to my SAT work, and then I never seem to get there ("there" = SAT work).

I'm scheduled to take a full, timed PSAT with my son tomorrow morning -- so hopefully that will be my "get back on the horse" moment.

Illustrations by Jennifer Orkin Lewis

 
17 Comments | posted October 8th, 2011
 

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Math

It’s A “Math Flavored” Test

That's what PWNtheSAT told me after I screamed on the top of my lungs for the umpteenth time because I'd fallen again for some deception in the "Math Section" that wasn't even "math."

"Does that make you mad?" he asked.

"YES,"  I screamed.

"Good, then don't let them do that to you again."

And then he told me to think of the Math Section like shrimp flavored Ramen Noodles: there could be some shrimp in there, but really it's a lot of other "stuff."*

Not sure if those were the words that inspired my unplanned, last second, impulsive shift in strategy -- but I took SAT #5 in 2011, all in first-serves. I was aggressive. There was not one iota of perseveration in my game that day.

Last Saturday morning, at DeWitt Clinton High School in the Bronx, NY -- I discovered my inner "don't mess with me" self.

No idea what this means for my score, and thank god this doesn't really count for anything. I am very curious though, as to how this "backwards-Debbie" plan worked out, and I'd be lying if I didn't admit that I woke up the next day just a little bit scared.

Here's what I know for sure:

I had a blast and enjoyed every second of the experience.  I distinctly remember thinking as I colored in those first bubbles with that deliciously soft and perfectly sharpened #2 pencil, "This feels soooooo good."

I will also say this: Every day I'm less sure about what, exactly, the SAT is testing. More and more it feels like a test of how not to be messed with -- especially the math (and least of all the writing).

And if that be the case (and I do believe that be the case), I'm going to highly recommend a book that I've highly recommended before: PWN the SAT Math Guide.

From the introduction:

"The SAT is not a math test........it's full of booby-traps, misleading diagrams, and intentionally difficult phrasing.  Even questions that look a lot like straightforward algebra questions are put there not to see if you can do the algebra, but to see if you can spot the shortcut that lets you avoid the algebra.

.....Taking the SAT like you'd take a regular math test is like bringing a knife to a gun fight......

.....The SAT is a test, above all, of how good you are at taking the SAT......

UPDATED: One last note: I wrestle a lot with what I think the SAT is really testing, and I don't agree with my own words at the end of the above quote implying that the SAT tests nothing other than how proficient one is at taking the SAT. That's not going to make it to print in the final draft. It's just not where I'm at anymore.**

*"Just to be clear, the fact that the SAT isn't a math test doesn't make it any less challenging. It just makes it different." -- @PWNtheSAT   See Full Comment Below for rest of clarification.

**Full comment below.

Illustrations by Jennifer Orkin Lewis

 
42 Comments | posted October 3rd, 2011
 

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Math

Inscribed with Love and Secret Sauce

Look what I made:

 

Make my T-4 day and give it a whirl. Yes, I'm showing off, but it's all I've got right now.

Actually, I've got this one too:

 

So what is it about this SAT question writing that's got me so obsessed?

I think this is it: Writing SAT questions is like learning the magician's trick.

Here's how it goes: I pick the questions that are hardest for me -- say, one of these:

And then, I write the hardest question I can in that style, but different.  It's got to be original work.  And then I make it even harder.

This process, more than any other I've tried in 9 months of trying, forces me into a deep relationship with my worst enemy.  And then they go down like butter when I see them on a test (or at least on the pretend tests I take at home).

It's not a quick fix, (though it is fun, after you get over the initial resistance), but I kid you not....you go through them like butter when you're done.

My friend Catherine says it's like learning the cognitive architecture of the SAT. Learning the trick yourself causes the trick to pop when you see it on a test.

So there you have it.  9 months of studying, 4 days till next test, and that's my big revelation:

Writing hard SAT Questions is the best way to study for this test.

Now humor me and answer my questions.

 

Illustrations by Jennifer Orkin Lewis

 

 
15 Comments | posted September 28th, 2011
 

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Math

I Prefer to Think of Myself as “A Postponer”

Don't even utter the Q word in my presence.

You have no idea how I agonized over this decision.

As soon as I heard that everyone quits Kumon on Level D,  I was like....No way -- that will not be me.  I'm in....I'm a lifer...You just watch.  La-di-da.

Even when I got sent back to "GO" on Level D, and had to start over with that long division, in my head, because I made too many mistakes -- I was in. I was committed.

But you try dividing 2345 by 43.....without carrying numbers.....after a few SAT Critical Reading sections and some SAT Math -- and picking through that knotty Writing section in search of comma splices and dangling modifiers -- and then let's talk.

I'm not going to lie: It hurt.

I started skipping days, and then feel I'd feel unbearably guilty.  Unendurably guilty. There were nights, after I'd fallen behind by a few days, that I felt so ashamed that I actually got out of bed and went downstairs after midnight and tried to catch myself up for before next day.

Anything, not to be a quitter.

Looking back, I think it's pretty clear where I slipped up:

1) I intentionally moved Kumon to the post-SAT portion of my day so that my fresh brain juice was used on the SAT stuff  -- and Kumon got the empty tank of gas.

2) Layer in a little teenage drama (see "Decision Fatigue" post for more details)

3) And then add a level of difficulty to Kumon that made the task of changing mixed numbers such as 333/19 --  into whole numbers, without scratch paper on a fatigued brain -- fast, and without mistakes -- hundreds of them (or at least it felt that way when I was behind by a few days) -- and I caved.

After days of mental fatigue, I took a cold hard look at everything on my plate: I've committed to this SAT thing, that's got to stay.  The kids, well, um, they can't go either. Cooking, bills, errands -- no no no.  Can't cut.

So it came down to Kumon, and let me tell you, it did not feel good to have to call Jennifer at my local Kumon Center and ask her if she could put my membership on hold.

Just to clarify.....this is a postponement.

I want my Level O Certificate, and I want my worksheet sculpture.

I've said it before, and I'll say it again:  I'm a believer.  If I could turn back the hands of time, I would have enrolled my kids before they knew what hit them.

I will be back!

Illustrations by Jennifer Orkin Lewis

 
6 Comments | posted September 26th, 2011
 

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Math

Did Someone Say Contest?

Please don't tell me I'm going to win PWNtheSAT's SAT Question Writing Contest by default, am I?

That will take all the glory out of it.

Come on people - submit your questions!   I'll try yours if you try mine.

Here's the one I submitted (typed, per the contest rules):

And here is the one I was going to throw in the hopper -- which I still may -- but first I need to figure out how to type up Absolute Value notations.

Submissions still open until tomorrow.  Akil, I expect to see you there.

Illustrations by Jennifer Orkin Lewis

 
18 Comments | posted September 16th, 2011
 

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Math

Aiming For Merciless

The fun continues.

Last week PWNtheSAT assigned me six more math questions to write for this coming week.  I also see he's got an SAT question writing contest going.  I'm in. (Nothing like a little competition to get me moving on a Sunday morning.)

In the meantime, here are two new questions that I wrote the other day.

1)  I call this one "The Double Stuffed Function."  I'm just warning you, it's been called "brutal" by a perfect scorer (hehe).  Let me know if you need help!

2) And voila, my "Quadrilateral Ratio Angles" question.   The SAT recipe tester described this one as "devious."

(Actually.....maybe he said I'm devious.)

I didn't think it was so hard, but you tell me....

I'm thinking "SAT question writer" could be my next act.  I love this!

Illustrations by Jennifer Orkin Lewis

 
21 Comments | posted September 11th, 2011
 

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Math

What’s a Sadness Gap, You Ask?

I almost don't even want to tell you if you're studying for the SAT, because you really shouldn't worry your pretty little head about this.

They're rare -- in fact, so rare that I couldn't even find a single one in the entire Blue Book.  Not one.

UPDATE: Ok, one.  Stacey Howe-Lott found one in the Blue Book: Test 1, Section 7, Question 7 on page 415.

So what is a "sadness gap?"

It's officially known as the "Triangle Inequality Theorem," though when I heard it referred to as a "sadness gap" in PWNtheSAT's SAT Math Guide Beta Access, I thought, huh, how apropos. I've shed tears over this triangle question. In fact, I believe I gave up on math entirely in the 10th grade because of this "theorem."

When I say I've spent hours pouring over SAT books 30 years later in an attempt to finally understand this theorem in a way that will stick for more than a minute, I am not exaggerating.

Ok, here it is, Sadness Gap Explanation:

The basic thrust is this: if one side were longer than the sum of the other two, then how would those two shorter ones connect to form the triangle? They couldn't. And if one side was equal to the sum of the other two, would you have a triangle? No, you'd just have a straight line.

To drive this home: imagine your forearms (apologies to my armless friends) are two sides of a triangle, and the imaginary line that connects your elbows is the third side. If you touch your fingertips together and pull your elbows apart, eventually your fingertips have to disconnect...that's when the length between your elbows is longer than the sum of the lengths of your forearms. Neat, huh?

Do you get it?

I do.  For a second.  And then I don't.  But I will.  Because I want my 800.  And they could serve one up.  In fact, I've heard they have (though have yet to verify with my own eyes).*

Now go have fun, unless you want an 800.  And then it's better to be safe than sorry, but I feel your pain.

And if you haven't ordered PWNtheSAT's SAT Math Guide Beta Access, do it.  It's got the funny, which makes "sadness gaps" much more bearable.

And, it's filled with gems like this, The Pythagorean Triple.....

......which I can verify, having just finished all Blue Book triangle problems today, are prevalent.

*UPDATE: No sooner than I wrote that I hadn't seen a Sadness Gap with my own two eyes, then I saw one with my own two eyes:

I'm sort of surprised this is a #10.  Feels like a #19 to me.

Illustrations by Jennifer Orkin Lewis

 
27 Comments | posted August 18th, 2011
 

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