### Innumeracy and the Persistence of Memory

All of my grades are based on percentages. I'm not one of these teachers who wants to convert someone's scores in my head, so I just weight grades differently. But all grades are based on 100 possible points. I can tell at a glance how a student is doing this way.

But this habit often makes it interesting when students are trying to figure out their grades on quizzes. I usually have a rather simple number of questions in terms of being able to calculate grades easily: 5, 10, 12, 20, 25, or 33 items. As I watched several of my AP students struggle with figuring out their grades, I had to suppress a groan of frustration. It was a 20 item quiz-- therefore each question would be worth 5 points, right? Young Frederick wanted to pull out his calculator to figure out what his score would be if he missed 7.

"No calculator. You can do this," I urged.

He couldn't begin to figure out how to determine his grade without a calculator. He is 16 years old and taking pre-calculus and other college-track classes (I never took a course beyond algebra 2, much to my chagrin). He doesn't immediately know that 7x5=35, and then subtract 35 from 100, nor can he figure out that 13x5=65. As a matter of fact, he stumbled over the 100-35 part and insisted the answer was 75.

It is obvious that his only problem is NOT that he didn't do his reading for my AP US history class carefully enough last night. His problem begins with a basic innumeracy. Of course, many would say that he is a victim of a larger educational trend which I pray to God is finally being placed on the pyre of idiotic educational theories: that rote memorization is bad, bad, baddety bad bad.

Frederick has to THINK about what 6x9 is, and he doesn't get that 6x9 is the same as 9x6 is the same as 3x2x9 is the same as (3 cubed) x2, and so on-- that's a related but different problem we could talk about all day. I think it's a crime that Frederick has to waste valuable thinking time on matters such as 6x5, much less 100-35. Frederick has much more complex things to think about, but by the time he gets there, his poor little thinker is all worn out on information he should have committed to recall 7 or 8 years ago.

The greatest civilizations of the ages depended upon rote memorization. The Torah was preserved through the power of memory for hundreds of years. The

*Iliad*and the

*Odyssey*were memorized and sung for generations. But somewhere along the line in the last forty or so years, memorizing was a skill that became shameful and vilified by someone among the educational cognoscenti. In the words of some of my students, I would like to find this dude and kick him in the shins.

I still remember huge chunks of poetry and music that I had to memorize over twenty years ago.

"Little Orphant Annie's come to our house to stay,

To wash the cups and saucers up and brush the crumbs away,

And shoo the chickens off the porch and dust the hearth and sweep,

And make the fire and bake the bread and earn her board and keep..."

...and I could keep going for the next 30 or so lines, trust me....

"But soft! What light through yonder window breaks!

It is the East, and Juliet the sun.

Arise, fair sun, and kill the envious moon

Who is already sick and pale with grief...."

Not to mention the lyrics to almost every song on the pop charts since 1974, much to my enduring shame in some cases (Some people call me the Space Cowboy, yeah; some call me the Gangster of Love; some people call me Maurice, 'cause I speak of the pompitous of Love-- YIKES!)....

My two youngest kids learned the names of the presidents in order to the tune of "Yankee Doodle Dandy." When they were 4. In preschool. Before they could read.

What is all the more appalling is that we live in the "Information Age." Never has so much information been at the fingertips of so many but been manipulated or understood by so few.

In this year's State of the Union address, President Bush called for creation of the American Competitiveness Initiative, the goal of which is to encourage more study of math and science. This is all well and good, but when students lack a fundamental understanding of the way that numbers work, I fear their ability to go any deeper into the subject. Let's also not overlook the fact that mathematics is also the language of science. Combine innumeracy with the frightful lack of vocabulary (there's that darn memorization thing again) and you've got a seemingly insurmountable problem. Further consider the default response of 90% of our students to delayed gratification, frustration or struggle-- which is to quit--and you've got a major crisis on your hands.

Then you've got this bubble headed bozo who assures students that algebra is unnecessary. More kicks in the shins for this dude.

I am on the verge of promising young Frederick and his classmates a pizza party if they learn their times tables. If we don't get them now, we may never get them. And this is too important to ignore.

Labels: educational philosophy, literacy, math

## 18 Comments:

Back in the day, after failing the last semester of Geometry, I took a class called "Business Math." This course focused more on consumer and practical math skills. There still is some measure of algebra skills in every day math, but some students need to see more relevance than just a bunch of problems in a textbook. Consumer math may not be on par with algebra to a college admissions board, but has the potential to be vastly more relevant. Students in high school need to know how to balance a checkbook, calculate interest, compare prices in a store and generally pay their bills. An algebra course is not the most direct and efficient to teach these critical skills.

dick

I totally agree with you. And as to the first poster, even a Business/Consumer Math class requires the basic skill of muliplication...In my opinion, the constructivist approach to math is to blame for what you're (and the rest of us) are seeing.

Memorization plus understanding: both are important! And you're right that memorizing things is so much easier when you're young. My kids listened for a couple of weeks to a borrowed CD (called Beethoven's Wig) that had the names of all the British monarchs set to a Purcell tune, and even the 4yo has been going around (days after the CD was returned) singing "First came William, then the second William, Henry, Stephen, then a second Hank."

Well, actually, no one balances their checkbooks any more, which is, BTW, very dangerous. But kids don't keep checkbooks-- they have ATM cards.

But to be able to balance out a ledger is an important example of the type of meticulous process in which our students receive so little practice.

GREAT post! So true! My kids are blown away when I tell them to figure out their percentage score. Basic math is lost on them! Let's not even talk about concepts of history...too abstract for them. *rolling eyes*

enjoyed my visit.

Not only do my students not know how to multiply and then subtract from 100, they cannot even bring a calculator to class in which to do these "intricate" calculations such as 1/2 x 4 x (6+9). They instead just copy down the problem and the information and the answer and go on. They do not try to understand the information much less the problem.

As to the need for Algebra, I use it almost daily in my life despite being a math teacher. Where is this person from, some other planet?

Memorize: like

"Tomorrow and tomorrow and tomorrow crepts in this petty pace from day to day until the last syllable of recorded time and all of our yesterday's have lighted fools the way to dusty death. Out out brief candle life is but a walking shadow. A poor player who struts himself upon this stage and is heard not more. This is a tale told by an idiot full of sound and fury and is heard no more." Shakespeare's Macbeth

How about all the transitive verbs (does anyone even know what they are and why we need to know them) appear, become, continue, feel, grow, look, remain, seem, smell, sound, taste and stay.

Do we need to know that the square of the hypotenuse is equal to the sum of the square of the sides? Have you seen many houses fall down or crumble if it had not been for Pythagoras.

What about "Four score and seven years ago our forefathers brought forth on this continent a new nation and dedicated to the proposition that ALL MEN ARE CREATED EQUAL..." Why do we not need to know this?

Memorizing (especially math facts) are some of the foundation of learning. It exercises part of the brain that our students to day have yet to find. Memorize is like asking for their right arm...what about I before E except after C or when sounded as A as in neighbor and weigh...No wonder no one can spell receive....How about "30 days have September, April, June and November...all the rest have 31 save February that hase 28 and no more until leap year comes and it has one more" How else can we remember the months?

PLEASE HELP OUR CHILDREN EXERCISE ALL OF THEIR BRAIN FUNCTIONS!!!

"Little Orphant Annie . . ."! ! !

No oneknows this poem but me -- really,no one! Wow! Aren't you somethin'!How about "'Twas brillig and the slithy toves did gyre and gimble in the wabe, all mimsy were the borogoves and the mome raths outgrabe." (I know the rest of it, too -- with gestures.)

The reflection of your post in the world of reading is looking at the first letter of a word and then just sorta guessing at it. In literature it's the Disney-fication of everything. Aaargh.

No one? oh, nonono.

Ahem.

"And all us other children when the supper things is done,

We sit around the kitchen fire and has the MOSTEST fun

a-listenin' to the witch-tales that Annie tells about

And the Gobble-uns that gits you

If you Don't Watch Out."

One of my friends and I can do it in stereo.

It must be almost FRIDAY, you're quoting Steve Miller Band lyrics..... How about this one: "I took off for a weekend last month just to try and recall the whole year.....all of the faces and all of the places, wonderin' where they all disappeared. I didn't ponder the question too long, I was hungry and went out for a bite. Ran into a chum with a bottle of rum and we wound up drinking all night."

As for math stuff, my seventh graders have a hard time figuring out their gpa, like yours, any kind of percent or even KNOWING that a 72% means they earned a "C-" on that assignment or quiz.

Buy stock in banks.....they will reap mighty profits in the future from this hoard of math dead students we have.......

Have a good weekend!

Ummm... Jimmy Buffett. But the actual song, I'm not sure. Not the one about Hush Puppies, or margaritas, or bananas, or cheeseburgers, though....

Hmm, margaritas! Woo hoo!

It's 5 o'clock somewhere!

I am halfway through a teaching course and am taking the facilitating math class.

My classmates and I, were surprised to learn that, on our state's high stakes do or die test, a student can have the wrong answer but get more points, because they labeled, graphed and explained, than the student with the right answer who didn't jump through all the hoops.

The very next week one of our school districts announced a huge immediate cut in programs and technology, followed by a staffing cut next year. Why? Because the budget contained an error to the tune of millions of dollars.

Now, I'm sure, that the budget report was neat, tidy, with graphs, labels and explanations...

but, darn it, that wrong answer doesn't seem to be getting the school district many points with parents and staff.

You are absolutely right. Students get points for showing the process even if they get the wrong answer.

And I have a sneaking suspicion that they get the wrong answer, more times than not, because they cannot do basic arithmatic.

Same thing with the reading example cited by my Jabberwocky-citing friend graycie-- BTW, hand gestures??? No one taught me that! Must have more info!-- students have no decoding skils due to the dominance of whole language for about 15 years, emphasizing sight words over phonemic awareness. Ah, memories of one of the reasons I stopped officially teaching English and now I am just an English pusher dressed up as an historian....

Why? Because the theorists have prized process over product. Perhaps we could even make this indictment of society in general. But that really doesn't matter.

To me, it doesn't matter if you know all the proceses in the world if you can't produce anything with them.

I teach a class in high school called "Numeracy" for students who are still below a 7th grade (and most below 5th grade) level. They have "learned" all of the algorithms that have been pushed into them by rote work and filling out worksheets, but they have no idea which algorithm to use when, or why. I would bet that your student knows how to do the multiplication problem, or could easily do the subtraction problem if you lined up the numbers nicely like on a worksheet. The deficit is in his ability to think mathematically. The real key to numeracy is being able to see into the mathematical nautre of a problem, and select the appropriate response - either something that has been learned and memorized, or a creative response synthesized from understanding the way numbers work. I completely agree that memorization of facts and algorithms is critical - but in math, this only has value once a concept is really understood.

Anyone who thinks that the majority of students can really learn to divide fractions (in a lasting way, in a way that will be applicable to rational functions in algebra, to solving word problems, etc.) by "invert and multiply" has never really tried to teach.

I think he knows he needs to multiply. He doesn't know 7x5 (Or 6x7, from another conversation we had later.) He doesn't know how to borrow correctly, either.

You're right about the fact that he can plug things in if they're put to him in a familiar format. Go outside the box, though, and you've got problems, which somewhat touches on the subject of the post I put up today (Friday.)

But I have to tell him that each item is worth 5 points-- he and his pals don't know this either, because they don't know that 20 goes into 100 5 times and what that means.

And yet he takes pre-calc-- in which he depends upon a programmable calculator. God forbid he and his similarly situated classmates ever are without that little piece of electronics.....

I suppose that y'all have read this: Where Is Mary Alice Smith? Riley writes about a real orphan who came to his house to stay when he was a little boy.

I taught my daughter about percentages the easy way - I told her to think about pennies, nickels, dimes, quarters, and dollars. Of course there are four quarters in a dollar, hence the term "quarter", and each one is 25 cents; and so forth. She never had a bit of trouble.

I hate the ^%^%&* graphing calculators. Hate them.

Oh - and the kid memorized "Lochinvar" for 8th grade English. I told her it would be easy because it tells a story and because of the word-pictures (the bridegroom stood dangling his bonnet and plume) and the way the cadences and rhymes just pull you along. She found it to be so.

laura,

Many years ago when I lived in Baltimore, friends of mine named their car "Lochincar" because it came from Detroit -- "out of the west."

I haven't thought of that in years!

Thank you for "Mary Alice Smith." It is entirely new to me, but the voice of Little Orphant Annie is hers.

Laura-- Oh my Lord, that was interesting!

Lord Lochinvar.... ah yes, my English major days come back to me now.

How about Childe Harold, as Bertie Wooster was so fond of quoting?

I can't get that Beethoven's Wig song out of my head! I love those CDs; the songs are catchy and informative, and definitly contain a few earworms :)

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