Closing the Achievement Gap - An Impossible Feat

The Fordham Institute released a new study today: High-Achieving Students in the Era of NCLB. The study consists of two parts:

Part 1 - An Analysis of NAEP Data
(The National Assessment of Educational Progress)
Part 2 - Results From a National Teacher Survey

Part 1 finds that although the rate of achievement has increased for the lowest 10% of students, the rate has remained virtually flat for the top 10% of students. Part 2 finds that the majority of teachers report that "low-achieving students receive dramatically more attention" than their high-achieving counterparts, yet the majority of teachers "believe that all students deserve equal attention". The majority of teachers (especially those in the nation's lowest-income schools) recommended that advanced students be in homogeneous classes, or magnet schools that bring advanced students together. (...so much for the concept of "de-tracking", ubiquitously taught in teacher training programs!)

According to the report summery, the pattern of bigger gains for low achieving students and lesser gains for high achieving students is "associated with the introduction of accountability systems". The term "accountability systems" refers to student testing "regimes" in general, and specifically to the accountability system of NCLB.

A New York Times article cited Amy Wilkins, a vice president at Education Trust, an education lobbying group:

“My concern is that this report makes it seem like we have to choose between seeking equity and excellence,” she said. “We need to strive for both.”

What? Of course we need to strive for both. The report is saying that it is not occurring, and it does not occur in the "high stakes" testing environment of NCLB.

From the Education Trust Web Site (italics added):

Mission Statement

The Education Trust works for the high academic achievement of all students at all levels, pre-kindergarten through college, and forever closing the achievement gaps that separate low-income students and students of color from other youth. Our basic tenet is this — All children will learn at high levels when they are taught to high levels.

What We Do

The Education Trust advances its mission along several fronts, from raising its voice in national and state policy debates to helping teachers improve instruction in their classrooms. Regardless of where it occurs, our work maintains a relentless focus on improving the education of all students, and particularly those students whom the system has traditionally left behind.

Closing the achievement gap is impossible (see explanation below). The gap can only be practically decreased by helping the lower achieving students, intensively, from birth. The achievement gap is a massive cultural problem that will not be solved by putting pressure on teachers to improve.

Closing the Achievement Gap

These graphs are hypothetical representations of learning achievement. They are for elucidation purposes only and do not represent actual data.


The assumptions are that at birth (age 0) children know virtually nothing and by the time they are age 15 there is an achievement gap between the upper 10% of students and the lower 10% of students.

Graph 1 is a baseline representation. The top 10% of students are achieving at at faster rate (steeper slope) than the bottom 10% of students. The distance between the two graphs at age 15, represents the "achievement gap".

In graphs 2 and 3, the achievement gap has narrowed from the base line graph. In graph 2 the top students' achievement rate remained constant, but the lower 10% of students achieved at a faster rate than in the base line graph. In Graph 3, the the achievement rate of the lower 10% of students remained constant, but the achievement rate for the top 10% of students declined.

In graph 4, the rate of achievement for both groups increased. The rate of increase doubled (increased by 100%) for the lowest students but only increased by 50% for the highest students. Even though the rate of achievement was twice as much for the lower students, the gap remained the same.

A major problem with the NCLB act, is that it is narrowly focussed. It assesses student achievement with testing, then focuses on overall school performance and teacher improvement. This has put an impossible burden on teachers. Administrators come under scrutiny by the public when test scores indicate that a school needs to improve. They, in turn, put pressure on the teachers? It would be interesting to see if the NCLB correlates with an increased number of teachers fleeing the profession.

Planting the Seed in Kindergarten

Germany is suffering from a shortage of engineers. According to this article in Money, there are 90,000 positions to fill and only 40,000 trained engineers to fill them. German companies, like their American counterparts, find themselves looking to Asia to fill those vacancies. A few prominent German corporations have decided it would be a good idea to convince six-year-olds that engineering is a good career choice. Why not? As one German representative who was interviewed on NPR explained (loosely quoted),

"There are doctors and lawyers on the soaps, but when is there ever an engineer? Teenagers are using their ipods, their computer games, and a lot of other technology, without realizing the engineering behind those products."

I think the U.S. should look into borrowing this idea.

Anecdotes and Rationale About Why Math is Important, cont.

Anecdote #2 – Panic Attack at the Deli! What Happens When the Customer Wants 1/3 of a Pound of Salami?

When I was a young mom, on my way to a picnic with my two small children, I stopped at the deli and ordered a 1/3 of a pound of salami. I suppose that seems absurd, but ½ a pound was too much and ¼ pound wasn’t enough, so there you have it.

It occurred to me that it was taking a long time to get my order and I wondered where the clerk was. I found her standing in front of the electronic scale in a daze.

In the olden days, when televisions had knobs and phones had dials, the scales at the deli were marked with ounces and fractions of pounds. The clerk would put slices of meat on the tray until the correct number of ounces or the correct fraction of a pound was indicated. (Back then, I would wager that most clerks knew that 1/3 of a pound was close to 5 ½ ounces or thereabouts, but that is the topic for a different post).

Back to the deli clerk… She was standing in front of the relatively new digital scale, frozen in a mild panic attack. It took me a moment to realize that she didn’t know the decimal equivalent of 1/3 and was too embarrassed to ask anyone. So, I helped her out with 0.33 (or so), and we were on our way.

Anecdote #3 - How Does One Make a ½ Sandwich?

Fast-forward twenty years into the future. I was teaching high school one summer and a student of mine, who coincidentally worked in that very same deli from the last anecdote, shared the following story:

One day a customer came into the store and ordered half a roast beef sandwich and half a turkey sandwich (the deli sold half-sandwiches). So, the teenage, soon-to-be-off-to-college coworker of my student made a whole turkey sandwich, and a whole roast beef sandwich, cut them in half, and gave one of each half to the customer.

My student told this story in class and got the desired laughs from most of his classmates, especially when he told the part about asking his coworker what she was planning to do with the left-over halves. Apparently, having been embarassed by the question, she told him exactly where she thought they should go and included some colorful explatives. The class thought that was hilarious.

Both of these stories have several points in common. The problems involve parts of wholes. They, when juxtaposed with each other, illustrate the importance of numeracy, particularly with fractions and decimals, as well as mathematical thinking. It is striking to realize that one young woman was a recent high school graduate and the other, would be off to college within a year. The skills involved in the deli tasks should have been mastered by the 6th grade, and that is a generous estimate.

In his recent testimony before the Congress, Dr. Skip Fennell, member of the National Mathematics Advisory Panel, stated the following regarding conceptual understanding of mathematics:
"As students learn mathematics they need to have the mutually reinforcing benefits of conceptual understanding, procedural fluency, and the opportunity to solve problems applying and extending the mathematics learned."
Regarding fractions he stated:
Some would argue that fractions may be the most critical of the Panel's Critical Foundations for algebra. Fractions are defined here as fractions, decimals, and percent, leading to work with ratio and proportion. Several of the Panel's task groups, as well as the Panel's teacher survey, substantiated that difficulty with fractions is pervasive and an obstacle for far too many students to success in algebra."
And on the abysmal state of our cultural thinking (actually Dr. Fennell called the section "Effort Matters"):
"So, once and for all, we need to stop the parent conference that begins with the phrase, 'Well, you know I was never good in math either.' Math is important - for our children and for our country."

Bravo!

Anecdote #4 – The Geometry Teacher has the Last Laugh

If you don’t teach math, try for a moment to put yourself back in your high school fill-in-the-blank math class. One of the questions students repeatedly ask is, “What am I ever going to use this for?” This particularly happens in Geometry class. I was delighted to see one such student behind the counter of the carpet store, using geometry everyday no less, only several years after he had left my class. Ironic!

The moral to these stories is that it is a good idea to pay attention in math class. One probably does not have 20/20 foresight to know whether or not he/she will need to know given mathematical concepts at some point in the future.

Anecdotes and Rationale About Why Math is Important

Anecdote #1 – The Curtain Ring Problem

A couple I knew, college educated I might add, needed to make a curtain for a closet opening. Curtain rings come in packages of 12. This might seem very practical, 12 being a dozen and all.

So, the couple divided the fabric into 12 spaces, easily done by folding in halves and thirds.  When they attached the rings, they found that they were one ring short, thus no ring for the end.  They discovered that they needed 13 rings when the curtain has 12 spaces.  Alas, they just left the curtain flapping.  See the diagram. 

Clearly they were using a mathematical approach, but unfortunately, it wasn’t the best one.

Using 12 rings means the curtain needs to be folded into 11 spaces, and 11 is a prime number, meaning it has no other factors except itself and 1. Therefore the folding method to determine the spacing of the rings is impractical. The curtain needs to be measured, then the measurement number needs to be divided by 11 or alternately multiplied by 1/11.

Example: Let us say that the fabric is 5ft. wide.














Yes, I used the frightening "fraction" to help solve the problem. The result: A curtain that doesn’t look ridiculous, lot of money saved. And some say that math isn’t practical and they have no use for it!

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