decline at the top

a comment left by Miller Smith in the Direct Instruction thread at joannejacobs:

70 to 80% of the time I do DI. My students don’t know enough about the math they should be perfect at in order to complete activities in the constructivist method.

For example: I wanted the students to find the mass and volume of five selected metals and then plot that data on a mass vs. volume graph, find the slopes of the lines (find density of the metals) and then compare the order of the densities to the metal’s position of on the Periodic Table to show the trend of density of the elements.

The students ALL have taken Algebra I and II and Geometry with very good grades in all (I have all honors classes and in 11th or 12th grade).

They could not find the mass of the samples using electronic scales (didn’t know about the tare), or the volume of the metals (didn’t know about finding volume by diffence), could [not] plot a graph on paper (they used graphing calculators), couldn’t find the % error from a provided equation, on and on. They couldn’t DO the constructivist method of ‘discovering’ the trend of the elements in the Periodic Table since they did not know how to do the math and science in the classes they already passed with wonderful grades!

When the University of Maryland science professors held a meeting with the science department heads in Prince George’s County this past fall, they told the science folks for my county that is was assumed that students from the county didn’t know anything about math or science.

I do DI almost all the time. I directly teach the lower level skill the students should have learned years before before I put the students in the lab. This is very slow - at first. Since we use math all the time in chemistry (ha! Who’d a thunk it!) the student start getting very good at these skills. They then start getting the point of the labs.

These students have been so abused academically by my county with constructivism. DI should be first and foremost. When basic skills are mastered then, and only then, can you put students in an environment to discover things using the tools they have.

A couple of years ago I talked to the Dean of Liberal Arts (I think it was) at a college out on Long Island. He was a math guy (I'm thinking a mathematician, but he may have been a scientist).

When I asked him about students' knowledge of math he told me, "We can't assume students know anything we would want them to know."

This included being able to solve a linear equation with one variable.

(The phrase "decline at the top" isn't mine, but I don't remember who coined it. Waiting for Utopia discusses decline at the top.)

update: Diane Ravitch used the term in 1997.

Over the years researchers have debated the meaning of the decline in SAT scores. Some have concluded that it is solely a reflection of the democratization of American higher education meaning a growing number of minority, low-income, and low-ability students in the test-taking pool. Certainly, changing demographics contributed to the decline, yet something more was happening. Declines occurred at the top of the ability distribution, especially on the verbal part of the test. For example, in 1972 (the first year for which comparable data were available), 116,585 students - 11.4 percent of test takers -scored higher than 600 on the verbal test. By 1983 that number had fallen to only 66,292, or 6.9 percent of the total. Since then the proportion of high-scoring students has remained around 7 percent. By contrast, in mathematics the decline at the top was only temporary. In 1972, 17.9 percent of test takers scored over 600. That proportion dipped as low as 14.4 percent in 1981, but by 1995 it reached 21 percent - the highest proportion of students ever to exceed 600 on the math test.