LEAKS IN THE PIPELINE: WHERE OUR STUDENTS GO AND WHERE THEY DON’T

Leaks in the Pipeline Norma Agras Miami-Dade College Mercedes McGowen William Rainey Harper College (Retired) William Waller University of Houston, Downtown Robert Mayes University of West Virginia Sheldon Gordon Farmingdale State University of New York

CBMS Survey 2000 Of the 3.2 million students enrolled in math and statistics courses : 981,000 (31%) were in remedial courses 653,000 (20%) took precalculus courses 1,321,000 (41%) placed into introductory courses 245,000 ( 8%) were enrolled in Calculus I

Current State of Mathematics Calculus enrollments are declining. Greatest growth in non-calculus based courses. Increased precalculus enrollments have not translated into increased calculus enrollments. Increased AP enrollment and success have not resulted in increased advanced math enrollment.

What Courses Are Students Taking? Despite an 18% increase in undergraduate mathematics enrollments since 1980 Calculus enrollments declined 13% at 4- year colleges & universities. Non-mainstream calculus enrollments declined 29%. 2-year college calculus enrollments increased 15%. Non-mainstream calculus enrollments declined 48%.

Four-year & University Enrollments Since 1990, course enrollments increased in: Pre-calculus/Elementary Functions 46% College Algebra 5% Combined College Algebra/Trig 6% Since 1990, course enrollments decreased in: Trigonometry 11%

Two-year College Enrollments Since 1990, course enrollments increased in: Pre-calculus/Elementary Functions 37% College Algebra 13% Since 1990, course enrollments decreased in: Combined College Algebra/Trig 11% Trigonometry 23%

College Algebra and Precalculus Each year, about 1,000,000 students take college algebra and precalculus courses. The focus in most of these courses is on preparing the students for calculus. We know that only a relatively small percentage of these students ever go on to start calculus.

Some Questions How many of these students actually ever do go on to start calculus? How well do the ones who do go on actually do in calculus?

Some Questions Why do the majority of these 1,000,000+ students a year take college algebra courses? Are these students well-served by the kind of courses typically given as “college algebra”? If not, what kind of mathematics do these students really need?

Calculus and Related Enrollments In 2000, about 676,000 students took Calculus, Differential Equations, Linear Algebra, and Discrete Mathematics (This is up 6% from 1995) Over the same time period, however, calculus enrollment has declined.

Calculus and Related Enrollments In comparison, in 2000, 171,400 students took one of the two AP Calculus exams – AB or BC. (This is up 40% from 1995) In 2004, 225,000 students took AP Calculus exams Reportedly, almost twice that many students take calculus in high school, but do not an AP exam.

Some Implications Today more students take calculus in high school than in college And, as ever more students take more mathematics, especially calculus, in high school, we should expect: Fewer students taking these courses in college The overall quality of the students who take these courses in college will decrease.

Associates Degrees in Mathematics In 2000, There were 564,933 associate degrees Of these, 675 were in mathematics This is one-tenth of one percent!

Bachelor’s Degrees in Mathematics In 2000, There were 457,056 bachelor’s degrees Of these, 3,412 were in mathematics This is seven-tenths of one percent!

Who Are the Students? Based on the enrollment figures, the students who take college algebra and related courses are not going to become mathematics majors. They are not going to be majors in any of the mathematics intensive disciplines.

The Focus in these Courses But most college algebra courses and certainly all precalculus courses were designed to prepare students for calculus and most of them are still offered in that spirit. Even though only a small percentage of the students have any intention of going into calculus!

Some Interesting Studies Steve Dunbar has tracked over 150,000 students taking mathematics at the University of Nebraska – Lincoln for more than 15 years. He found that: only about 10% of the students who pass college algebra ever go on to start Calculus I virtually none of the students who pass college algebra ever go on to start Calculus III. about 30% of the students who pass college algebra eventually start business calculus. about 30-40% of the students who pass precalculus ever go on to start Calculus I.

Concluding Thoughts The title of this session is: Leaks in the Pipeline But what is a pipeline?

Concluding Thoughts Picture the Alaska pipeline that carries oil from Prudhoe Bay to Valdez. Every drop of oil lost en route is a valuable commodity that is, at best, a complete loss, and at worst, a potential threat to the environment.

Concluding Thoughts Do we really want to view the roughly 1,000,000 students who take college algebra courses each year and do not end up majoring in one of the SMET fields as a complete loss? Maybe the pipeline metaphor has outlived its usefulness!

Concluding Thoughts The pipeline metaphor causes us to apply a very negative psychological image to the overwhelming majority of our students. In turn, it leads many of us to think of the courses we offer to these students as second- class courses for students who are not important to the mathematical enterprise.

Concluding Thoughts The students who “leak out” are not losses. They are simply going into other fields that require less math or even different math. The overwhelming majority of our students are not “losses”. The courses we offer should them not be thought of as second-class courses for students who are not important to the mathematical enterprise.

A Better Metaphor Picture a river, particular one in the southwest. Very little of the water from the headwaters ever reach its end; many of these rivers eventually peter out and all that remains are dry stream beds. But the water that doesn’t make it all the way downstream is diverted to irrigate huge areas and has been used to bring the desert to life.

A Better Metaphor What a wonderful metaphor for how we should view our students. Those who only take college algebra or statistics or finite mathematics should not be thought of as losses; they should be thought of as valuable commodities who, with the right emphases in these courses, can irrigate all these other fields and enrich them by bringing the value of mathematics to bear.

Today’s Panelists Norma Agras, Miami-Dade Community College; Mercedes McGowen, William Rainey Harper College Robert Mayes, University of West Virginia; William Waller, University of Houston-Downtown Sheldon Gordon, Farmingdale State University