Sunday, July 29, 2012

Is Algebra Necessary?

Andrew Hacker, emeritus Professor of Political Science at City University of New York, has an op-ed in the New York Times today, asking Is Algebra Necessary?  ( CIP found this article provocative, too!)

Hacker's main point is that flunking in algebra is the cause for students to drop out of high school, not qualify for university, or to drop out of university.   Therefore, eliminating such math requirements would lead to more success, and anyway most people don't use these skills later.

To my view, high school algebra is the simplest first exercise of abstract thinking; and if students are failing it, it should be viewed as the canary in the coalmine of school - it is a signal that the students have not acquired the learning process.  Eliminating the canary will not improve matters.

But there is something else Hacker writes that I want to focus on here:

"Another dropout statistic should cause equal chagrin. Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math. The City University of New York, where I have taught since 1971, found that 57 percent of its students didn’t pass its mandated algebra course. The depressing conclusion of a faculty report: “failing math at all levels affects retention more than any other academic factor.”  (emphasis added).
The faculty report appears to be the February 2006 "CUNY Task Force on Retention: Creating the Conditions for Students to Succeed (PDF)" led by the University Dean for Undergraduate Education, Judith Summerfield.

Here is the entire list of conclusions, with the one conclusion cited by Hacker highlighted:

(Note: ESL == English as a Second Language)

Student persistence: Findings at Critical Junctures
  • About 27% of our freshmen entering associate programs and 44% of our freshmen entering baccalaureate programs graduate in 6 years[1]. Although these rates have improved over the last several years, we can do better. 

    1 Based on University-wide figures for first-time/full-time Freshman, entering class of Fall 1998, graduating from a CUNY college.

  • The first year remains the most critical time of a student’s career. One year after enrolling as freshmen at CUNY in Fall 2003, roughly 32% of associate students (at community and comprehensive colleges) and 17% of baccalaureate students (at comprehensive and senior colleges) have left the University. The most precipitous drop is at the end of the second semester and during the summer between the first and second year. 

  • Students experience difficulty with reading and writing and mathematics courses throughout, but especially at the beginning levels and more especially when combined with ESL status. Only 40% of our associate degree students make it to the 45th credit (the point at which they are required to sit for the CPE). 

  • While many factors contribute to this number, academic standing is key. 26% of baccalaureate and 41% of associate students (when tracked for 6 years) leave the University in bad academic standing (GPA< 2.0). Another 20% of baccalaureate students and 25% of associate students leave in good standing. 

  • Too many students are not getting through developmental education, particularly in remedial math and writing. Students who earn college credit during their first semester are more likely to remain enrolled (Appendix E, #5; Task Force on Reading and Writing). Those who do complete developmental education have a good chance of earning a college degree. The implications for ESL students are especially strong here. 

  • Last fall, 32% of the grades awarded in ESL courses were “F”s. ESL students are three times as likely as other students to reach the 45th credit without having reached minimum proficiency in reading or writing or without having completed freshman composition.
  • Many introductory and developmental courses are taught by adjuncts and part- time faculty. Teaching students at these critical junctures is not seen as a priority. 

  • Failing math at all levels affects retention more than any other academic factor. 

  • Failing gateway courses impedes the ability of students to progress toward their degree. Introductory science courses, freshman composition, and other gateway courses need to be carefully addressed. 

  • Full-time students have greater persistence than students enrolled part-time. 

  • Transfer students with an AA/AS have a better chance of earning a BA/BS than those who transfer without the degree. However, too many qualified students cannot enter the majors or professional program of their choice. 

  • Students in Special Programs (SEEK) at the associate level have a 5% higher retention rate than regularly admitted students. 

  • 34% of students in 2004 Satisfaction Survey say they are dissatisfied with information about their “college requirements.”

Among an equally long list of recommendations, we find the one pertaining to mathematics to be:

  • Redesign math curriculum to emphasize contextualized quantitative reasoning, pedagogical excellence and innovations, and alternatives to the traditional sequences. 
There is also this significant passage, quoting in full (emphasis added, it may be worth noting that  Hacker belongs to the older generation of CUNY faculty mentioned below)

First and foremost, the committee agreed that CUNY, to use a vernacular phrase, suffers from “an attitude problem.” It is no secret that within the hallways in too many of our institutions, among both faculty and administrators, a message is persistently conveyed that CUNY’s students are not expected to succeed, that they are woefully “under- prepared” for college, and that even if they do get through the associate degree, they are not up to snuff for senior college level work.

There is a pervasive “passing of the buck.” The senior colleges blame the community colleges for not preparing students for the upper division. And everyone blames the New York City high schools for the problem, particularly, as we shall see, in remedial/developmental education and in math and science.

The remedial taint is insidious: it is a remnant of CUNY’s open admissions experiment. The attitude prevails most egregiously among a segment of an older generation of faculty, along with a deep longing for an old CUNY, when students presumably were better prepared. This, of course, is a common national lament about the way college students – and the culture of the university – used to be, and ignores national trends, particularly in the public colleges and universities. When we measure CUNY’s performance against the national data, as we do in this report, we are not doing so badly. But that does not let us off the retention hook. We are losing far too many students at critical junctures of the educational process, and we need to do better.

The remedial question at CUNY came to a show-down during the last decade, when, in 1998, CUNY’s Board of Trustees determined that remediation should no longer be provided at CUNY’s senior colleges, but, rather, relegated to the associate degree colleges. Thus began a phase-out of remediation at the top-tier senior colleges, with the others to follow in the ensuing years. By 2001, the end of remediation at baccalaureate colleges was presumably complete.

Our Task Force agreed that our study of retention at CUNY and the work of the other Task Forces are all, in a very real sense, confronting the consequences of the Board’s 1998 resolution. We agree that it is in the best interests of the University to study what we all see as the results of this historic decision, and to look to how we, as a University, are providing a quality undergraduate education.
Later in the report, "What Needs to Be Fixed?"

  1. Preparedness:
    • Lack of basic math skills proficiency affects retention more than any other factor
      in the category of level of college preparation. 

“Killer Courses”—Mathematics, Science and English:
According to data from the Office of Institutional Research, all the colleges have “killer courses,” or high fail-rate courses, 2 particularly in math (including algebra, pre-calculus, calculus, and quantitative analysis). Accounting and economics also appear to be high-risk subjects. At many colleges, chemistry poses the largest threat among the sciences, but biology and physics also enter into the equation. Our math initiative will be further informed by a study on math preparation being conducted by Dean David Crook and Professor Geoffrey Askt at Borough of Manhattan Community College. 
At many community colleges, failure rates in developmental reading and writing courses surpass those in math and science courses, especially in those colleges with the highest ESL populations. Nearly all community and comprehensive colleges exhibit high failure rates in composition courses.
Of the 86 courses with the highest fail rates at the senior colleges, 36 of them are math courses (nearly 42%), with the highest numbers in calculus and algebra. Roughly 34% of the “killer courses” at comprehensive colleges are in mathematics (20 out of 59, with the highest number in algebra), and at the community colleges that number is 30% (most of them algebra as well). Out of the 265 “killer courses” identified University-wide, 92 of them are in mathematics, representing 34.71% overall.
(Rhetorical question - would Hacker advocate removal of the other 65% of "killer courses" covering accounting, economics, chemistry, physics, biology?)

Level of College Preparation
Research suggests that preparation for college plays a role in student persistence. At CUNY, lack of math basic skills proficiency, alone or in combination with other skill areas, seems to affect retention the most. At both the associate and baccalaureate levels, entering freshmen who failed the math basic skills test were less likely than students who were math proficient to re-enroll one year after entry. Reading proficiency has a much more tenuous relationship with retention. In fact, for both associate and baccalaureate freshmen, the small number of students who were math and writing proficient, but not reading proficient, were actually more likely to re-enroll one year after entry than students who were fully proficient in all basic skills upon application. The relationship between writing proficiency and retention is also fairly weak, which may explain why ESL students, who, on average, encounter the most difficulty with the writing test have higher or equal retention rates to students whose primary language is English. Further research should address differences between depth and breadth of remedial needs in terms of their effects on student persistence.
It would be interesting to one's hands on:

Akst, G., Crook, D., Moreno, V., Littman, C., & Grima, A. (2006, February).Performance in selected Mathematics courses at the City University of New York:Implications for retention. CUNY Office of Institutional Research & Assessment.
 This is also interesting:
More Than Rules :College Transition Math Teaching  for GED Graduates at The City University of New York, Steve Hinds, 2009 (PDF)
 which includes this statistic:
The national data shows that students fail the GED math test more than twice as often as the writing and science tests and more than three times as often as the social studies and reading tests. New York State students have a  higher math failure rate than all other states except Mississippi and the District of Columbia.
  Until New York State students are near the top, it would not be wise to base national mathematics education policy on the advise of a CUNY political science professor.