Continuing the series of responses from Trinity faculty to the New York Times article Is Algebra Necessary?, Dr. Sita Ramamurti of the Mathematics Program offers some terrific thoughts, below. By the way, congratulations are in order to Dr. Ramamurti who recently earned promotion to full Professor of Mathematics!
Dr. Sita Ramamurti’s Reply to Is Algebra Necessary?:
I am convinced that one cannot ask the question ‘Is Algebra Necessary?’ by clubbing both the middle/high school students and college freshman together in the same pool (which is what Dr. Hacker seems to be doing with his argument.) Thinking of alternative math courses is relevant and appropriate at the higher education level but not at the secondary level. The content of traditional algebra should be taught at the middle and high school levels, but what needs to change is the requirement that a certain proficiency in algebra is necessary for high school diploma. I would also like to add that Maryland’s MCPS Algebra I curriculum does include the topics of probability and statistics (Dr. Hacker talks about the need for educating secondary students in “citizen statistics”).
ALGEBRA FOR COLLEGE FRESHMEN
The higher education mathematical community debated this issue and the MAA (Mathematical Association of America) undertook the College Algebra Reform project, a national movement to refocus college algebra. Laurie (Dr. Laurie Johnson, former Luce Professor of Math at Trinity) and I became participants of the HBCU Consortium for College Algebra Reform. The vision of the movement was to ask math departments across the country “to create programs that empower all students to become confident problem solvers. These programs, motivated by real-world problems, address the quantitative needs of other disciplines as well as those for citizenship and the workplace. They incorporate strong communication components and employ technology to enhance conceptual understanding and computing. These programs should also prepare and encourage students to take additional quantitative courses.” (http://www.contemporarycollegealgebra.org/national_movement/an_urgent_call.html).
College Algebra Reform at Trinity
In December 2001, Laurie and I were invited to attend the AMS-MER workshop entitled, Excellence in Undergraduate Mathematics: Mathematics for the ‘Rest of Us,’ at Arizona State University. I had also attended a Project Kaleidoscope Workshop, Bridges in Undergraduate Education: Connecting Mathematics and Partner Disciplines, at West Point in June 2000. As a direct result of these discussions with various mathematics faculty members from across the nation, we began to re-evaluate the goals of the mathematics program here at Trinity. I returned from these conferences with a renewed enthusiasm and interest for changing our mathematics course sequence to make it more relevant for students in different disciplines.
We examined the grade spread for both the College Algebra and Intermediate Algebra courses and were surprised to find that not only were students performing almost as poorly in Intermediate Algebra as they were in College Algebra, but the D-F-W rate in College Algebra had actually increased since the introduction of Intermediate Algebra. Under the then system, students who did not place into one of the Foundation for Leadership Curriculum (FLC) courses were required to take College Algebra before they were allowed to take their FLC required course. We therefore started questioning the relevance of the traditional College Algebra course to students who would not go on to take Calculus. We met with faculty colleagues in related fields and through discussions with them we examined the skills that would be useful for students in these other majors. We determined that the skills we should be focusing on are the ability to read and interpret a graph, the ability to work with real world data, the ability to use mathematics to model data, and the ability to make predictions using the model. We decided to develop a new course based on these ideas, which had been discussed in the workshops mentioned above. These were the first steps in moving towards a quantitative reasoning course to fulfill Trinity’s general education requirement.
At the end of three semesters of teaching the reformed course MATH 108, we examined the D-F-W rate for this new course and found that it was at 26%, which was still higher than what we liked, but markedly less than the D-F-W rate for College Algebra of 45%. Also, a very significant fact emerged from our assessment data analysis: not one student had dropped the course in the three semesters it had been running; students felt more confident with their performance in this new course than they felt in the traditional College Algebra course, which had a drop rate of 8%. In January 2004, we found an opportunity to make this work public. We gave a presentation, Making Mathematics Relevant: College Algebra Reform at Trinity College, at the AMS-MAA-MER special session on mathematics education reform.
Trinity’s mathematics program continued its reform efforts in 2008 by developing a proposal to add a quantitative literacy component to the Math 109: Foundations of Mathematics, a required course for all non-science/non-math majors at Trinity. Using & Understanding Mathematics, a Quantitative Reasoning Approach (Custom Edition for Trinity) is the textbook we currently use for the Math 109 course, and is designed for a college-level general education mathematics course that is intended to develop “quantitative literacy” skills in students. In the words of the authors, “Students need to learn quantitative reasoning and to become quantitatively literate”. Chapter 3 of the textbook does include the Consumer Price Index computation (Dr. Hacker mentions this in the article)!
The program is also currently implementing parts of the Math across the Curriculum Project (MACP), a project envisioned in the summer of 2009. The purpose of the project is to infuse the study of mathematics much more broadly throughout the new CAS General Education curriculum. The project is interdisciplinary and envisions a multi-pronged approach that will include in its agenda, the (i) development of new math seminar courses, such as Ethnomathematics and Mathematics and Literature, (ii) reconceptualization of existing courses, such as adding a quantitative literacy component to Foundations of Mathematics (MATH 109) and a community-based learning component to Introduction to Statistics (MATH 110), (iii) development of new mathematical applications courses, such as Mathematics and Politics and Mathematics and the Arts, and (iv) revitalization of Trinity’s Math and Science Club.
ALGEBRA IN SECONDARY SCHOOLS
While the above arguments and efforts are convincing and appropriate at the Higher Education level, one must be wary about how we examine this issue at the Secondary Level.
Before we answer the question “Is Algebra Necessary”, we have to decide what the aim of school education is. A century ago, the aim was to make a “complete” person, fit to face life. Jobs were neither critical, nor specialized and an educated person could fit in anywhere. So schools sought to provide knowledge over a wide spectrum – including algebra- and the question whether a particular subject was necessary was redundant, a person had to know a bit of everything known.
Today, the aim of education appears to have changed- to fit a person for a job; jobs have become necessary and specialized. The amount of knowledge itself has grown enormously. It is no more possible to know a bit of everything, nor is there time for redundancy. The basics of the specialized knowledge required for a skilled job can barely be acquired in the time-span of school education.
But what then should be taught? Since each person gravitates toward different careers, the curriculum cannot be the same for all, nor should the required degree of proficiency. If a person could choose a career at the age of five, then we could limit his school education to just what that career needs and ignore all else. But in practice, one is not able to decide what he or she would like to do in life till almost the end of school education period. So necessarily the school has to teach all subjects to all students, at least till a stage of differentiation of careers is reached. But there is no need to insist on a degree of proficiency in each subject. Rather the proficiency attained in each subject should be an indicator as to the student’s aptitude. A student proficient in a subject should be permitted to go deeper into it.
One must also remember that the student does not know what the different disciplines truly mean at the secondary level – without that knowledge how can the student choose what he or she wants to do in life? So the student must be exposed to the basics of several disciplines, then he or she will be able to decide what he or she likes; what he or she is good at. Algebra cannot be left out of such a general exposure.
The question asked about Algebra can well be asked of every subject. Is History necessary? Who uses History in life? Is English Composition necessary? Of what use is it in a technical job? If a student securing a bare minimum of say 30% in every subject gets a degree, of what significance will such a degree be? So, while it will be logical to pass a student with 30% in Algebra, it should be insisted upon that he or she show high proficiency in some other subject. That will ensure that every person graduating out of school will be proficient in at least one or two subjects, with possibly average proficiency in all others.
The crux of the argument Dr. Hacker makes in the NYT article appears to be that algebra is not necessary because a large number of students fail to get their diplomas as a result of not being able to pass the algebra exam. The remedy for this is not to do away with algebra in schools but to explore ways to ensure that most of the students qualify for the school diploma.
To sum up, ALGEBRA IS NECESSARY for “sharpen(ing) our minds and mak(ing) us more intellectually adept as individuals and a citizen body”. However mandatory passing score for each subject, including algebra, is certainly not necessary for going through a secondary school education program successfully. What seems reasonable is to have a combined passing score for the “exit exams” as a whole. The State of Maryland already has such an option for the HSA. The adoption of this combined passing score option by other state school districts will resolve the issue raised by Dr. Hacker.
See Also: Dr. Laurie Johnson, “Making Mathematics Relevant: College Algebra Reform at Trinity College,” Fall 2004, Mathematics and Education Reform Forum