## Basic Algebra Mandate

We have had an ongoing question of just what is really important in mathematics that "everyone" should learn. Perhaps this shows best my feeling on this issue.

**Letter sent to NJ Chancellor of Higher Education Feb. 8, 1992:****Dear Chancellor Goldberg:**

I appeal to you for an opportunity to convey some major concerns regarding the algebra mandate and its impact on the colleges of New Jersey. I have some suggestIons for a reexamination of the question of what should be mathematics for life skills.

First permit me to introduce myself. I am a Professor of Mathematics and Mechanical Engineering Technology at County College of Morris. I am a founding member of the faculty at CCM and previously on the original faculty of Middlesex County College. For about ten years I was on the Department of Higher Education Advisory Council on Technology, serving as its chairman for several years. I believe we may have met during that period.

My primary area of expertise is in quality and applied statistics. In addition to teaching at CCM, I have been a consultant and trainer at a variety of major New Jersey companies. I have published in the field, am active in the related standards writing community and, in the early 80's, spent a sabbatical at Bell Telephone Labs at the invitation of Blan Godfrey (the current CEO of the Juran Institute). I have worked with managers, engineers, scientists, technicians and a wide variety of other individuals.

I am deeply committed to the idea that everyone should be quantitatively literate. I believe a particularly important goal of all colleges should be to ensure that all persons graduating from college be proficient in those quantitative skills which are truly critical to their lifelong activities. However, the current mandate calls for remediation in algebra for all students who "fail" the algebra portion of the Basic Skills Placement Test. I strongly believe that this mandate hampers the possibility of meeting the real challenge of addressing the broader quantitative needs, and, in fact, erodes the institutional capacity to consider any other efforts.

It appears that the real effect of the Board's resolution has been to force massive crash noncredit programs in basic 9th grade algebra. The colleges' objectives have become directed to "successful" passage of the post test in order to demonstrate efficacy of their remediation programs.

Large numbers of the students, especially those coming to the community colleges, may never have had algebra. Many others have had a lapse of a minimum of 2 years, with perhaps an average of 5-10 years, since taking any mathematics, and especially any algebra. This time lag may in fact be the most critical factor in describing why students fail the exams. Since very few courses actually require any algebra, the vast majority of the college students will be required to use only a very minimum of the basic algebra from the remediation course, and probably none in their post college activities. Furthermore, if they do encounter courses needing algebra, the retention of the remediation will probably be marginal by the time they take those courses. Please understand that I am not objecting to the use of a placement test to detennine preparation for any specific courses. My real concern is the implication that algebra, especially as defined by the exam, has become designated as the most critical mathematical subject to be understood by all educated individuals.

I suggest that we ignore some of the rhetoric and examine those quantitative skills that business and industry is currently struggling to integrate into its own culture. The major efforts today to integrate the use of mathematical principles within all types of organizations and at all levels of those organizations, including your own, could be broadly described under the umbrella of "The Quality Movement". The only way Total Quality Management, Statistical Process or Quality Control, or the host of other related "programs" will be truly successful, will be when all the participants are conversant in the appropriate quantitative principles and when they continually seek to make intelligent data driven decisions.

To meet this challenge involves a true shift in emphasis. Traditional algebra, and even the rote arithmetical skills tested on the computational portion of the Basic Skills Test are not necessarily critical to managing a quantum leap in the ability of people to reason with quantitative information. Very different intellectual demands, such as developing an understanding of measurement and variation and their relation to all data, become central to an alternate approach to fundamental mathematical training. These concepts, in fact, may stand in strong contrast to the algebraic training which often emphasizes getting a single right answer. The NCTM Standards have recognized the need for alternatives by giving statistics a more prominent role in the K - 12 mathematics curricula. I believe that the mathematical aspects to be considered life skills are also more likely found in this alternate direction. I believe that all individuals need quantitative skills and the colleges should be encouraged to require them. However, which skills to emphasize should depend on what the individual pursues and alternatives should be permitted, especially for those not seeking specialized work.

I suggest that the computer literacy experience might provide an historical precedent for a radical reassessment of the quantitative skills issue. As computers became available in the late 60's we began to develop an idea that all students should "learn" computer principles. As early as 1967 I was teaching them. For the most part, we defined computer literacy as programming in some computer language such as Fortran, Cobol, and later, Basic. To others computer literacy meant machine or perhaps symbolic or assembler programming. Few students learned enough to apply their computer knowledge, and almost none used any programing in subsequent courses. Even engineering and science programs struggled to fmd meaningful uses of computer concepts in upper level courses. As a consequence most of computer instruction could be viewed as essentially terminal, and I believe this all contributed to the difficulty in generating a viable consensus of need.

An entirely new view of computer literacy emerged in the early 80's when Apple and IBM PC computers suddenly became widely available. However, it was not the cost or the availability of these microcomputers that caused the change, it was the fact that radically new ways of using the computers were presented in the form of application methods that included spreadsheets, word-processors, and drawing packages. As a consequence, teaching programming is no longer considered the fundamental principle underlying the concept of "computer literacy" and no longer is there a great need to justify the use of computers. Rather, computer usage is critical because it has become an integral requirement as a tool for the wide diversity of subjects across our academic institutions and throughout business and industry.

I believe that we may be at a similar point in the quantitative/mathematical literacy debate. Higher education should begin a major reevaluation of which mathematical and quantitative concepts are truly critical for a well educated individual.

I hope that this letter may serve to provide some constructive ideas. If there is some way I may be of further service I remain ready and willing to assist you and the Department.

Sincerely,

Neil R. Ullman