• Definition of Success
• Using the Definition
• Implications of the Definition

IV. Definition of Success in Post-Secondary Mathematics Learning

Contextual Definitions of Success

Any definition of student success in mathematics must be meaningful in the context of the individual student’s needs and goals. This implies that the definition must apply to any student, any major, and any choice of institution of higher learning. The overwhelming consideration is that mathematical skill, or the lack thereof, should not be the limiting factor in choice of major or career. For these reasons, we have established the following definition for a successful first year of post-secondary mathematics education.

Definition of Success

A student is successful in mathematics in the first year of college education if the following three conditions are met:

1. The student is prepared for the first college mathematics required by the student’s choice of major or interest.
2. The student completes each mathematics course attempted during the freshman year with a grade of C or better.
3. The student is able to transfer the mathematical knowledge gained in the mathematics course(s) into other courses, particularly into subsequent courses required by the major.

These conditions formulate a minimal definition of success in first-year college mathematics. It should be remembered that minimal success as a freshman does not automatically guarantee on-going success in the remainder of the post-secondary education.

Using the Definition

This definition of success deals simultaneously with background content, the ability to function at the collegiate level, and the ability to transfer knowledge within the context of the career choices of the student. To be useful, the definition must be applied in each of these three areas. For this reason, we must keep the following information in mind when making choices about mathematics courses and study.

• Calculus preparation makes available the widest choice of career possibilities. That is, there are more options open if you are prepared for the study of calculus. Most of the science majors and substantive business options are closed to students with lesser preparation.
• The traditional four courses of high school mathematics — algebra I and II, geometry, and pre-calculus — are the minimal course work necessary to prepare a student for calculus and are likewise known to be the best predictors of future success in post-secondary mathematics.
• The student who must take pre-calculus in college, after having taken it in high school, is not considered successful under this definition. That is not to say that the needs of this student should not be met; rather, the system and/or the student has failed prior to the start of the first year of college mathematics if pre-calculus material must be repeated. If the student was not able to take pre-calculus in high school, then successful completion of the pre-calculus course as a post-secondary course along with the completion of another relevant mathematics course could be considered a successful first year of mathematics.
• The factors impinging upon the completion of a college mathematics course include study skills, test-taking skills, and other external factors. These factors cannot be ignored prior to college nor during college.
• Non-mathematics courses which use mathematics, such as economics, physics, psychology, etc., require the student use mathematics outside the context of a particular mathematics text. This is a higher level of mathematics understanding which needs to be encouraged in high school curricula and continued in college curricula.

Non-traditional students and students who "get off-track" can re-enter the mathematics coursework at the appropriate level for them and continue in the correct sequence of courses -- adjusting this "definition of success" to meet their status and circumstances. On the other hand, the educational community has as its mission the success of as many of its students as possible. Therefore, the educational community needs to take this definition of success very seriously and work towards keeping as many students as possible, especially traditional students, within the boundaries of a successful transition from secondary to college mathematics.

The overwhelming use for this definition of success and likewise for this report is to provide the participants in the educational process with the best understanding of the factors for making successful transitions between secondary and college learning in mathematics. In all cases, the goal is to make available current thinking on the standards for mathematics education in South Carolina and to make students, parents, and teachers aware of the consequences of individual educational decisions. These standards for success provide a basis for the improvement of mathematics education in the state.

Implications of the Definition

The cumulative nature of science in general, and mathematics in particular, makes it necessary to plan ahead when making course decisions; it also stretches out the consequences of poor decisions into the future.

• The decisions made in early middle school regarding pre-algebra can determine whether or not a student can take calculus in high school which in turn influences which university admissions criteria will be met. It is possible to change to a stronger option later, but this involves extra time and extraordinary pressures.
• The study skills and test-taking skills necessary to succeed in college courses are developed through high school experiences.
• Businesses today are looking for two major attributes in employees: the ability to learn new methods and processes and the ability to work with others. These attributes require that a person be able to go through the learning process independently and at the same time communicate information effectively by transferring information into a new setting.
• The ability to learn new methods and processes and the ability to work with others are improved by new pedagogical methods and can also improve the understanding of the basic skills of mathematics; in no case do they replace the goal of a mathematics course – that students be able to individually perform mathematical processes.
• Although it is preferred to state benchmarks in positive terms, it is sometimes helpful to give examples of negative criteria. Individually, a student is not successful if the student believes that the mathematics taken was not and will not be used in the career or major area of study. A student is not successful if his/her graduation is imperiled by a senior year grade in a general education course in mathematics. In these cases, however, it necessary to evaluate on a case by case basis to determine if this is a failure of the education community or a failure on the part of the student.

The next sections of this report refer to recommendations for background/content in mathematics and teaching practices as well as recommendations for addressing external factors which impact learning. Combined, these sections represent the specific recommendations for implementing the definition of success in first-year college mathematics. Recommended strategies include actions which encourage the following:

• Advising the student early regarding how to keep open the most choices for areas of study and for careers.
• Emphasis on the conceptual without compromising skills.
• Activities which encourage the transfer of material between processes, classes, or areas of study.

Once again, it should be remembered that these recommendations are for a definition which is the minimal definition of success in first-year college mathematics. Minimal success as a freshman does not automatically guarantee on-going success in the remainder of the college career.

Visitors since April 30, 1999

Last updated: May 11, 1999
Site design by Tim Humphrey, zzhumphreyt@kagi.com