Elimination of Precalculus


In a report of the office of the Dean of Academic Affairs, entitled Informe al Senado Académico: Consejo de Implantación del Nuevo Bachillerato- Parte II of January 31, 2003, it is stated:

“El Comité (Timón) a nivel de Facultad (de Ciencias Naturales) recomendará: … eliminar el curso de pre-cálculo como un requisito, de modo que el estudiante que aspira a tomar un bachillerato en ciencias, tiene que haber aprobado este curso en escuela superior. En el verano se llevó a cabo un experimento para ofrecer el curso de precalculo a los estudiantes aceptados en la Facultad, previo a comenzar sus estudios universitarios.

In light of this recommendation, the Faculty of Natural plans to eliminate the course MATH 3018, Trigonometry and Analytic Geometry (and its two semester equivalent Pre-calculus MATH 3023-MATH 3024), from the B.S. degree. The purpose of this article is to analyze this recommendation.

On the Justification for Eliminating Precalculus

The elimination of the pre-calculus courses from the B.S. assumes that students interested in the Natural Sciences will have the opportunity to study this material in the high school. Indeed, in well organized high school systems, the material in these courses is typically covered between the tenth and twelfth grades and this should certainly be a goal of the Puerto Rico Department of Education. However, the current situation, as witnessed by deteriorating College Board scores and by the Natural Science entrance exam, is that most students receive very poor to almost negligible mathematical training, especially in the public schools. Basic and important mathematical topics are not covered, either because they are not in the curriculum or because no teacher with the necessary expertise is available. For these reasons the precalculus course is critical for a large majority of those students who wish to study science. If these courses are not required for the degree, students will either be forced to pay for them or use valuable elective credits which would otherwise enable them to take more important courses in their majors. More worryingly, many will cut corners and simply not take them, and thus many of our students will be hampered in their progress by very serious gaps in their basic mathematics.

The Summer 2002 Experiment

In connection with the plan to eliminate pre-calculus from the baccalaureate, the report of the Dean of Academic Affairs, mentioned above, refers to the “experiment” carried out in the Summer of 2002, in which new students were invited to take MATH 3018 (Trigonometry and Analytic Geometry) as an “immersion” course, prior to entering the University. The course which is normally about 72 hours long, was given in under four weeks (17 contact days excluding the final exam) at a rate of 4 hours lecture and 3 hours tutorial per day. This is a grave pedagogical error. It is impossible for most students to properly absorb complex material such as mathematics at such a grueling pace. In some days the course actually covered 4 or more sections of the text! This so called “immersion” course was in reality death by drowning. Some of the teaching assistants involved have informed me that the students could not absorb the material at the rate it was presented. The fact that everything was not working as it should was evidenced by the fact that halfway through the course (i.e. after about two weeks) most students were given the option of changing from MATH 3018 to MATH 3023 which normally covers half the material at about half the velocity and the course was begun over again! Although this experiment has been extolled as a success by some of the professors involved, and as “promising” by the Dean of Natural Sciences, the evidence for this is largely anecdotal. There are obvious and serious flaws in the statistical methodology employed including:

  1. The study was essentially a “stand-alone” experiment with no control group.
  2. The students who were changed from MATH 3018 to MATH 3023 (or even the remedial course MATH 3001) because they were failing MATH 3018, were counted as a success in MATH 3023! Normally, when a student drops the course for which he is registered, the grade given is an F or W. He/she is not counted as a success.
  3. The results are biased by the presence of the top scoring students on the College Board exam. The UPR-RP Mathematics Department has traditionally made a special invitation to this group to take MATH 3018 in the Summer prior to entry.
  4. The course was given as a pass/fail course and grades were allocated by professors on the basis of this premise yet the statistical analysis of this experiment was carried out on the basis of letter grades!. The flaws in this procedure are obvious.
  5. The study lacked any reviews of the literature concerning similar “immersion” courses elsewhere.
  6. The study lacked (blind) independent graders.
  7. As far as we know, the subsequent progress of the students in this experiment has not carefully followed up.

In conclusion, there is little scientific evidence to justify proclaiming this course a success. Therefore, it should not be used as a reason to justify the elimination of the Pre-calculus course MATH 3018 from the B.S.


The eliminating MATH 3018 from the B.S. is motivated by the, not unreasonable, desire that material in this course be covered the high-schools. However, given the shortage of qualified mathematics teachers, this is unlikely to happen in the near future. Moreover, the evidence that students can cover this material by an immersion course prior to entry is not at all convincing. For these reasons, the Faculty of Natural Sciences should carefully reconsider the reasons why it is abolishing the course MATH 3018 as a faculty requirement.

Philip Pennance