From: Klaus Hoechsmann, Math. Dept. UBC, November 1993.

Academic preparation of secondary teachers.

Questions 1-20 in the brief prepared by the B.C. College of Teachers all seem to deal, in one way or another, with the problem of assessing the academic (as opposed to “professional”, i.e., pedagogical) preparation of prospective teachers. In response, I would like to offer some opinions and observations regarding the following points:

1. The distinction between primary and secondary teaching, especially the importance of academic competence for the latter. Though it may be true that an experienced pedagogue can usually find ways of compensating for a lack of training in specific disciplines, I believe that there is no ultimate substitute for competence. At the very least it is reassuring, and at best it can be inspiring — especially at an age where young people first discover the fissures and inadequacies of the adult world. Its absence is felt most acutely in subjects which purport to teach definite skills, e.g. athletics, computers, languages, mathematics, music.

It should not be overlooked that good pedagogy must finally be learned on the job, that lectures and seminars can only provide a first orientation, whereas academic skills can be perfected to a high degree in the university environment.

2. The need to decentralize and open up the assessment procedures, in particular, to incorporate checks and balances. It seems reasonable that the primary responsibility for assesssing academic credentials should lie with the people who see more of the candidates than just pieces of paper (e.g. a faculty’s admissions office). Unfortunately, such a agency will likely be too limited in resources to do justice to the entire spectrum of transcripts, diplomas, and certificates coming its way. Errors are probable, and a second, independent adjudication is desirable.

However, it would be difficult for any organization (e.g. the College) to perform this role without making extensive use of the expertise residing in the universities (which, after all, generate those documents). The departmental offices of any faculty routinely assess the credentials of transfer students: given their stake in the educational enterprise, it should not be hard to enlist their help.

3. The impossibility of arriving at a reasonable assessment by a cursory reading of academic transcripts. There may have been a time when academic transcripts were sufficiently uniform and standardized, as to be intelligible to any informed and patient reader. It seems to me that this time is no more: new market forces are in the process of breaking up the old system of fixed standards (and it behooves the buyer to beware).

In order to meet the needs of an ever more diverse student population, universities have greatly diversified their courses of instruction as well as their grading practices. The resulting flexibility makes traditional distinctions such as “junior” versus “senior” rather meaningless, at least prima facie. Only an insider can know (even approximately) what is meant by a course taken and a grade obtained in a certain year.

The case of mathematics.

The following thumb-nail sketch is based on current conditions at UBC, but I believe that these are fairly typical for Canadian universities.

For the purpose of assessing the preparation of secondary teachers, I would distinguish between three types of mathematics courses.

(A) Basic Courses. These are the “service courses” taking up most of teaching time of the typical mathematics department (usually Calculus I and II, as well as Linear Algebra I). They are prescribed as compulsory by many other departments or faculties. Consequently, most students take them without any intention of retaining what they have learned — especially since the syllabus (pushed forward by external requirements and upward by internal scruples) is usually over their heads, and the grapevine assures them that they will never need this knowledge. For average students, the prevalent mode of operation seems to be the obedient application of undigested rules — not a good preparation for prospective teachers. At present, the average grade hovers around B.

(B) Intermediate Courses. This is where the confusion starts. Some of these courses (Calculus III, Differential Equations I, Linear Algebra II) fit into a sequence, and are labeled according to their place in a typical programme of studies — not by their scientific level. At UBC, for instance, Math 307 (Lin. Alg. II) is certainly no more “senior” than Math 215 (Diff. Eq. I). Incidentally, the latter was numbered 315 until this year, and it is expected that 307 will soon be demoted to 222 — all without major changes in content or level.

Other courses (e.g. Elementary Number Theory, Geometry, and Linear Programming) run outside the normal sequence and are of an introductory nature in spite of their “senior” 300+ label. They are definitely less advanced than UBC’s Math 201 (Calculus IV — Stokes’s Theorem, etc.), and much less so than the “honours stream” calculus courses Math 226/227 and the algebra course Math 223. Their level of sophistication is at best comparable to that of the “baby analysis” course Math 220. In all these courses, I would consider a grade of B acceptable.

(C) Advanced Courses. These are the “senior” courses, properly speaking. For simplicity, one might lump all 400+ courses into this category, as well as the typical Third Year introductions to higher algebra and analysis (Math 322/323 and 320/321). These are incomparably more demanding than the other 300+ courses, with the possible exception of the introductions to complex functions and conformal mappings (Math 300/301) and to partial differential equations (Math 316). A grade of C+ obtained in one of these is still honorable.

Obviously the system is in flux (not only at UBC), and the only way to read an academic transcript is with the aid of the appropriate university calendar — paying careful attention to any hint (e.g. the list of prerequisites) as to the real status of a course.