Annotated problem sets are the focus of the Preparation for Technical Careers project. Reasons for this focus are described in Objectives; here we explain the problem sets themselves.
In brief, these are short collections of examples that illustrate and embody educational objectives. They are not problem databases, nor are they intended to be directly used for tests or practice.
See Polynomial Products, Polynomial Division, and Polynomial Factors and Roots for examples.
Problem sets are short
The problems in a set should be different enough that it is worth reading all of them, and few enough that this is reasonable. Mature problem sets will not be static — novel question types are especially welcome — but an effort will be made to incorporate suggestions by modifying or replacing problems rather than by making the set longer.
Goals are long-range
Problems are strongly influenced by experience and needs of later courses. In the discussion of roots of quadratic polynomials for example, roots in the problems are almost all complex or irrational. This contrasts with the common practice of focusing almost entirely on integer roots and using tricks special to this case. Integer roots may satisfy a standards requirement that students learn to find roots of quadratics, but it leaves them at a disadvantage in later courses where integer roots are rare.
Problems are primary
Problems implement educational objectives. Objectives, however, are implicit and not always evident. Annotations are provided to explain objectives but annotations are considered secondary to the problems themselves. Reasons for this priority are:
- Problems are unambiguous. Abstract statements are ambiguous and do not satisfactorily guide implementation.
- Problems are ideologically neutral. Disagreements on abstract principles is secondary as long as the job gets done.
The following example makes these general principles more explicit in the context of a specific problem set:
