Objectives

The Preparation for Technical Careers project seeks to address problems in the high-school/college transition in mathematics. The principal aim is to develop a sense of the mathematical community about student skills needed for vigorous coursework at the college level.

The current focus is on community development of annotated problem sets. 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.

Why Problem Sets

hide this

Most project materials are organized around annotated problem sets. These are short collections of sample problems, not problem databases. Reasons for the problem orientation are:

Skills needed.

Problem-solving skills are the foundations on which advanced training is built. Students without effective skills are at a disadvantage no matter what other learning they may have.

Educational effectiveness.

At this level problems can be designed so that understanding of abstract structure has an immediate payoff. Carefully designed problems can therefore develop abstract understanding as well as mechanical skills.

Clarity.

Sample problems communicate educational objectives clearly and unambiguously. This approach should minimize the confusion and disagreement that often attends high-level descriptions such as standards documents.

Usefulness.

Sample problems are immediately useful in developing tests, lesson plans and other materials.

Why high-achieving students

hide this

The mathematical community has a strong interest in, and is a natural advocate for, the most capable students. This community also - for the most part - lacks the pedagogical expertise needed to develop materials for general-level K-12 students.

Even though the emphasis is on high-achieving students, we expect that nearly all materials will concern standard K-12 topics. Differences are in perspective and emphasis rather than in content. For instance even for high-achievers complete command of Algebra II is much more important than exposure to integral calculus, probability or statistics. The concern with standard topics should make the materials a valuable resource for developing high quality materials for any level.

Why a community effort

hide this

Breadth.

No individual or small group can cover the topics or resolve the issues involved.

The goal is to tap the collective wisdom and experience of the entire community rather than a handful of “experts”.

Continuity.

To be useful this is not static product. It should evolve in response to experience, feedback, and new perspectives.

Potential uses

hide this

Potential uses:

• provide resources for teachers and text and curriculum authors;
• support development of better tests;
• guide development of courseware and online materials;
• make Standards documents more effective by enabling references to specific examples.

A possible future objective of the Working Group is to develop sample computer-based tests based on the materials. A related effort is being undertaken by the AMS Task Force on the first year of college mathematics, see http://firstyearmathematics.blogspot.com/ .