EXTEND: Producing Team Players

Producing Team Players

"Articulating, Coordinating, Communicating" was the subject of a Roundtable held on February 15 at Seattle Central Community College to provide a forum for discussion among educators and employers. Issues that emerged in this discussion are summarized in the following report. Statements from some of the participants are given in subsequent sections.

Mathematics, not surprisingly, means different things to different people.

To the public, mathematics means "problems on a page" or "scores on a test." One participant characterized this as an "emaciated" view of mathematics.
To many teachers, mathematics means "mathematical power" as expressed in the NCTM Standards--a robust mixture of problem solving, communication, and reasoning.
To employers, mathematics is just part of the teamwork required for employees to do their jobs well. "In today's workplace, communicating ideas is far more important than applying technical skills."

With Fear and Trembling

School mathematics is the mathematics we love to hate: rote memorization, mindless procedures, timed tests. Fear of mathematics is widespread, especially among politicians and managers whose backgrounds are not in science or engineering. "They turn pale when I come with my graphs and charts. Quantitative arguments strike terror in their hearts. Their cognitive processes just shut off." No wonder the self-help book "Everyday Math for Dummies" is a best seller.

This widespread fear poses significant challenges for the mathematical community. Mathematics educators need to help students learn to communicate about mathematical ideas with those for whom quantitative thinking is not a welcome mode of discourse. Students' future jobs will likely depend on their skill in this endeavor.

At the same time, mathematicians and mathematics educators themselves need to communicate to the public that mathematics is not really as they imagine it in their terror-filled dreams. The world is changing, and so is mathematics--both at work and in school.

Mathematics at Work

To illustrate the "new math" of the workplace, several participants gave examples of ways in which they see mathematical thinking used in their business:

To develop a plan to sterilize laboratory equipment in an autoclave, a worker must gather and organize sufficient information to convince various supervisors and review boards that the plan is defensible. This requires analysis of data to prove that the plan will work, discussion of alternatives to be sure that nothing less costly would do the job, consideration of extreme cases that may not fit the typical scenario, and responsiveness to relevant safety regulations.
To reconcile inconsistencies in monthly inventories, a worker needs to think backwards to determine all the possible ways in which records might be wrong or items misplaced. This requires the ability to imagine the workings of a complex system, to identify plausible sources of error or failure, and to consult with various individuals in order to gather ideas and confirm (or refute) hunches.
To design an airplane in a modern competitive economy, one needs more than the traditional airfoil analysis that produces optimal lift for the wings. Now one seeks to minimize not only fuel consumption, but also manufacturing costs: for a given lift, which design of an airfoil is cheapest to manufacture? To answer that question requires the combined skills of construction workers, design engineers, financial experts, and senior management.

These problems illustrate several features of modern problem solving that are rarely addressed or developed in the schools For example, individuals are expected to recognize weaknesses in their own analysis of a problem, and then to seek assistance from their team (or their supervisors) in addressing these weaknesses. The habit of volunteering possible flaws in an argument does not come naturally to students who have become habituated by the pressure for grades to living in a world of bluff and desperation.

Whether in retail or manufacturing, finance or health, students who enter the world of work must be prepared to put forth their ideas and then to work with others to improve on these initial thoughts. School only prepares students to answer questions posed by others. Instead, students need to learn to say: "Here's my idea. Where are the holes?"

Mathematics in School

Mathematics in school is also changing. Reformers argue that children's motivation to learn arises from rich problem-solving contexts, not from isolated drill on basic skills. Effective teachers no longer make memorization of times-tables "the measure of a child's worth in mathematics." We now know that very young children can understand and solve problems involving simple multiplication and division well before they have the maturity to learn all their arithmetic facts.

Yet the public, and many employers, still emphasize acquisition of basic skills and scores on standardized tests. Many believe that mastery of basic skills is a prerequisite to higher order problem solving, and that calculators provide young children with an excuse for not mastering these basic skills. "You must first master fundamentals, or little else can be accomplished."

Because test scores are the public surrogate for mathematical achievement, the basic skills monitored by these tests become a bellwether for public support of mathematics education. "If we don't satisfy the public that students' basic skills are OK, then they will not trust us with the changes we want to make in other parts of the curriculum." The issue is not whether students should learn basic skills, but when and how. Are they best learned in context, in parallel with higher order problems, or in specific units to be mastered before moving on?

Although nearly everyone agrees on the fundamental skills of elementary school mathematics, there is not much agreement among teachers, parents, employers, and others concerning the "basic skills" of high school mathematics. How important is it, really, that every citizen be able to use the quadratic formula, or factor algebraic expressions? Many believe that what really matters about school mathematics are not specific facts or procedures but experience in working with patterns, in thinking logically, in recognizing that the order of operations matters.

Developing Teamwork

Competition and litigation now compel industry towards higher standards of reliability and efficiency. So employees need strong analytical skills. But they also need more than experience at solving problems on paper. They need experience working in teams.

If employees are to solve the kinds of problems they face every day at work, they need to recognize that all input is valuable. Asking questions and challenging orthodoxy is often an individual's most important contribution to the group. Those who can only see their own viewpoints, or who put others down, tend to destroy creativity and cancel the benefits of the group. Unfortunately, this strong commitment to individual performance is all too often a correlate of high achievement in school mathematics.

There are several compelling reasons that the study of mathematics highlights individual effort over teamwork. First, major parts of school mathematics (routine problems) do not require or benefit much from group work. Other parts (complex projects) that are more suited to teamwork account for only a small portion of the curriculum. Second, students and their parents know that college admission is based on individual effort, including SAT scores, course grades, and writing samples. Parents want high schools to focus on preparation for college, and are thus very nervous about highlighting teamwork as a priority. Third, and ironically, assessing an applicant's potential as a team member is often not a priority in business hiring practices. "People who may do a good job as part of a team may have difficulty getting in the front door."

Nonetheless, employers stressed that teamwork produces a synergy not possible from individual effort. "I expect team solutions. People have different skills, and contribute differently to a team. Educators too often force all students in to the same mold. The era of the lone gunman is over."