Problem solving

School Science and Mathematics, May 1996 by Meir, Sherry L, Hovde, Robert L, Meier, Ronald L

Features of common problem-solving models in mathematics and science, as well as those found in business and industry today, are discussed. Commonalties in the models are used to advance a case for interdisciplinary or integrated instruction in mathematics, science and technology. The Integrated Mathematics, Science and Technology (MaST) program's problem-solving model is presented as an example of a curriculum project that draws upon the commonalties in the problem-solving models as a basis for a seventh grade integrated curriculum.

As our nation prepares to enter the twenty-first century many issues face our society. The need to be competitive in a global economy has become critical, and workers must be both mentally and physically fit, enabling them to absorb new ideas, adapt to change, cope with ambiguity, perceive patterns, and solve unconventional problems (National Research Council, 1989; Goldman, Nagel & Preiss, 1995). More and more value is assigned to workers who can think and reason, as well as utilize various mathematical techniques and principles to solve problems (Lappan & Schram, 1989). As companies implement practices that focus on customer satisfaction, such as Total Quality Management (TQM) or Market-Driven Quality, employees are being required to work cooperatively to make decisions, and solve problems (Commission on Workforce Quality and Labor Market Efficiency, 1989).

Public outcry over education has often resulted in a demand for moving "back to the basics." However, companies are demanding much more of employees than just mastery of the old basics. In fact, what is considered "basic" is changing. Companies cite the need for workers with excellent communication skills, with an understanding of statistics, and the ability to creatively solve problems (Rosenfeld, 1988). Pollack (1987) reported the following mathematical expectations for future workers in industry.

1. The ability to set up problems using appropriate procedures and mathematical operations. 2. The knowledge of a variety of techniques to solve problems. 3. The ability to identify and utilize the underlying mathematical features of a problem. 4. The ability to work with others to solve problems. 5. The ability to see the applicability of mathematical ideas to common and complex problems. 6. The preparation for problem situations which are not well formulated. 7. The understanding and belief in the utility and value of mathematics. In general societal goals for education are changing. Society now expects education to provide opportunities for all students to become mathematically literate, lifelong learners, and to comprise an informed electorate (National Council of Teachers of Mathematics [NCTM], 1989).

Unfortunately, the national education goal of becoming first in the world in mathematics and science achievement by the year 2000 is already out of reach. Students who will graduate from high school in the year 2000, are already in the eighth grade. For some students, the desire to learn mathematics and sciencerelated content has already been stifled, along with their confidence in their ability to solve problems. "Many students view the current mathematics curriculum in grades 5-8 as irrelevant, dull and routine" (NCTM, 1989, p. 65). It is one of the goals of the National Council of Teachers of Mathematics (NCTM) to change this view. Toward this goal the NCTM Standards (1989) place an emphasis on problem solving, communication, connections, and reasoning. The National Science Education Standards, (National Research Council, 1995) and technology educators (McCade,1995), are reiterating the same themes. While the terminology may vary from "scientific inquiry" to "problem solving," and from "reasoning" to "thinking skills," the ideas are the same. Problem solving and reasoning are of paramount importance, as are being able to connect knowledge to other information, and communicate that knowledge effectively. Teachers' Perceptions of Problem Solving and Instruction

Problem solving has been defined as the process used to obtain a solution to a perplexing question or situation (Meier, 1989). However, teachers generally have a narrow view of problem solving, centered around the content area in which they teach. Mathematics teachers often focus on simple "word problems" or applications which are directly related to the content they are teaching at the moment (Meier,1989). Some science teachers have a slightly broader view, focusing on the general scientific method of inquiry.

Too often, though, they become mired in terminology, and forget that science is as much about asking why, and encouraging students to question and find answers to those questions, as it is about specific knowledge of facts (Rutherford & Ahlgren, 1990). Industrial technology teachers often have a slightly broader view. Perhaps this is because their content is more "real world" and must utilize concepts from science and mathematics as well as technology in order to solve problems. But when evaluating students' knowledge and understanding, technology educators also often revert to asking simple application questions, which require students to demonstrate less thought and little application of problem-solving processes.