Making Problem-Solving Simulations More Realistic: Simply Stated, Do the Mathematics to Predict the Design Outcome

Problem solving is a popular instructional strategy used in modern technology education classrooms. Many problem-solving activities include the direct of mathematic principles. Students do not always fully utilize these principles during the design and experimentation phases by mathematically testing hypotheses before creating a prototype or product (Merrill, C., 2001; Engstrom, D., 2001; Lewis, 1999; Hatch, L., 1988). Trial and error is a common strategy used to solve the simulated problems, with the related mathematics only being explored after the problems are solved. In some cases, the applicable mathematics may be discussed or presented in class but not used to identify a potential solution. In business and industry, scientific and mathematic theories are used extensively prior to beginning prototype development, production, construction, or applying a new process. By having learners apply these theories in a similar way, they will begin to appreciate the need for theoretical applications as well as physical applications in designing and using technology. Research indicates that workers need to be able to think critically as well as creatively and must be able to utilize problem-solving skills in order to solve manufacturing problems (Wicklein R. C. & Schell J. W., 1995; Barnes and Erekson, 1991). By applying mathematical theories during problem-solving activities, learners will often learn to better appreciate its importance in the design process. Often, technical programs are questioned relative to the value of mathematics applied or learned in common problem-solving activities. Activities routinely expose students to mathematical possibilities for design, but frequently do not require the theory to successfully complete a task. Since many forms of mathematics are essential in real design problems, why are learners often not expected to effectively and appropriately apply the necessary scientific and mathematical skills? Discussing, presenting, or even demonstrating useful mathematical skills will not always help a learner understand how to apply or effectively use mathematics in design. Design is not a random set of actions that result in a useful product or process. As stated in Standards for Literacy (ITEA, 2000), Technological design must be systematic. Because so many different designs and approaches exist to solving a problem, a designer is required to be systematic or else face the prospect of wandering endlessly in search of a solution (p. 91). Mathematics is but one of the systematic tools frequently needed in design for structures or manufactured products. In a review of careers, Walter Deal (1994) stated that, Engineers apply the theories and principles of science and mathematics to solve technical problems. Frequently the engineer's work makes the connection between scientific discovery and real-world application (p. 15). If organized problem-solving is the goal, and mathematics play a vital role in real-world processes, then they should also play an important role in simulated activities. For activities that traditionally use trial and error as the primary design approach, it is suggested that applying theory to the problem before developing or testing the product, structure, or process would more effectively replicate design procedures used in industry. Simply stated, do the mathematics to predict the design outcome. A popular problem-solving project is the mousetrap car. This activity is ripe with opportunities to apply mathematics throughout the design process. By indicating a specific distance a car must travel, learners can then begin working with ratios and geometry to determine the number of times an axle must turn to move the vehicle the desired distance. They can be further encouraged to apply mathematics by requiring the use of multiple gears or pulleys to transfer energy. This activity could even include alignment as a design problem (which is a common, serious design flaw). …