Discusses problem solving and why employees need to be trained and educated to solve problems. Highlights include domain knowledge and its role in problem solving; instructional design issues; types of problems; discrete problems versus metaproblems; and the need to prescribe instructional design processes for each type of problem. (LRW)

Describes a decision-making process that guarantees continuing success for college facility management in discovering effective solutions that are process-focused, data-driven, and results-oriented. (GR)

Design research is a valuable tool to help the designer understand the problem that he/she needs to solve. The purpose of design research is to help state or understand the problems better, which will lead to better solutions. Observational research is a design research method for helping the designer understand and define the problem.…

The preproblem pondering strategy of "anticipate the answer" involves attempts to anticipate the form of the answer and the answer's relationship to the conditions of the problem. It draws on the skills of recognition, identification, interpretation and builds confidence.

A mathematical problem is solved using the extension-reduction or build it up-tear it down tactic. This technique is implemented in reviving students' earlier knowledge to enable them to apply this knowledge to solving new problems.

Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.

The heliocentric, or Sun-centered model, one of the most important revolutions in scientific thinking, allowed Nicholas Copernicus to calculate the periods, relative distances, and approximate orbital shapes of all the known planets, thereby paving the way for Kepler's laws and Newton's formation of gravitation. Recreating Copernicus's…

Prediction is a great skill to have in any walk of life: it can, in fact, save lives at times. While the two investigations posed in this column may not be that dramatic, they might just increase one's appreciation of some important connections between grids and rectangles and the divisors of numbers that appear in the dimensions of those…

This article focuses on the research program on mathematical problem solving conducted by the Center on Accelerating Student Learning (CASL). First, a subset of CASL themes, illustrated in the mathematical problem-solving studies, is highlighted. Then, the theoretical underpinnings of the mathematical problem-solving intervention methods are…

The breadth and heuristic merits of Harold (Buddy) Goodall's scholarship exemplify the teachings and influence of Gerald Phillips. One nominator applauds Goodall's leadership and dedication to furthering the visibility and utility of applied communication. Goodall's research is also widely used in other fields such as sociology and anthropology,…

In project-based learning, students work in groups to solve challenging problems. They decide on an approach and what activities to pursue. Their teachers guide and advise them rather than direct the work. The process that students use is to gather information from many sources, analyze the value of what they find, and derive knowledge from it.…

The origins of this paper lay in making beds by putting pieces of plywood on a frame: If beds need to be 4 feet 6 inches by 6 feet 3 inches, and plywood comes in 4-foot by 8-foot sheets, how should one cut the plywood to minimize waste (and have stable beds)? The problem is of course generalized.

Poisson integral formula is revisited. The kernel in the Poisson integral formula can be derived in a series form through the direct BEM free of the concept of image point by using the null-field integral equation in conjunction with the degenerate kernels. The degenerate kernels for the closed-form Green's function and the series form of Poisson…

This classroom note presents a final solution for the functional equation: f(xy)=xf(y) + yf(x). The functional equation if formally similar to the familiar product rule of elementary calculus and this similarity prompted its study by Ren et al., who derived some results concerning it. The purpose of this present note is to extend these results and…

Hadamard's two integral inequalities are generalized and the quadrature formulae associated with them are demonstrated.