Top of Page One would logically expect that the consulting process starts with Step 1, where one or more individuals in the organization sense that something is wrong or that some problem exists. A problem is here defined as a discrepancy between what is such as current performance and what could or should be such as organizational goals. For example, the turnover rate in an organization may be 15 percent per year, which could be expected given the nature of the labor force and the general mobility in the industry. However, if the turnover rate became as high as 40 percent, individuals may very well perceive some problems, for this rate significantly exceeds their expectations or threshold levels.
Change the objects under study. Remove a condition, or add new conditions. Remove or add context. Each of these potential changes is discussed in more detail below. Change the Numbers This is the most obvious way to change a problem.
Give your students one or more problems and ask them to identify any stated or implied numbers. For example, in the cow problem, in addition to the three stated numbers, there are the following implicit conditions: We can change any of these numbers. The geometry becomes much trickier in this final case.
Strategy games can be a good source of research problems and often have many alterable features. Two players take turns rolling a die. After each roll, that player must decide whether to add the value of the roll or ten times the value of the roll to his or her score e.
After seven rolls, the person with the highest total less than or equal to is the winner. A score over counts as 0.
Again, ask your class to find all the stated and assumed numbers in this game. Stated values that might be changed include the number of players, the target totalthe number of turns, the multiples of the die result 1 or 10 Problem posing method of education, and the number of dice rolled per turn.
Assumed values include the number of faces on a die, the values on each face, and even the probability of each face appearing. When considering numerical changes to a problem, many different domains and representations can prove interesting.
For example, what if we limit the domain for some variable to whole numbers, or extend it to the reals? What if we allow negative or rational numbers?
What happens for particularly small or large values? What if we change base e.
A Problem Posing Approach. A Problem-Posing Approach An excerpt from "Teaching Critically as an Act of Praxis and Resistance" by: Mary E. Boyce Freire's () metaphor for traditional education is banking education, in which teachers make deposits of information and knowledge into the empty accounts of students. The Kilmann-Mitroff article discusses how the five steps of problem management enhance management consulting. Functionalism Theory of Education - There are three main theoretical perspectives (or theories) that represent the views of sociologist and educators, these views are the conflict perspective, symbolic interactions, and functionalism.
Can we change a finite quantity to an infinite one or a fixed quantity to an unlimited one e. What if we change from zero to a non-zero value e. Change the Geometry Any problem with a geometric setting is ripe for new variants. The simplest problem-posing maneuver is to change the shapes involved.
Different categories of shapes that suggest possible substitutions include polygons and their number of sides, regular versus non-regular polygons Is the cow problem with different tether lengths simpler with a square barn?
Try a shape that is more general but that includes the initial object of study, such as parallelograms rather than rectangles or more specific look at a subset of possibilities, such as regular solids rather than all polyhedra.
Changes of dimension can yield exciting challenges and patterns. What if we look at pyramids rather than triangles or hyper-cubes rather than squares? What if we reduce the dimension of our problem by considering cross-sections or projections e. What happens when we study graphs in coordinate spaces with three or more axes?
What if our question was not about the two-dimensional area available for grazing but the one-dimensional length of the perimeter of the grazing area so that we can buy a fence and liberate the cow from its tether?
The shapes we are studying may not be the only targets of our experimentation. The structure of the space in which a problem is embedded can be changed as well e.
We can transfer games played on square grids to triangular, hexagonal, semi-regular, or other tilings.
We can move problems between Euclidean and non-Euclidean settings by changing the metric. Continuous and discrete spaces e. Spaces can also be made to "wrap around" the way video arcade games often do i. These spaces have the same topology as the torus which looks like the surface of a donut and may have properties that are different from those of a standard plane.
For example, the four-color theorem states that it is possible to color any planar map using at most four colors so that any two adjacent regions will have different colors.PROBLEM POSING. Students have asked me, on several occasions, "Is there any math after calculus?" These students have been given the impression that the world of mathematics is both finite and linear (the classic algebra-through-calculus sequence).
MATHEMATICAL PROBLEM SOLVING by James W. Wilson, Maria L.
Fernandez, and Nelda Hadaway. Your problem may be modest; but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the . BibMe Free Bibliography & Citation Maker - MLA, APA, Chicago, Harvard.
Problem Solving Problem Solving is the Capacity and the Ability to Evaluate Information and to Predict Future Outcomes. The Ability to Seek out Logical Solutions to Problems, Calmly and Systematically, without making things worse.
Decision Making - Cause and Effect. "There are no Problems, only Solutions" Every Problem can be solved, you just have to learn how to solve it. Learn why the Common Core is important for your child.
What parents should know; Myths vs. facts. The problem posing method is a very similar to the pedagogy idea of constructivism, where the basic principal is that a student learns better when they create knowledge, then when knowledge is created for them.
However, teaching in such a fashion is quite difficult.