Seizing the Initiative Through Creative Thinking Versus Reacting to the Enemy local copyby Grothe, SAMS paper, Leadership must be committed to learning, underwrite experimentation, and create an environment that generates creative thought and innovation. Doctrine must incorporate more aspects of innovation, creative and critical thinking and innovative leadership. The most critical area the Army must focus change in is within Professional Military Education for field grade officers.
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 tension and enjoy the triumph of discovery. Such experiences at a susceptible age may create a taste for mental work and leave their imprint on mind and character for a lifetime.
Problem solving has a special importance in the study of mathematics. A primary goal of mathematics teaching and learning is to develop the ability to solve a wide variety of complex mathematics problems.
Stanic and Kilpatrick 43 traced the role of problem solving in school mathematics and illustrated a rich history of the topic. To many mathematically literate people, mathematics is synonymous with solving problems -- doing word problems, creating patterns, interpreting figures, developing geometric constructions, proving theorems, etc.
On the other hand, persons not enthralled with mathematics may describe any mathematics activity as problem solving. Learning to solve problems is the principal reason for studying mathematics. National Council of Supervisors of Mathematics 22 When two people talk about mathematics problem solving, they may not be talking about the same thing.
The rhetoric Problem solving case studies for students problem solving has been so pervasive in the mathematics education of the s and s that creative speakers and writers can put a twist on whatever topic or activity they have in mind to call it problem solving!
Every exercise of problem solving research has gone through some agony of defining mathematics problem solving. Yet, words sometimes fail. Most people resort to a few examples and a few nonexamples. Reitman 29 defined a problem as when you have been given the description of something but do not yet have anything that satisfies that description.
Reitman's discussion described a problem solver as a person perceiving and accepting a goal without an immediate means of reaching the goal. Henderson and Pingry 11 wrote that to be problem solving there must be a goal, a blocking of that goal for the individual, and acceptance of that goal by the individual.
What is a problem for one student may not be a problem for another -- either because there is no blocking or no acceptance of the goal. Schoenfeld 33 also pointed out that defining what is a problem is always relative to the individual. Assume there is a single recording and the Outer beginning groove is 5.
The recording plays for 23 minutes. Mathematics teachers talk about, write about, and act upon, many different ideas under the heading of problem solving. Some have in mind primarily the selection and presentation of "good" problems to students. Some think of mathematics program goals in which the curriculum is structured around problem content.
Others think of program goals in which the strategies and techniques of problem solving are emphasized. Some discuss mathematics problem solving in the context of a method of teaching, i.
Indeed, discussions of mathematics problem solving often combine and blend several of these ideas. In this chapter, we want to review and discuss the research on how students in secondary schools can develop the ability to solve a wide variety of complex problems.
We will also address how instruction can best develop this ability. A fundamental goal of all instruction is to develop skills, knowledge, and abilities that transfer to tasks not explicitly covered in the curriculum. Should instruction emphasize the particular problem solving techniques or strategies unique to each task?
Will problem solving be enhanced by providing instruction that demonstrates or develops problem solving techniques or strategies useful in many tasks? We are particularly interested in tasks that require mathematical thinking 34 or higher order thinking skills Throughout the chapter, we have chosen to separate and delineate aspects of mathematics problem solving when in fact the separations are pretty fuzzy for any of us.
Although this chapter deals with problem solving research at the secondary level, there is a growing body of research focused on young children's solutions to word problems 6, Readers should also consult the problem solving chapters in the Elementary and Middle School volumes. Research on Problem Solving Educational research is conducted within a variety of constraints -- isolation of variables, availability of subjects, limitations of research procedures, availability of resources, and balancing of priorities.
Various research methodologies are used in mathematics education research including a clinical approach that is frequently used to study problem solving. Typically, mathematical tasks or problem situations are devised, and students are studied as they perform the tasks.
Often they are asked to talk aloud while working or they are interviewed and asked to reflect on their experience and especially their thinking processes.
Waters 48 discusses the advantages and disadvantages of four different methods of measuring strategy use involving a clinical approach. Schoenfeld 32 describes how a clinical approach may be used with pairs of students in an interview. He indicates that "dialog between students often serves to make managerial decisions overt, whereas such decisions are rarely overt in single student protocols.Problem-solving is, and should be, a very real part of the curriculum.
It presupposes that students can take on some of the responsibility for their own learning and can take personal action to solve problems, resolve conflicts, discuss alternatives, and focus on thinking as a vital element of the curriculum.
Creative Problem Solving for Managers Developing skills for decision making and innovation Second edition Tony Proctor. Problem-Solving Skills — Creative and Critical. An important goal of education is helping students learn how to think more productively while solving problems, by combining creative thinking (to generate ideas) and critical thinking (to evaluate ideas).
Both modes of thinking are essential for a well-rounded productive thinker, according to experts in both fields.
The basis for most mathematics problem solving research for secondary school students in the past 31 years can be found in the writings of Polya (26,27,28), the field of cognitive psychology, and specifically in cognitive science.
The case method is a teaching approach that uses decision-forcing cases to put students in the role of people who were faced with difficult decisions at some point in the past. It developed during the course of the twentieth-century from its origins in the casebook method of teaching law pioneered by Harvard legal scholar Christopher C.
ashio-midori.com sharp contrast to many other teaching methods. Multicultural Problem Solving: The Model. Return to Collaborative Problem-Solving: Case Studies..
Monday, Oct. 8. Dear Journal: This is much too early in the semester for this to be happening. Tension is once again brewing between Cody and Philip.