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Topic: Problem solving

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	What Is Problem Solving? (Site not responding. Last check: 2007-10-03)
		An incidental benefit is that often the very attempt to represent the problem explicitly forces a problem solver to be clear about what it is he or she is trying to do and about what stands in the way.
		Metacognition is essential for any extended activity, especially problem solving, because the problem solver needs to be aware of the current activity and of the overall goal, the strategies used to attain that goal, and the effectiveness of those strategies.
		First, we need to recognize when we are engaged in problem solving and accept as natural, normal, and expected the stepwise and discursive path toward a goal through the application of general and specific heuristics.
	www.gse.uci.edu /doehome/DeptInfo/Faculty/Martinez/problem_solving.html (3740 words)

	Mathematics Through Problem Solving
		Problem solving is an important component of mathematics education because it is the single vehicle which seems to be able to achieve at school level all three of the values of mathematics listed at the outset of this article: functional, logical and aesthetic.
		Cockcroft (1982) also advocated problem solving as a means of developing mathematical thinking as a tool for daily living, saying that problem-solving ability lies 'at the heart of mathematics' (p.73) because it is the means by which mathematics can be applied to a variety of unfamiliar situations.
		One of the aims of teaching through problem solving is to encourage students to refine and build onto their own processes over a period of time as their experiences allow them to discard some ideas and become aware of further possibilities (Carpenter, 1989).
	www.mathgoodies.com /articles/problem_solving.html (2275 words)

	Problem-solving
		A problem is a situation which is experienced by an agent as different from the situation which the agent ideally would like to be in.
		Problem states will generally involve objects, which are the elements of the situation that are invariant under actions, and properties or predicates, which are the variable attributes of the objects.
		Problem representations are usually also models of the situation as experienced by the agent.
	pespmc1.vub.ac.be /PROBSOLV.html (977 words)

	Synthesis of Research on Problem Solving
		However, constructivism is consistent with current cognitive theories of problem solving and mathematical views of problem solving involving exploration, pattern finding, and mathematical thinking (36,15,20); thus we urge that teachers and teacher educators become familiar with constructivist views and evaluate these views for restructuring their approaches to teaching, learning, and research dealing with problem solving.
		Problem posing (3) and problem formulation (16) are logically and philosophically appealing notions to mathematics educators and teachers.
		Problem solving as a method of teaching may be used to accomplish the instructional goals of learning basic facts, concepts, and procedures, as well as goals for problem solving within problem contexts.
	jwilson.coe.uga.edu /emt725/PSsyn/PSsyn.html (7645 words)

	Problem Solving
		A representation of the problem, often in the form of a tree diagram, with possible states and associated operations.
		Problems in which there is uncertainty in either: the given information, the permissible operations, or the final state.
		In this problem there are three missionaries and three cannibals on one side of a river.
	www.mtsu.edu /~sschmidt/Cognitive/Problem/problem.html (746 words)

	Research Sampler 4: Expert Problem Solvers
		Problems can be routine textbook exercises or they can be difficult mathematical tasks which take weeks, months, or even years to solve.
		Good problem solvers exhibit productive responses to insufficient understanding, while others, not wanting to admit deficiencies in their mathematical knowledge, may feel they "should" know and this may lead them to guess or use plausible, but inappropriate, procedures.
		For example, if a positive pathway is invoked at the onset of problem solving, curiosity may motivate the solver to better understand the problem and lead to exploratory heuristics; frustration at a subsequent impasse can cause a revision of strategies.
	www.maa.org /t_and_l/sampler/rs_4.html (2198 words)

	Standards for School Mathematics: Problem Solving (Site not responding. Last check: 2007-10-03)
		Problem solving is an integral part of all mathematics learning.
		Problem solving should not be an isolated part of the curriculum but should involve all Content Standards.
		Problem solving means engaging in a task for which the solution is not known in advance.
	standards.nctm.org /document/chapter3/prob.htm (375 words)

	Problem solving - Wikipedia, the free encyclopedia
		There are several methods of studying problem solving, including; introspection, behaviorism, simulation and computer modeling, and experiment.
		Duncker's "X-ray" problem; Ewert and Lambert's 1932 "disk" problem, later known as Tower of Hanoi) that appeared novel to participants (e.g.
		Instead, these researchers have frequently focused on the development of problem solving within a certain domain, that is on the development of expertise (e.g.
	en.wikipedia.org /wiki/Problem_solving (2321 words)

	Success in Mathematics
		Each problem of types 4 or 5 usually requires you to use a multi-step approach, and may involve several different math skills and techniques.
		The first and most important step in solving a problem is to understand the problem, that is, identify exactly which quantity the problem is asking you to find or solve for (make sure you read the whole problem).
		In the book each problem appears at the end of the section in which you learned how do to that problem; on a test the problems from different sections are all together.
	euler.slu.edu /Dept/SuccessinMath.html (2317 words)

	Problem Solving 2.0 (Site not responding. Last check: 2007-10-03)
		As a nation — as a nation of businesses — we face problems of greater complexity, with often torturous histories, with larger and more contentious sets of stakeholders, and sometimes with painful tradeoffs rather than clean solutions.
		While the site focuses on the concepts behind better problem solving, there is also a brief description of services available.
		Our most fundamental assertion is that determining the essential nature of a problem is the first and most powerful decision to be made in problem solving.
	www.problemsolving2.com (616 words)

	Problem Solving
		While relationship problems are varied and complex, we believe that most relationship problems are by-products of ineffective or counterproductive communication within the relationship.
		Marital research shows that about 80% of problems don't even have to be solved when the couple talks through the issues and reaches mutual understanding.
		Reaching understanding of the problem requires that you communicate with a joint desire to understand what the problem is. It does not require that you agree on any solutions at this time.
	www.positive-way.com /problem.htm (1582 words)

	Problem Solving (Site not responding. Last check: 2007-10-03)
		Math problems to figure out which teams won their games, reading a graph; plus designing a superbowl commercial and a general knowledge crossword puzzle.
		Teaching the strategies for solving problem solving is as important as the answer.
		Strategies for Problem Solving: Have your students write, or cut and paste the problem in their Problem Solving Notebook.
	www.abcteach.com /directory/basics/math/problem_solving (732 words)

	TeacherSource . Recommended Links . Math \| PBS
		The objective of Fermi problems is to arrive at reasonable estimates and state the assumptions you use.
		There are six problems with experiments and six different methods for calculating the number of seconds for each plane to arrive at the point where their routes merge or for the trailing plane to catch up with the leading plane.
		Problems "with a Point" are written for middle and high school students and build on previous math concepts and how the relate to new concepts.
	www.pbs.org /teachersource/recommended/math/lk_problemsolving.shtm (4737 words)

	Problem Solving (Site not responding. Last check: 2007-10-03)
		Above all you must understand that the solution to a problem is not usually going to grab you by the collar and introduce itself.
		Very simple problems may be that easy, but for a problem of any complexity you will have to go in and drag it out of hiding.
		This is constructed using dimensional analysis from information given in the statement of the problem or from "common" knowledge.
	home.att.net /~v.d.singleton/genchem/probsolv.htm (1826 words)

	NU Math Problem Solving Group Web Page
		Note: Problems from magazines discussed and solved in the MathPSG emailing list may be submitted to the magazines in the name of the Northwestern University Math Problem Solving Group.
		Ideally we should try to solve at least one problem from each issue and submit it to the magazine before the deadline.
		Problems from magazines like the American Mathematical Monthly are traditionally (but not always) harder than the ones proposed in the magazines mentioned above.
	www.math.northwestern.edu /~mlerma/problem_solving (812 words)

	Kinematic Equations and Problem-Solving
		The use of this problem-solving strategy in the solution of the following problem is modeled in Examples A and B below.
		The solution to this problem begins by the construction of an informative diagram of the physical situation.
		The two example problems above illustrate how the kinematic equations can be combined with a simple problem-solving strategy to predict unknown motion parameters for a moving object.
	www.glenbrook.k12.il.us /gbssci/phys/Class/1DKin/U1L6b.html (1101 words)

	Problem Solving
		Problems are things which you can change - obstacles to be overcome, challenges to meet.
		If you are defining a fact as a problem you are simply setting yourself up for a mountain of frustration.
		The other major advantage of outcome definition is that it's crucial to the planning stage of problem solving.
	www.mental-health-today.com /articles/problem.htm (1206 words)

	Amazon.com: Problem Solving: Books: Marty Marten (Site not responding. Last check: 2007-10-03)
		Chapters include common ground-handling problems such as being hard to catch and pulling back when tied, typical riding problems such as spooking and crossing water and the solutions to the ever-common problem of trailer loading.
		Therefore, all problems lead back to building or rebuilding a stronger foundation, both on the ground and in the saddle.
		Problem Solving, Volume 2 is a continuation of Marty Marten's popular first book on solving common horse behavior problems both in the saddle and on the ground.
	www.amazon.com /Problem-Solving-Marty-Marten/dp/0911647430 (1411 words)

	EMAT 4600/6600 Page
		This is the web site page devoted to EMAT 4600/6600 Problem Solving in Mathematics, at the University of Georgia, as led by Jim Wilson.
		This is a paper on the development and demonstration of Heron's formula for the area of a triangle given the lengths of its three sides.
		Problems and explorations are included for using Heron's formula.
	jwilson.coe.uga.edu /emt725/EMT725.html (397 words)

	Evaluating the National Outcomes: Youth--Social Competencies; Problem Solving
		Since many of these interpersonal relationship problems differ from those of childhood and thus, are essentially being encountered for the first time, they can bring with them a measure of personal difficulty and self-consciousness (Christoff, et.
		They contend that research concerned primarily with methods and knowledge acquisition is incomplete because the processes used when solving a problem may depend both on the characteristics of the problem and on the knowledge possessed by the problem-solver.
		Additionally, programs and practitioners have approached problem solving from a variety of context problem areas such as shyness (Christoff, Scott, Kelley, Schlundt, Baer, and Kelly, 1985), suicide (McLeavy, Daly, Ludgate, and Murray, 1994), delinquent behaviors (Leadbeater, Hellner, Allen, and Aber, 1989), acculturation (Garcia-Vazquez and Ehley, 1994), and gender differences (Murray and Ross, 1987).
	ag.arizona.edu /fcs/cyfernet/nowg/sc_problem.html (543 words)

	mezzoblue § CSS Problem-Solving
		To that end, the CSS Crib Sheet was meant to aid the process of debugging, and it covers a few points, but I realized this morning that there are some tricks I use to diagnose a problem that don’t show up on any resource guides.
		One of the biggest problems I’ve faced is visualizing what exactly is happening, and why.
		Reduce and isolate the problem as much as you can, to make sure other elements aren’t having a deleterious effect.
	www.mezzoblue.com /archives/2004/03/10/css_problems (664 words)

	Problem Solving
		There are many approaches to problem solving, depending on the nature of the problem and the people involved in the problem.
		The more traditional, rational approach is typically used and involves, eg, clarifying description of the problem, analyzing causes, identifying alternatives, assessing each alternative, choosing one, implementing it, and evaluating whether the problem was solved or not.
		The activities of problem solving and decision making are closely intertwined, so the reader will often find mention of the two topics together.
	www.managementhelp.org /prsn_prd/prob_slv.htm (298 words)

	TIP: Concepts (Site not responding. Last check: 2007-10-03)
		Theories of problem-solving are dominated by the work of Newell and Simon on GPS (General Problem Solver).
		The Gestalt psychologist Wertheimer also conducted research on problem-solving and emphasized the importance of understanding the structure (i.e., the relationship among parts) of the problem.
		The issue of transfer is highly relevant to problem solving.
	tip.psychology.org /problem.html (246 words)

	21st Century Problem Solving - Home Page
		Reliable problem solving in all subjects that use mathematics for problem solving.
		The problem solving processes used on this site are based use of the mathematical processes that have been developed over the past several thousand years.
		This serves to replace the plethora of artificial problem solving schemes currently in use with methods that are appropriate to the 21st century.
	www.hawaii.edu /suremath/home1.html (149 words)

	The Math Forum - Math Library - Problem-Solving
		Pages on Word Problem Solving Strategies explore multiple step problems logical reasoning, choosing a calculation method, problems with more than one answer, deciding when to estimate, using data from a chart, and more.
		Examples of problems solved using reliable problem solving methods; discussion of the principles of reliable problem solving; a FAQ; and an evolving encyclopedia of solved problems in mathematics, physics, and chemistry.
		Self-scoring problems, new with every click, to gauge a student's preparedness for college level math: operations, solving for a variable, solving linear equations, word problems, solving absolute value equations, solving inequalities, distance between...more>>
	mathforum.org /library/topics/problem_solving (2013 words)

	PCMI Problem Solving Resources
		Francis Su ran a problem session called The Extreme Principle on analyzing problems by considering extreme cases.
		Here is a problem set on induction and the latex source file.
		Problems are handed out each week and the students are expected to have worked at least one problem and to be ready to present it in class.
	www.math.hmc.edu /~ajb/PCMI/problem_solve.html (694 words)

	Ole Miss Problem of the Week Contests (Site not responding. Last check: 2007-10-03)
		The Problem of the Week is an educational web site that originates at the University of Mississippi.
		All the prizes are generously donated by CASIO electronics.
		All contest winners are chosen randomly from the pool of contestants that successfully solve that week's problem.
	www.olemiss.edu /mathed/problem.htm (43 words)

	UMUC-Verizon Virtual Resource Site -- Module 1: Examples of Problem Solving
		This site demonstrates how the massing of sources used in traditional archival research may be used in an online environment to stimulate historical interpretation, problem solving, and the formulation of questions about evidence and context.
		This assignment, undertaken as part of an Arctic Circle series on social equity and environmental justice, asks students to form teams and analyze a U.S. Army and Navy project using radio waves to enhance military communications and surveillance systems.
		More specifically, the assignment asks students to understand the range of problems raised by HAARP by breaking them first into smaller, manageable units, then viewing all the issues with greater understanding, and finally writing a position paper.
	www.umuc.edu /virtualteaching/module1/problems.html (702 words)

	The Center for Court Innovation - Problem-Solving Justice
		Today, there are literally thousands of problem-solving courts that are testing new approaches to difficult cases where social, human and legal problems intersect.
		For all of their diversity, these emerging court models share some unifying principles—starting with their problem-solving orientation.
		With no extra funds, in 1995 the court began to identify defendants’ social problems and link them to needed services.
	www.problem-solvingcourts.org (341 words)

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