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Home : Math Ed Topics : Teaching Issues/Strats : General Approaches : Problem-Solving

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  Selected Sites   (see also All Sites in this category)

  1. Common-Sense Questions (Learning and Mathematics) - G. Polya; Math Forum
    In his 1957 book, How to solve it, Polya describes a four-stage approach to mathematical problem-solving. He bases his approach on common-sense questions that would naturally occur to an experienced problem-solver. Polya claims teachers should pose these questions to students in as natural and unobtrusive a way as possible, the goal being to encourage independence and internalization of this framework. A geometry.pre-college newsgroup discussion. more>>

  2. Don Knuth's Home Page - Donald E. Knuth, Stanford University
    From the author of The Art of Computer Programming. "Computer Musings" chronologically documents Knuth's informal lectures at Stanford. It also links to Musings Online, digitized versions of videos from the lecture series that included Dancing Links; The Joy of Asymptotics; Bubblesort at random (one-dimensional particle physics); Finding all spanning trees; Trees, Forests, and Polyominoes; and Mathematical Writing (1987). See, in particular, "The 'Aha' sessions," over 25 hours of graduate CS students tackling five previously unsolved programming problems in number theory, code-breaking (cryptagrams), high-speed chip testing, distributed control, and computer graphics (a self-portrait). "You could literally see the Aha taking place. People can watch the problem-solving process as it occurred." Frequently Asked Questions include "What's your favorite programming language?" and "Why do you pay $2.56 for every error found in your books?" and "Who will answer my questions about TeX?" Also, Knuth's recent news, preprints of recent papers, encapsulated PostScript graphics to download, and CWEB and other programs to download, featuring two demonstrations by different methods that exactly 2,432,932 knight's tours are unchanged by 180-degree rotation of the chessboard. more>>

  3. Problem Solving in Mathematics - Jim Wilson; Univ. of Georgia
    Problems in algebra, geometry, conversion, cryptarithm, "mean," trigonometry, and a mixture of all, many with comments and solutions, from a course given in the Dept. of Mathematics Education at the University of Georgia. The site also provides links to papers, including "Mathematical Problem Solving" (Wilson, Fernandez, & Hathaway), a synthesis of research on problem solving [published as ch. 4 in Wilson, P. S. (Ed.) (1993), Research Ideas for the Classroom: High School Mathematics, New York: MacMillan]. more>>

  4. Problem Solving Strategies - Finlay McQuade, Boğaziçi University (Turkey)
    Strategies for solving problems, each illustrated with sample math challenges and worked solutions: draw a diagram; make a list; guess and check; divide and conquer; look for a pattern; start at the end. Also available in Turkish. more>>

  5. Problems with a Point - Education Development Center, Inc. (EDC)
    A collection of problems designed to help students in grades 6-12 learn new mathematical ideas by building on old ones. Varying in difficulty and approaches, these problems are useful for teachers, students, parents, math clubs, home-schoolers, and others. Problems are classified by topic, time required, suggested technology, required mathematical background, and habits of mind that students develop or use as they work. Synopses of the problems are keyword searchable. Answers and solutions are provided, and many problems include hints. more>>


 

Mason error

 
component stack:   /library/branch.html
/library/dhandler
code stack:   /var/lib/mason/obj/library/branch.html:208
/usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Commands.pm:70
/var/lib/mason/obj/library/dhandler:90

debug info:   Debug file is '/var/lib/mason/debug/anon/5'.

raw_error





























raw error:
 






























error while executing /library/branch.html:
Server message number=1105 severity=17 state=4 line=1 text=Can't allocate space for object 'syslogs' in database 'catalog' because 'logsegment' segment is full/has no free extents. If you ran out of space in syslogs, dump the transaction log. Otherwise, use ALTER DATABASE or sp_extendsegment to increase size of the segment.
Statement=INSERT INTO keystorage ( keys ) VALUES ( '77047;77203;76317;19655;77205;77432;16904;77140;77708;75212;62456;76431;76118;77715;7438;75226;4290;76837;5009;77289;12606;77234;76322;77418;75980;76166;4848;76291;77356;76384;77014;66815;77057;77357;75452;166...
HTML::Mason::Interp::__ANON__('Server message number=1105 severity=17 state=4 line=1 text=Can\'...') called at /usr/lib/perl5/site_perl/5.6.0/Forum/Key.pm line 284
Forum::Key::store('Forum::Key=HASH(0x8ecd1c0)') called at /var/lib/mason/obj/library/branch.html line 208
HTML::Mason::Commands::__ANON__('passed_args', 'HASH(0x8e8729c)', 'tree', 'ed_topics', 'branch', 'methods_solving') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Component.pm line 131
HTML::Mason::Component::run('HTML::Mason::Component::FileBased=HASH(0x8f0473c)', 'passed_args', 'HASH(0x8e8729c)', 'tree', 'ed_topics', 'branch', 'methods_solving') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
HTML::Mason::Request::comp('HTML::Mason::Request::ApacheHandler=HASH(0x8e1b2f4)', '/library/branch.html', 'passed_args', 'HASH(0x8e8729c)', 'tree', 'ed_topics', 'branch', 'methods_solving') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Commands.pm line 70
HTML::Mason::Commands::mc_comp('/library/branch.html', 'passed_args', 'HASH(0x8e8729c)', 'tree', 'ed_topics', 'branch', 'methods_solving') called at /var/lib/mason/obj/library/dhandler line 90
HTML::Mason::Commands::__ANON__('start_at', 1, 'num_to_see', 50, 'keyid', 38312341) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Component.pm line 131
HTML::Mason::Component::run('HTML::Mason::Component::FileBased=HASH(0x8e68c00)', 'HTML::Mason::Component::FileBased=HASH(0x8e68c00)', 'HTML::Mason::Component::FileBased=HASH(0x8e68c00)', 'start_at', 1, 'num_to_see', 50, 'keyid', ...) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
HTML::Mason::Request::comp('HTML::Mason::Request::ApacheHandler=HASH(0x8e1b2f4)', 'HASH(0x8e61e90)', 'HTML::Mason::Component::FileBased=HASH(0x8e68c00)', 'start_at', 1, 'num_to_see', 50, 'keyid', ...) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 159
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 159
HTML::Mason::Request::exec('HTML::Mason::Request::ApacheHandler=HASH(0x8e1b2f4)', '/library/ed_topics/methods_solving', 'start_at', 1, 'num_to_see', 50, 'keyid', 38312341) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/ApacheHandler.pm line 914
HTML::Mason::ApacheHandler::handle_request_1('HTML::Mason::ApacheHandler=HASH(0x8de4734)', 'Apache=SCALAR(0x8e75a14)', 'HTML::Mason::Request::ApacheHandler=HASH(0x8e1b2f4)', 'HASH(0x8e2e080)') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/ApacheHandler.pm line 560
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/ApacheHandler.pm line 560
HTML::Mason::ApacheHandler::handle_request('HTML::Mason::ApacheHandler=HASH(0x8de4734)', 'Apache=SCALAR(0x8e75a14)') called at /etc/httpd/conf/handler.pl line 97
HTML::Mason::handler('Apache=SCALAR(0x8e75a14)') called at /dev/null line 0
require 0 called at /dev/null line 0