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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>> 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>> 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>> 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>> 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>>

All Sites - 83 items found, showing 1 to 50

Andrew M.H. Alexander JavaScript by Alexander includes "the gear seer," which shows not just bike gear ratios but gear inches and meters development. Input wheel and tire size to see speed at a given cadence. This bicycle drivetrain visualizer further compares different drivetrains, ...more>> Arbelos Internet Math Society - Bert Liberi and William F. Widulski, Westchester Communtiy College A mathematics society dedicated to the pursuit of elegance in problem-solving. Every month, solve challenging problems that require "more imagination than memorization." Also, access old problems and solutions; and study a list of heuristics of problem-solving, ...more>> The Benezet Centre - Richard Hake & Sanjoy Mahajan In 1929, Louis Benezet tried an experiment, "abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite." The experiment was successful; this site includes Benezet's ...more>> Bowland Maths - Bowland Charitable Trust Case study problems and lessons designed to develop thinking, reasoning and problem solving skills in UK math pupils ages 11-14. In particular, download series of stand-alone assessment items that challenge students to estimate the number of descendants ...more>> Brain Science & ICT in Mathematics Education - Dave Moursund An exploration of three major topics from a math education point of view: Brain Science Craft & Science of Teaching & Learning (C&S of T&L) Information & Communications Technology (ICT). Read the author's thoughts on constructivism, ...more>> Bridging The Gap - Nicora Placa Blog by a former elementary and middle school math teacher pursuing a Ph.D. in teaching and learning. Posts, which date back to April, 2013, have included "The subway ad that changed my life," "Transforming the Teaching Profession: It starts with RESPECT," ...more>> Casting out Nines - Robert Talbert, The Chronicle of Higher Education Blog from The Chronicle "where math, technology, and education cross." Posts, which date back to December, 2005, have included "Inside the liberal arts math course," "Not to be a calculus heretic or anything, but...," "A taste of Tufte," "A proposal about ...more>> Classic Fallacies - Philip Spencer; University of Toronto Mathematics Network Mathematical "proofs" demonstrating, among other things, that 1 = 2 and that all people in Canada are the same age. Each consists of several steps, and users search for the flaws. For every step there is explanation of why the flaw is or is not in that ...more>> cognitive acceleration - Cognitive Acceleration Associates Cognitive acceleration (CA) emphasizes "'big ideas' or organizing conceptual strands in mathematics, rather than procedures and algorithms." Published collections of math lessons include Thinking Maths, Primary Cognitive Acceleration through Maths Education, ...more>> Common Mistakes in College Mathematics - Eric Schechter Pointers for students about mistakes in general mathematics and calculus. Errors include: everything is additive, loss of invisible parentheses, incorrect writing of fractions, derivative of x to the x, unbalanced differentials, and naive answers for ...more>> The Cow in the Classroom - Ivars Peterson (MathLand) Math Curse by Jon Scieszka and Lane Smith spoofs the types of word problems that educators and textbook writers invent to dress up arithmetic exercises and, supposedly, to demonstrate the relevance of math to everyday life. Canadian economist and humorist ...more>> Department of Science & Mathematics Education: Research and Development - Univ. of Melbourne, Australia Read faculty research and learn about their projects and interests: children's understanding of statistical and probabilistic concepts; the negotiation of meaning in mathematics & science classrooms (The Classroom Project); the expression of algorithms ...more>> Drawing on Math - Tina Cardone Blog by a public high school math teacher in Massachusetts who has participated in Boston University's PROMYS and the Institute of Advanced Studies' PCMI. Posts, which date back to August, 2011, have included "End of Year Reflections: Geometry Favorite ...more>> Educational Aspirations "Ramblings from a 21st century educator" who specializes in differentiating math and seeks to make the subject "more engaging and relevant to students' lives." Blog posts, which date back to July, 2011, have included "Measuring Student Growth," "Twitter ...more>> The Educational Gaming Environments group (EdGE) - TERC "At the forefront of the 'Games for Good' and 'Serious Games' movements," this research design and development team investigates game-based learning environments. Funded in part by the National Science Foundation (NSF), EdGE supports and measures engagement ...more>> EduSoft: Education for Excellence - EduSoft Ltd. EduSoft develops and markets multimedia educational titles, with programs in over 20 different languages grouped in four major product lines: English Learning, Early Learning, Math & Science, [Every Day Mathematics - Problem Solving Courseware] ...more>> Finding Ways to Nguyen Students Over - Fawn Nguyen Nguyen blogs mostly about her teaching middle school math. Posts, which date back to November, 2011, have included "Teaching 101 -- How I Got Like This," "Puzzles and Brainteasers, Set 11," "Pi Day Activities," "Always Sometimes Never," "Using Excel for ...more>> Focus on Student Practice - Suzanne Alejandre Article about how students worked on the Problem of the Week (PoW) "Wooden Legs" in a way that developed the Common Core State Standards (CCSS) Mathematical Practice of "making sense of problems and persevering in solving them." This article, originally ...more>> Future of Math - Jamie Tubbs This site supports the use of blogs, digital cameras, digital portfolios, discussion forums, spreadsheets, and other digital media to enhance student understanding of mathematics. Find suggestions on how to teach with journals, problem-solving, learning ...more>> Harold Reiter's Home Page - Harold Reiter, Department of Mathematics, University of North Carolina at Charlotte Freely downloadable puzzles and problems from the founder of teachers circles and math clubs in Charlotte and Mecklenburg, longtime writer of MathCOUNTS questions, and member of the ETS/College Board CLEP (College-Level Examination Program) Pre-calculus ...more>> Helping with Homework - Math Forum, Teacher2Teacher FAQ Answers to a frequently asked question: How can I help my child with math homework? ...more>> I Choose Math - Justin Lanier Blog by a high school teacher in Brooklyn Heights. Posts, which date back to August, 2011, have included "SBG: Affective Quizzing," "Free-Choice Time: Origins," "Introducing Proof Using Formal Systems," and "Math is Personal: A smOOC about Meaning, Sharing, ...more>> Infinite Sums - Claydon Blog by a high school math teacher in Houston, Texas, who "decided the corporate engineering world was not for me, so now I joke around with teenagers and teach them math. And soccer." Posts, which date back to June, 2011, have included "Standards Based ...more>> Inquiry maths - Blair, Andrew; and Martin, Caitriona Inquiry prompts for topics related to number, algebra, and shape to use in secondary school mathematics. Accompanying notes support teachers who "want to make their lessons more open and, thereby, encourage student independence and leadership." ...more>> The Insight Method of Teaching Math - Robert Frick How and why to teach math via mental models, as articulated by a cognitive psychologist who describes the "learning is memory" approach as "a disaster and a tragedy." See, in particular, Frick's sample problems: reverse arithmetic, expressing patterns, ...more>> Interactive Mathematics Miscellany and Puzzles - Alexander Bogomolny "The peculiar beauty of Mathematics lies in deduction, in the dependency of one fact upon another. The less expected a dependency is, the simpler the facts on which the deduction is based - the more beautiful is the result." This award-winning site offers ...more>> Interactive Mathematics Program (IMP) - Key Curriculum Press A four-year integrated problem-based secondary mathematics curriculum and professional development program for teachers that meets college entrance requirements and prepares students to use problem-solving skills in further education and on the job. Information ...more>> Jo Boaler From the author of What's Math Got to Do with It?: How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject. Watch a YouTube clip of Boaler teach using Inquiry Based Learning method, or click through her presentation entitled ...more>> John Mason's Projects - John Mason Projects by the author of Thinking Mathematically and former director of the Centre for Mathematics Education: Structured Variation Grids and other animations and applets; studies in algebraic thinking; mathematical explorations; MEMEs (Meaning Enquiry ...more>> Joy of Problem Solving - Deepak Kulkarni Math olympiad programs for elementary and middle school kids by a Ph. D. in computer science and former NASA researcher. See, in particular, the section of Kulkarni's site entitled "How to Work on Problems," which includes essays such as Problem Solving ...more>> Kangaroo Maths - Kangaroo Maths Ltd Free maths resources to download in number, algebra, shape and space, and data handling. Assessments include homework sheets and "make the grade" tests; games and puzzles offer World Cup spreadsheet simulations. Kangaroo Maths also hosts Microsoft Word ...more>> langer.kogut.math "One year, two math teachers in Boston decided to throw everything out the window and start from first principles. Here's what happened...." Blog posts, which date back to March, 2013, have included "An Illustrative Example -- Version Kogs/Whole Child" ...more>> Learning to Learn: Problem Solving - Greg Gay, Learning Disabilities Resource Community (LDRC), University of Toronto Find out about your learning style by solving challenging arithmetic, logic, and mathematical story problems. Puzzles include analogy exercises which reveal our abilities to infer, map meaning, classify, and alter knowledge in the face of novel learning; ...more>> The Legacy of R. L. Moore - Educational Advancement Foundation The Legacy of R.L. Moore Project promotes the study of inquiry-based learning (IBL) and teaching methods that Moore propagated while teaching topology at The University of Texas. The "Moore Method" eschews textbooks; calls for only the briefest of lectures ...more>> Making Learning Real - Nashville State Technical Community College and WGBH Educational Foundatio Videos, professional development, and other resources for teachers already teaching Problem-Based Case Learning (PBCL) or considering such instruction grounded in real-time workplace situations. PDFs available for free download include a Need to Know ...more>> Math and Problem-Solving - Dan Rosard This site offers help with procedures, particularly in areas which have been observed to cause problems to some students; and unstructured problems with clues and questions. The first problem attempts to emulate the thinking used in the development of ...more>> MATHCOUNTS - MATHCOUNTS Foundation A national math coaching and competition program that promotes 7th and 8th grade math achievement through grass-roots involvement in every U.S. state and several territories. At the beginning of each school year, the MATHCOUNTS Foundation distributes, ...more>> MathEd.net - Raymond C. Johnson Blog begun in October, 2009, by a math education graduate student. Dedicated to "building bridges between research, policy, and practice," Johnson's posts have included "Patterns of Patterns," "RYSK: Erlwanger's Benny's Conception of Rules and Answers ...more>> Mathematics and Biology - Cut the Knot!, Alexander Bogomolny A discussion of evolution, inheritance, genes and mutation, the Prisoners' Dilemma, and how these and other biological themes relate to mathematics, with an applet that applies a genetic algorithm to solving the Toads and Frogs puzzle. An interactive ...more>> Mathematics - WestEd Descriptions of WestEd's Science and Mathematics Projects, with supporting print and online resources: 24® Game Demonstration Project, California Mathematics Implementation Study, Evaluation of Interactive Multi-Media Exercises (IMMEX), Evaluation: ...more>> Math in Everyday Situations (Learning and Mathematics) - Richard Lesh; Math Forum In his 1985 article, "Processes, skills, and abilities needed to use mathematics in everyday situations," Dick Lesh, of the Educational Testing Service (ETS) in Princeton, New Jersey, writes that if students are provided with everyday situations for practicing ...more>> Math Minds - Thornburg, Nancy; and Gray, Kristin Blog by K-5 math specialists, one Nationally Board Certified in Early Childhood, the other in Middle Childhood. Thornburg and Gray teach Intensive RTI groups and enrichment groups in grades K-5 daily. Posts, which date back to April, 2013, have included ...more>> MathPro Press - Stanley Rabinowitz MathPro Press specializes in the publication of compendiums and indexes of mathematics problems. Purchase MathPro Press books of problems from math olympiads and contests. Link to math competition web sites; or browse a bibliography of books of problems ...more>> Math Reasoning Inventory - Scholastic An online formative assessment tool for the Common Core State Standards (CCSS) math domains of number and operations. Watch Math Reasoning Inventory (MRI) clips of face-to-face interviews of students as they reason and explain their strategies, demonstrate ...more>> Maths? No Fear! - Matt Skoss Wiki for sharing practical ideas that engage kids in working as a mathematician, strategies for using Web 2.0 tools, and more. Become a member to access notes and other resources on the structure of maths tasks, problem solving, and more. ...more>> Math Thinking - David Wees "Sharing thinking about math from students": a collection of work by students that teachers have not taught them explicitly how to do. Wees elaborates that "the idea or technique a student uses does not itself have to be completely original, just new ...more>> Math Towers - Dr. Geoff Roulet, Queen's University Math-towers.ca is a website where groups of Grades 7 and 8 students can collaboratively explore open-ended mathematics problems. Students are presented with a problem context and provided with a laboratory, interactive tools and recording space to support ...more>> Mathy McMatherson - Daniel Schneider Blog by a public high school teacher in Tucson, Arizona, who graduated from the University of Arizona Secondary Mathematics Education Program. Posts, which date back to July, 2011, have included "Teaching as Creation," "Fixing Bugs Part 2: Algebra & ...more>> The NASA SCIence Files - NASA Langley Research Center A series of free instructional programs consisting of a broadcast, print, and online elements. Emphasizing standards-based instruction and problem-based learning, the NASA Sci Files motivate students in grades 3-5 to become critical thinkers and problem ...more>> The National Numeracy Strategy - Department for Education and Employment, United Kingdom The Standards Site: Numeracy. Frameworks for teaching mathematics from Reception through Year 7, key elements of the training materials that will support the U.K.'s Numeracy Strategy. Assessment in and planning the National Numeracy Strategy, schools ...more>>

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