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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 - 46 items found, showing 1 to 46

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>> 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>> 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>> 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>> Helping with Homework - Math Forum, Teacher2Teacher FAQ Answers to a frequently asked question: How can I help my child with math homework? ...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>> 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>> 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>> 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>> 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 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>> 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>> The Nuffield Foundation Math teaching and learning resources include freely downloadable Free-standing Mathematics Activities (FSMAs) and Applying Mathematical Processes (AMP) activities, a mix of investigations and practical explorations. The Nuffield Foundation works to improve ...more>> Off The Hypotenuse - Glenn Kenyon Kenyon started this blog in pursuit of "a good discussion of resources, ideas, and innovative ideas for teachers of Algebra." Humorous videos, comic strips, and posts, which date back to March of 2007, have included "Math Lessons learned from Karate," ...more>> Open-Ended Assessment in Math - Cooney, Thomas J.; Sanchez, Wendy B.; Leatham, Keith; and Mewborn, Denise S. Over 450 open-ended, field-tested assessment items, distributed more or less equally among elementary, middle school, and high school grade levels. The questions relate to five major content areas, based on the NCTM Standards: number and operation; probability ...more>> Open-Ended Math Problems - Gwenn Holtz and Mary Lee Malen, Levering School and the Franklin Institute An eight-month slate of open-ended problems for middle school students to solve in preparation for standardized testing. The authors have composed and selected problems that lend themselves to multiple solution paths, and then organized them into three ...more>> Place-Value: Problem-Solving and Written Assessment Using Digit-Correspondence Tasks - Ross, Sunflower This study examined the effects of researcher-developed lessons on students' understanding of two- and three-digit numeration. Digit-correspondence tasks, often used for individual interview assessment of place value understanding, were adapted to be ...more>> Potent Problems - Institute for Studies in Educational Mathematics A database of problems that deepen understanding of mathematics through multiple answers, approaches to an answer, interpretations, extensions, perspectives on a mathematical idea, layers of complexity, or algorithms. Potent problem content topics include ...more>> Problems of the Week - Math Forum @ Drexel Our goal with the Problems of the Week is to engage students in non-routine, constructed-response mathematics investigations that integrate writing with problem solving in the math classroom. In addition to the Current PoWs and the Problems of the Week ...more>> Problem Solving Island - Samuel A. Rebelsky Challenging open-ended word problems on the topics of games, such as Blockade, Finger Multiplication, and The Word Pyramid; puzzles such as Error Correction, Error Detection, The Fake Coin, Friday the 13th, and Leap Birthdays; and problems based on figures, ...more>> PROMYS: The Program in Mathematics for Young Scientists - Boston University Department of Mathematics and Statistics PROMYS encourages ambitious high school students to explore the creative world of mathematics. Each summer, approximately 60 high school students from around the country gather on the campus of Boston University for six weeks of rigorous mathematical ...more>> Rich Maths Tasks to Engage - East Midlands Maths Network These teacher-made rich maths tasks in number, algebra, shape, and data handling emerged from a collaborative project run by Jon Stratford, Lead Practitioner for the Specialist Schools and Academies Trust (SSAT): arrangements, clock face, chocolate dilemma, ...more>> Rich Starting Points for A-Level Core Mathematics - Jonny Griffiths Download PDF task files of 40 open-ended investigative activities for the A Level Pure Mathematics classroom: basic algebra, coordinate geometry, polynomials, curve sketching, uncertainty and inequalities, indices and surds, sequences and series, differentiation, ...more>> Seedbed - Tom O'Brien, ed. Throughout the 1980s, Seedbed published articles on "the intellectual growth of children, and teachers' participation therein." Editor Tom O'Brien described the publication as a practical one, "where teachers are the principal authors and where teachers' ...more>> Suffolkmaths.co.uk - Mark Greenaway Greenaway hosts a select collection of third-party resources in the public domain, many drawn from the UK's Department for Education (DfEs): teaching materials for Great Britain's different grade levels; problem solving documents on problem-solving strategies, ...more>> Teaching Resources: Mathematics - McGraw-Hill School Division Activities and lesson plans for grades 1-6, linked to McGraw-Hill's program Math in my World; also MathTalk - conversations about key issues and teaching strategies (e.g. cultural diversity; manipulatives; technology; problem solving); and "Ask CyberScout!" ...more>> Tools for Understanding - John Woodward; University of Puget Sound A resource guide for extending mathematical understanding in secondary schools, for educators who teach mathematics and are interested in integrating common technologies into their daily instruction. Onsite strands (Math Concepts with lessons related ...more>> Topics in Arithmetic and Elementary Mathematics - E. Lee Lady; University of Hawaii Materials used in a university course for prospective elementary school teachers, to teach them how to be interested in mathematics. Materials are in PDF and DVI, and include: representing numbers in other bases, divisibility tests, periodic decimal expansions, ...more>> UBUYACAR - Maricopa Center for Learning and Instruction An online problem-based learning manual for students that poses the question: "You are interested in purchasing a new vehicle. What should your annual salary be to afford the car you want?" Students move through a problem-solving process. A Tutor's Manual ...more>> What Does It Take to Be an Expert Problem Solver? - Annie and John Selden; Mathematical Association of America Organized into five sections: Expert-Novice Studies Have Often Concentrated on Textbook Problems; Solving Nonroutine Problems; Are Mathematicians Expert Problem Solvers? How Might One Teach Problem Solving? and The Importance of Affect. From the MAA's ...more>> Where to Start? - Cut the Knot!, Alexander Bogomolny A discussion of math education: the intent of the NCTM Standards, reflections on the history of constructivism, classroom practices (with a link to Marilyn Burns' Math Solutions page), and a simple applet for solving linear equations. An interactive column ...more>>

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