Selected Sites   (see also All Sites in this category)

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>> Searching for Solutions - Judy Campf A Web-based unit that introduces students to strategies and real-life practice activities for applying problem-solving skills. Individual lesson activities are grouped under: finding a pattern; reading and making a table; making an organized list; using a graph; drawing a diagram; choosing an operation/multi-step problems; working backward; and solving a simpler problem. Real-life applications provide problem-solving opportunities for students. Includes a rubric for evaluating the final independent activities, and a list of relevant sites on the Web. more>>

All Sites - 41 items found, showing 1 to 41

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>> 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>> 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>> Evaluation Update: IMP Students Demonstrate High Achievement - Interactive Mathematics Program (IMP), Key Curriculum Press Studies Target 21st Century Skills and Needs: The development of the Interactive Mathematics Program (IMP) parallels many important changes taking place in the American workplace. Computers and calculators are now considered part of our basic tool kit. ...more>> Everyday Learning - Everyday Learning Corporation Mathematics curricula for elementary, middle, and high school that emphasize problem-solving skills. Includes newsletters for elementary and secondary teachers with articles about specific curricula and general classroom approaches. Curricula include: ...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>> Hispanic and Anglo Students' Misconceptions in Mathematics (ERIC Digest) - Jose Mestre "[M]any students have misconceptions about mathematics -- sometimes called "naive theories' -- that can turn them into clumsy learners. This digest describes misconceptions in math -- what causes them and why they interfere with learning. Next it considers ...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>> 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>> Making Mathematics Work for All Children: Issues of Standards, Testing, and Equity - Alan H. Schoenfeld, University of California, Berkeley "To fail children in mathematics, or to let mathematics fail them, is to close off an important means of access to society's resources." This article discusses the potential for providing high quality mathematics instruction for all students. Sections ...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>> 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>> 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>> The Pathways of Math's Ways - Mel Levine A short essay examining some of the challenges to thinking with numbers, given differences in learning. Paragraphs provide helpful hints for knowing what you're doing; remembering what to do; becoming a good problem solver; and taming math. With 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>> Problem Isomorphism - Michael J. Capps, Radford University Three different problems -- one each from geometry, arithmetic, and combinatorics -- lead to the "same" solution, the sequence of Catalan numbers. The author presents the problems, mathematical opportunities, triangulation solutions, path negotiating ...more>> Problem Solving In Mathematics - Chuck Peterson Thirty problems for each of the five problem solving strategies of guess and check, look for a pattern, make a systematic list, make a drawing or model, simplify the problem. ...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>> Teacher Radio Past Programs - Math - Scholastic, Inc. Listen to Marilyn Burns RealAudio files: Multiplication Facts; Teaching Math in 1st or 5th Grades; Math Basics and Number Sense; Teaching Manipulatives; Math & Writing; Literature & Math; Making the Parent Connection; Understanding Math Standards; ...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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