 Applications and Misapplications of Cognitive Psychology to Math Education  Anderson, Reder, Simon
A critical view of constructivism by three leading cognitive psychologists at Carnegie Mellon University. Decomposition and decontextualization; situated learning; constructivism; recommendations for research and instruction; overall conclusions; references.
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 APStatistics Dissertation  Kim Robinson, Clayton College & State University
A qualitative research study focused on students' learning and their performance on the Advanced Placement Exam with respect to conceptoriented instruction as recommended by the AP Statistics Test Development Committee. Organized into chapters, including
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 A B Cron Portal  Auston B. Cron
GeoGebra applets by a teacher who has taught high school and early college students since 1970, and uses his dynamic geometry animations and interactive sketches in his classes to teach angle sums; perimeters and areas of rectangles and squares; reference
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 BetterExplained  Kalid Azad
Discover and share the "intuitive insights that make complicated ideas simple. Our 'ahha!' moments are different, and that's ok. There's no single way to explain an idea...." Preferring the construction of maps over the memorization of directions, the
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 Beyond the IndividualSocial Antimony in Discussions of Piaget and Vygotsky  Cole, Wertsch
A discussion of the ongoing debate about the relation between the ideas of Vygotsky and Piaget, emphasizing a cardinal difference between them: their views concerning the importance of culture, in particular, the role of mediation of action through artifacts,
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 A Bibliography of Mathematics Education  Paul Ernest, University of Exeter, U.K.
A 1994 electronic bibliography prepared for students at the University of Exeter, U.K. Contents: Society, Diversity And Mathematics Education; The Learning Of Mathematical Topics; The Psychology Of Learning Mathematics; Teaching Approaches And Resources
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 Calculus, Concepts, Computers, and Cooperative Learning (C4L)  Ed Dubinsky, David Mathews, and Keith Schwingendorf
"Constructivist learning theory in practice," following six principles: research into student learning is critical; conceptual understanding is primary, but calculations play a major role; the good use of technology can be valuable; cooperative learning
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 Carousel Numbers. A Leadin to Number Theory  Gary Klatt; Univ. of Wisconsin  Whitewater; The Math Forum
A connected series of four problems in elementary number theory that are ideal for discovery learning at several levels. Each problem generates interesting questions and conjectures, and their surprising connections add interest and allow each to shed
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 Center for Inquiry Based Learning  University of Michigan
Promoting "the teaching and development of inquirybased learning in mathematics." See, in particular, the Center's descriptions of undergraduate math and math education courses.
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 Classroom Compass  Adams, Powell, Assoc. Editors; Southwest Educational Development Laboratory
A magazine published from 1994 to 2005, with ideas, activities, and resources for teachers interested in improving instruction in science and mathematics, and links to simple classroom activities with ideas about learning and instruction. Each issue presents
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 Constructivism and Mathematical Concepts  Pathways to School Improvement
A discussion of constructivism as it relates to teaching mathematics. A list of reflective questions for teachers and references is included.
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 Constructivism and the Five E's: The pH Factor  Miami Museum of Science
Constructivism is a philosophy about learning which proposes that learners need to build their own understanding of new ideas. To introduce the pH factor to students in a constructivist way, the Miami Museum of Science adapted their "Seven Es" (Excite,
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 Constructivism  Classroom Compass
The winter 1994 issue of Classroom Compass explores this theory of learning, including a brief literature summary and suggestions for the constructivist classroom. Two instructional activities (Which Container Holds the Most? for younger children and
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 Constructivism in mathematics education  what does it mean?  John and Annie Selden; The Math Forum
A presentation given at the Joint AMS/MAA Mathematics Meetings, January 1996, Orlando, Florida. Includes an annotated bibliography: Kinds of Constructivism.
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 Constructivism in Science and Mathematics Education  Michael R. Matthews
Matthews discusses constructivism, its scope and influence, and looks at the particular case of New Zealand, in this article from the 99th Yearbook of the National Society for the Study of Education.
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 Constructivism: Vygotsky and the Internet  Mathematics Education at The Math Forum
The ideas of Lev Semenovich Vygotsky have sparked considerable thought on the topic of constructivism. The Math Forum has collected a list of links to sites, projects, and articles about Vygotsky, constructivism, and the Internet, including comparisons
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 Constructivist Mathematics and Unicorns  Lee V. Stiff
The thenpresident of NCTM lays out distinctions among various forms of constructivism, and how they relate to the Principles and Standards, in this 2001 article.
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 A Constructivist View of Science Education  University of Massachusetts Physics Education Research Group (UMPERG)
Four premises of constructivism: knowledge is constructed, not transmitted; prior knowledge impacts the learning process; initial understanding is local, not global; and building useful knowledge structures requires effortful and purposeful activity;
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 Constructivist Views of Learning in Science and Mathematics (ERIC Digest)  Drew K. Ishii
An examination of constructivism and its implications for the classroom, with web and print resources for additional study.
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 Dave's Mathematics, Education, Philosophy and Chreods Server  Dave Wilson
Searchable math and mathematics education resources: an archive of preservice teachers' essays, the Teaching and Learning Enquiry Group, Chreods, a journal covering math education, and other writings.
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 Dipping math scores heat up debate over math teaching...  Bridget Murray, American Psychological Association (APA) Monitor
... psychologists differ over the merits of teaching children 'whole math'. An APA newsletter article that outlines the debate over the effectiveness of whole math, a demonstrative approach where manipulatives help children understand math concepts. "Some
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 Downloadable Articles, Papers & Materials  Michael de Villiers; Mathematics Education, Univ. of DurbanWestville, South Africa
Articles by Villiers related to geometry and geometry education some in PDF format, including: An Extended Classification of Quadrilaterals; A Mathematical Treasure Hunt; Place Kicking Locus in Rugby; Sketchpad Solutions and Results; A Dual, and Generalizations,
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 Epistemology and Learning Group  Massachusetts Institute of Technology (MIT)
Constructionism asserts that knowledge is not simply transmitted from teacher to student, but is actively constructed by the mind of the learner, and that learners are particularly likely to create new ideas when they are actively engaged in making external
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 The Euclid Project  Dr. Robert E. Mason IV, The Dalton School
Description of a math program that uses visualization, analysis, informal deduction, and formal deduction to engage students in the study of geometry in an integrated manner. For example, a 7th Grade Geometer's Assignment on circles uses the Geometer's
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 Excel Math  Brad Baker, Janice Raymond, et al.
A curriculum that presents math in a spiraling fashion for kindergarten through sixth grade students. Features include selfcorrection through Excel Math's CheckAnswer system, which allows students to check their own work. Download a sample packet or
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 From Constructivism to Active Learning  Siegfried M. Holzer
Summary of an essay defining constructivism and outlining its implications for education: active learning, authentic activities, students' views, authentic assessment, and innovative curriculum. Published in the hypermedia publication of SUCCEED: The
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 The handling of geometry definitions in school textbooks  Michael de Villiers; Mathematics Education, Univ. of DurbanWestville, South Africa
Some historical background and a discussion of the value of students constructing their own understanding of mathematical proofs; misconceptions that arise from readymade definitions; and the advantage of a constructivist approach, which allows pupils
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 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."
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 John Pais' Teaching Portfolio
Helping students do math visually  from the St. Louis College of Pharmacy (STLCOP). An approach that seeks to refocus and reprioritize the learning goals of traditional precalculus and calculus courses, in order to make the material appealing and useful
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 Kinds of Constructivism: An Annotated Bibliography  Annie & John Selden; The Math Forum
A bibliography prepared by Annie and John Selden as a supplement to "Constructivism in Mathematics Education  What Does It Mean?"  a talk they gave at the 1996 Joint Mathematics Meetings in Orlando, Florida.
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 Lev Semenovich Vygotsky Centennial Project  A.J. Lock, Dept. of Psychology, Massey University, New Zealand
A 1996 site cataloguing resources on Lev Semenovich Vygotsky (18961934), marking the centenary of Vygotsky's birth by setting up the equivalent of a Web conference on his opus. The site invites people to submit a piece of around 1000 words as comments
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 The Logo Foundation
A nonprofit educational organization devoted to informing people about Logo and supporting them in their use of Logobased software and learning environments. The site includes links for workshops and seminars; books and videos; Logo software (at discount
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 Math Education References (NCREL)  Pathways to School Improvement
A list of references relating to an article on constructivism, "Providing HandsOn, MindsOn, and Authentic Learning Experiences in Mathematics." From the North Central Regional Educational Laboratory (NCREL).
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 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
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 Mathematics in the City  The City College of New York
A national center of professional development for K8 mathematics education where "context, representation, and discourse are critical to learning." See, in particular, the summer institutes, workshops, and other professional development opportunities
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 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 MultiMedia Exercises (IMMEX), Evaluation:
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 Mathetics (Learning and Mathematics)  Seymour Papert; Math Forum
In Chapters 5, 6, and 7 of his 1993 book, The Children's Machine, Papert examines the art of learning, a topic that he contends has been widely ignored by educational researchers and practitioners. In Chapter 5 he introduces the concept of 'mathetics',
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 Mathwire.com  Terry Kawas
Standardsbased activities and worksheets that support a constructivist approach to learning mathematics. Browse resources by NCTM standard or math topic, which include enrichment topics, glyphs, instructional strategies, morning math routines, seasonal
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 MicroWorlds In Action  OpenWorld Learning
MicroWorlds Logo resources: folders of themerelated MW projects of
increasing difficulty, with minilessons and extension activities. FAQ,
activity cards, vocabulary. Children or adults can learn programming in a
flexible, constructivist fashion.
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 Midwest Consortium for Mathematics and Science Education (MSC)  North Central Regional Educational Laboratory (NCREL)
A resource for mathematics and science instructional materials that provides direct technical assistance to state education agencies, intermediate state educational units, and local school districts. Activities reflect a commitment to learning based on
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 NCTM San Diego Sessions on Constructivism  Mathematics Education at the Math Forum
A selection of presentations from the 74th Annual NCTM Meeting, 2528 April 1996, San Diego, CA.
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 Orlando Sessions on Constructivism  The Math Forum
The 1996 AMS/MAA Joint Mathematics Meetings in Orlando, Florida featured presentations on constructivism. The goal: to disseminate innovative, successfully classtested pedagogical theoretical view of how mathematics is learned.
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 Providing HandsOn, MindsOn, and Authentic Learning Experiences in Mathematics (NCREL)  Cathy Cook; Pathways to School Improvement
A linked essay giving overview, background, and issues around constructivist theory and its implementation. "When educators begin to see learning as knowledge construction, they change their thinking about curriculum, instruction, and assessment, developing
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 Report to the President on the Use of Technology to Strengthen K12 Education in the United States, March 1997  President's Committee on Science and Technology
A paper by the Panel on Educational Technology. Sections include: Introduction; Potential Significance; Hardware and Infrastructure; Software, Content and Pedagogy; Teachers and Technology; Economic Considerations; Equitable Access; Research and Evaluation;
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 Resources for Teachers  Lawrence Hall of Science (LHS)
The LHS at the Univ. of California at Berkeley has been a pioneer in precollege science and mathematics programs that emphasize the "learning by doing" approach, offering many different types of educational programs for all ages. Each of the Lawrence
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 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'
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 Teachers Becoming SelfDirected Learners: A Work in Progress  Horwitz, Hallam; Eisenhower National Clearinghouse
How the Annenberg Tuning Protocol is used by the PennMerck Collaborative for Science Education to foster a constructivist view of learning with reflective, internally motivated practitioners. The program involves a 13month graduate course designed to
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 Teaching & Learning Perspective: Constructivism  John Pais
Communicating Mathematics Using Heterogeneous Language and Reasoning. Mathematics is the science of patterns... Precisely how humans accomplish selforganization is still essentially unknown, but nevertheless has important consequences for structuring
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 To teach definitions in geometry or teach to define?  Michael de Villiers; Mathematics Education, Univ. of DurbanWestville, South Africa
This paper argues from a theoretical standpoint that students should be actively
engaged in the defining of geometric concepts like the quadrilaterals, and
presents some data relating to a teaching experiment aimed at developing
students' ability to
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 Two Points of View  Tom O'Brien
"Children are not stones or recording devices. They are, first of all, sensemakers." In summarizing his work with practicing teachers on the four basic operations, the author responds to H. H. Wu's article, "What's Sophisticated about Elementary Mathematics?"
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