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4434Mathematical Visualization Toolkit
http://www.merlot.org/merlot/viewMaterial.htm?id=89767
This site consists of a collection of plotting and solving applets featuring a uniform user interface. This site was selected as the 2005 MERLOT Classics Award winner for the Mathematics discipline due to its value and effectiveness as a set of teaching/learning tools. Visualizing mathematical concepts, especially in three-dimensional space, can be quite difficult for students. These tools and applications enable students to see the concepts in action and to come a deeper understanding of the underlying mathematics. In addition, the collaboration between the faculty, students and Sun Microsystems staff who together designed and constructed these tools was quite unusual and impressive. The collaboration itself is an inspiring model.Cut-the-Knot!
http://www.merlot.org/merlot/viewMaterial.htm?id=78198
This site is the parent site of an extensive collection of interactive mathematics authored by Alexander Bogomolny and includes an interactive monthly column . The content is accessible to the casual reader but offers much depth along with links to other high-quality resources. Altogether, this site is a mathematician's delight.Fibonacci Numbers and the Golden Section
http://www.merlot.org/merlot/viewMaterial.htm?id=89324
This excellent site contains a large and interesting selection of material on Fibonacci Numbers and their myriad related concepts. It includes web and text references to the rich literature of Fibonacci numbers. It also features a variety of images, graphics and animations. Many of the topics include student investigations for NCTM standard type explorations. The content includes standard motivational examples and applications in nature, but also mathematical explanations and puzzle pages. The site has already won several awards.MacTutor History of Mathematics Archive
http://www.merlot.org/merlot/viewMaterial.htm?id=89142
An award-winning site concerning the history of mathematics. In-depth coverage of numerous people, topics, mathematical curves, and more. Extensively cross-linked; powerful search engine. Rich and growing source of materials.Exploring Multivariable Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=437177
The main goal of this project is to improve student understanding of the geometric nature of multivariable calculus concepts, i.e., to help them develop accurate geometric intuition about multivariable calculus concepts and the various relationships among them.To accomplish this goal, the project includes four parts:· Creating a Multivariable Calculus Visualization applet using Java and publishing it on a website: web.monroecc.edu/calcNSF· Creating a series of focused applets that demonstrate and explore particular 3D calculus concepts in a more dedicated way.· Developing a series of guided exploration/assessments to be used by students to explore calculus concepts visually on their own.· Dissemination of these materials through presentations and poster sessions at math conferences and through other publications.Intellectual Merit: This project provides dynamic visualization tools that enhance the teaching and learning of multivariable calculus. The visualization applets can be used in a number of ways:- Instructors can use them to visually demonstrate concepts and verify results during lectures.- Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own.- Instructors can use the main applet (CalcPlot3D) to create colorful graphs for visual aids (color overheads), worksheets, notes/handouts, or tests. 3D graphs or 2D contour plots can be copied from the applet and pasted into a word processor like Microsoft Word.- Instructors will be able to use CalcPlot3D to create lecture demonstrations containing particular functions they specify and/or guided explorations for their own students using a scripting feature that is being integrated with this applet.The guided activities created for this project will provide a means for instructors to get their students to use these applets to actively explore and “play” with the calculus concepts.Paul Seeburger, the Principal Investigator (PI) for this grant project, has a lot of experience developing applets to bring calculus concepts to life. He has created 100+ Java applets supporting 5 major calculus textbooks (Anton, Thomas, Varberg, Salas, Hughes-Hallett). These applets essentially make textbook figures come to life. See examples of these applets at www.monroecc.edu/wusers/pseeburger/.Broader Impacts: This project will provide reliable visualization tools for educators to use to enhance their teaching in calculus and also in various Physics/Engineering classes. It is designed to promote student exploration and discovery, providing a way to truly “see” how the concepts work in motion and living color. The applets and support materials will be published and widely disseminated through the web and conference presentations.Demos with Positive Impact
http://www.merlot.org/merlot/viewMaterial.htm?id=80956
Demos with Positive Impact is a collection of quick classroom demos that enhance the learning of mathematics content through animations, experiments etc. Each demo comes with stated objective, prerequisites, instructor notes and platform info, plus the level of the demo and credits. This setup appears conducive to quick inclusion into a class. To view a video of the award winning author, go to http://about.merlot.org/Videos/Math_Demos/Math_Demo.html" target=״_blank״>Demos with Positive Impact - the Mathematics Award Winner 2008 videoThe author also participated in the MERLOT Classics Series on Elluminate: " target=״_blank״>https://sas.elluminate.com/site/external/jwsdetect/playback.jnlp?psid=2010-03-25.1727.M.9E9FE58134BE68C3B413F24B3586CF.vcr Geogebra
http://www.merlot.org/merlot/viewMaterial.htm?id=274019
GeoGebra is a free and multi-platform dynamic mathematics software for education in secondary schools that joins geometry, algebra and calculus. On the one hand, GeoGebra is a dynamic geometry system--you can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards; on the other hand, equations and coordinates can be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum. These two views are characteristic of GeoGebra: an expression in the algebra window corresponds to an object in the geometry window and vice versa.Instructor-Made Videos as a Scaffolding Tool
http://www.merlot.org/merlot/viewMaterial.htm?id=768947
Abstract: Instructors have frequently found that some content, such as mathematical formulae, chemistry laboratory experiments, and business practices, are unusually difficult for students to comprehend through text-centered approaches, and that this is especially so for online students. In response, instructor-made videos (IMVs) of three to 10 minutes in length on problematic topics or subject matter areas were produced for business, chemistry, and mathematics courses. The IMVs were intended to scaffold student learning. Initial findings revealed that multimodal IMVs involving the demonstration, illustration, and presentation of key terms, knowledge, skills, and resources can help students understand important procedures, structures, or mechanisms in previously problematic content. Simply stated, IMVs can have a positive impact on student learning.Volume 8, No. 4, December 2012, pp. 298-311HTML / PDFNational Library of Virtual Manipulatives
http://www.merlot.org/merlot/viewMaterial.htm?id=76833
Large collection of platform independent, interactive, java applets and activities for K-12 mathematics and teacher education.Interactive Mathematics--Games and Puzzles
http://www.merlot.org/merlot/viewMaterial.htm?id=78195
This site contains an extensive collection of games and puzzles in the form of java applets including Nim, the Tower of Hanoi, Cryptarithms, Latin Squares, and much more. Written by Alexander Bogomolny, these applets are designed to engage the reader in interactive investigations. Background material is provided and the site serves as an excellent educational resource.