"In this article we introduce the free educational mathematics software GeoGebra. This open source tool extends concepts of dynamic geometry to the fields of algebra and calculus. You can use GeoGebra both as a teaching tool and to create interactive web pages for students from middle school up to college level. Specifically designed for educational purposes, GeoGebra can help you to foster experimental, problem-oriented and discovery learning of mathematics. We will illustrate the basic ideas of the software and some of its versatile possibilities by discussing several interactive examples."
NSDL Science Literacy Maps are a tool for teachers and students to find resources that relate to specific science and math concepts. The maps illustrate connections between concepts as well as how concepts build upon one another across grade levels.
"Street-Fighting Mathematics:
The Art of Educated Guessing and Opportunistic Problem Solving" by
Sanjoy Mahajan, published in 2010. "Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool-the general principle-from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest." Available as a free download (Creative Commons License), .pdf): http://mitpress.mit.edu/books/full_pdfs/Street-Fighting_Mathematics.pdf
A nice collection of online maths tools, including a colour spinner, coin thrower, graph & chart tools, fractions illustrator and many more.
http://ictmagic.wikispaces.com/Maths
Conceived by Mathematica creator and scientist Stephen Wolfram as a way to bring computational exploration to the widest possible audience, the Wolfram Demonstrations Project is an open-code resource that uses dynamic computation to illuminate concepts in science, technology, mathematics, art, finance, and a remarkable range of other fields.\n\nIts daily-growing collection of interactive illustrations is created by Mathematica users from around the world, who participate by contributing innovative Demonstrations.
Rangoli based symmetry exercise - An activity based on Rangoli Patterns to provide opportunities for illustrating reflective and rotational symmetry of order 4.
"Usually, being able to visualise mathematical concepts to students is an important step in helping them understand techniques to illustrate connections with previous learning, helping them master maths notions to progress their skills. The importance of visualising concepts is clearly integral for Peter Mattock who has collected together a valued resource of mathematical activities that can be used with manipulative across the age and ability range."
Published 2012. "Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation for its elegant proofs and often surprising conclusions.
Heavenly Mathematics is illustrated throughout with stunning historical images and informative drawings and diagrams that have been used to teach the subject in the past. This unique compendium also features easy-to-use appendixes as well as exercises at the end of each chapter that originally appeared in textbooks from the eighteenth to the early twentieth centuries."
From the abstract: "Studies on creative mathematics conducted in the past decades revealed that the importance of
creation of learning and teaching environment favourable to the identification and nurturing
creativity in mathematics. Based on psychological, methodological and didactical models created
by Krutetskii (2006), Shchedrovtiskii (2008), Brousseau (2007) and Sierpinska (2004), we have
developed our challenging situation approach. During 5 years of field study in the elementary
grade VII classroom, we collected sufficient amount of data that demonstrate how these
challenging situations help to discover and to boost mathematical creativity in very young
children, keeping and increasing their interest towards more advanced mathematics curriculum.
This article is an humble attempt to present our model and illustrate how it works in the mixedability
classroom. We will also discuss different roles that teachers and students might play in
this kind of environment and how each side could benefit from it."
Forthcoming June 2012: "From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines this with an in-depth look at their aesthetics, history, and structure."
Prometheus Books The Glorious Golden Ratio [978-1-61614-423-4] - "For centuries, mathematicians, scientists, artists, and architects have been fascinated by a ratio that is ubiquitous in nature and is commonly found across many cultures. It has been called the "Golden Ratio" because of its prevalence as a design element and its seemingly universal esthetic appeal. From the ratio of certain proportions of the human body and the heliacal structure of DNA to the design of ancient Greek statues and temples as well as modern masterpieces, the Golden Ratio is a key pattern that has wide-ranging and perhaps endless applications and manifestations.
What exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena.
With their talent for elucidating mathematical mysteries, veteran educators and prolific mathematics writers Alfred S. Posamentier and Ingmar Lehmann begin by tracing the appearance of the Golden Ratio throughout history. They demonstrate a variety of ingenious techniques used to construct it and illustrate the many surprising geometric figures in which the Golden Ratio is embedded. They also point out the intriguing relationship between the Golden Ratio and other famous numbers (such as the Fibonacci numbers, Pythagorean triples, and others). They then explore its prevalence in nature as well as in architecture, art, literature, and technology. "
Abstract: "The purpose of this chapter is to provide pedagogical strategies and discuss ideas about teaching mathematics using GeoGebra that promote effective use of visualization in a technology-integrated dynamic environment. The author describes his work with prospective secondary mathematics teachers enrolled in a methods course. The results of the study revealed that their perspectives on teaching and learning mathematics with technology were enriched as they worked individually and in small groups to develop and present lessons with GeoGebra, suggesting that creating a collaborative environment for our prospective teachers is as important as incorporating dynamic mathematics software into our teacher education courses." (Full text requires subscription or purchase)
"The aim of this article is to illustrate a pedagogical strategy originally introduced elsewhere [8, 9]
of linking the application-oriented, computer-enabled experiential approach to K-12 mathematics with the
applied, project-based approach to the teaching of university mathematics at the undergraduate level."
"In this section, you will find some fun ways to learn about math. You can start out with Estimation of Length, Place Value and Weight and Capacity. If you want something more challenging, take a look at Line Symmetry, Patterns and Tangrams."
This multimedia resource includes interactive math activities, print activities, learning strategies, and videos that illustrate how math is used in everyday life. The resource addresses the following mathematics topics: Fractions; Integers; Percentages; Rate/Ratio/Proportion; Square Roots; Exponents; Patterns; Algebra; Linear Equations; Polynomials; Angles; Circles; Surface Area and Volume; Area and Perimeter; Triangles; Pythagoras; Trigonometry; Similarity and Congruence; Transformations; Shape Classification; Data Display and Graphs; Central Tendency and Distribution; and Probability.
A great general maths site with lots of tutorials, activities and games which will help your students at school and at home.
http://ictmagic.wikispaces.com/Maths
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